universidade federal de uberlândia - INCT-EIE

UNIVERSIDADE FEDERAL DE UBERLÂNDIA
FACULDADE DE ENGENHARIA MECÂNICA
Instituto Nacional de Ciência e Tecnologia “Estruturas Inteligentes em Engenharia”
Laboratório de Mecânica de Estruturas Prof. José Eduardo Tannús Reis
PARTIAL REPORT: INCT-EIE
April 2010
unesp
UNIVERSIDADE ESTADUAL PAULISTA
“JÚLIO DE MESQUITA FILHO”
Câmpus de Ilha Solteira
Introduction
This technical report presents the most significant activities of the INCT-EIE that were developed
during its first year. It is worth mentioning that the financing of the Institute was not available since the
approval of the project in December 2008 (FAPEMIG credited the funds in May 2009 and CNPq in
August 2009). This required some re-planning and delay, however any further problem was created.
This report is focused on the scientific activities and does not correspond exactly to its Portuguese
version.
1. Coordinating Board
The first meeting of the was held on August 24th, 2004 in Uberlândia – MG. According to the
composition proposal of the INCT, the Coordinating Board was formed as below:
- USP-SC: Prof. Flávio Donizete Marques (Laboratory of Aeroelasticity)
- USP-SC: Prof. Marcelo Areias Trindade (Laboratory of Dynamics)
- UnB: Prof. Edson Paulo da Silva
- UFCG: Prof. Carlos J. Araújo
- COPPE: Prof. Marcelo Savi
- UNESP-IS: Prof. Vicente Lopes Jr
- ITA: Prof. Ayrton Nabarrete
- UFU: Prof. Domingos A. Rade
- Petrobrás: to be defined
- UFU: Prof. Valder Steffen Jr – General Coordinator
Decisions: propose the organization of a mini-symposium on Smart Structures to be held during the
National Congress of Mechanical Engineering to be held in Campina Grande (PB) in August 2010;
invite EMBRAER to participate of the INCT-EIE; create a homepage and a logo for the Institute; define
coordination procedures; define strategies to give visibility to the Institute‟s activities.
A second meeting of the coordinating board was held during the 20th International Congress of
Mechanical Engineering that was held in Gramado (RS) in the period 15-20 November 2010.
Decisions: define priorities for the acquisition of laboratory equipments for the various partners; define
criteria to implement the scholarships for the students; define topics for the August 2010 minisymposium on smart structures; create the secretariat of the INCT-EIE in Uberlândia – MG.
2. Technical and Scientific results
In the following the most significant results of INCT-EIE are present, according to the various subprojects approved.
2.1 Shape Memory Alloy Structures: Manufacturing, Characterization, Modeling and
Applications
Despite numerous applications of SMAs (Machado & Savi, 2003, 2002; Paiva & Savi, 2006),
constitutive theories used to describe their thermomechanical behavior are still not able to describe all
alloy characteristics. This research, make an effort to explore constitutive models, proposing an
alternative model.
This research has the participation of the following researchers: Prof. P. Pacheco (CEFET/RJ), Prof.
Theodoro Antoun Netto (COPPE/UFRJ), Prof. A. Paiva (UFF), Dr. P.C.C. Monteiro Jr.
(COPPE/UFRJ), Dr. L.G. Machado (Texas A&M University), Eng. M.A.N. Sá and M.Sc. S.A. Oliveira.
It is also important to highlight the participation of Prof. Alexander Kalamkarov (Dalhousie
University – Canada). The main results were published in conferences COBEM 2009, CONEM 2008,
COBEM 2007, McMat 2007 and in journals: International Journal of Solids and Structures, Archive of
Applied Mechanics, Mechanics Research Communications, Journal of Intelligent Material Systems
and Structures and Smart Materials and Structures.
The proposed model allows the description of different aspects related to themomechanical behavior
of SMAs, being flexible (Paiva et al., 2005a,b, Paiva & Savi, 2006; Savi & Paiva, 2005; Baêta-Neves et
al., 2004; Savi et al., 2002a). In brief, the model considers four macroscopic phases: an austenite and
three martensitc variants (M, M+ and M), respectively representing temperature induced martensite
and stress-induced related to tensile and compressive behavior, respectively.
The model is developed within the framework of generalized standard materials in such a way that the
model is thermodynamically consistent. The model also includes plasticity, thermal expansion, and
transformation induced plasticity (TRIP) and there are coupling among these phenomena. Proper
constraints are employed in order to describe internal subloops due to incomplete phase
transformation that is a relevant point.
This novel model shows to be capable to represent different aspects of SMAs, presenting coherent
results. Figure 1 shows the pseudoelastic effect of NiTi alloy comparing numerical and experimental
results. The shape memory effect is shown in Figure 2, while Figure 3 shows the two way shape
memory alloy due the thermo-plastic-phase transformation coupling, which is na important contribution
of this research.
Figure 1 – Pseudoelastic effect.
Figure 2 – Shape memory effect.
Figure 3 – Two way shape memory effect.
Internal subloops due to incomplete phase transformations are shown in Figure 4, together with
experimental data. On the other hand, Figure 5 shows the TRIP effect.
Figure 4 – Subloops.
Figure 5 – TRIP.
Besides all these aspects, the thermomechanical coupling is also of concern. This is essential for the
comprehension of rate dependence behavior of SMAs. Figure 6 shows some results comparing
numerical and experimental tests.
1,0
Shaw & Kyriakides (1995)
Coupled model
Uncoupled model
0,8
35
Shaw & Kyriakides (1995)
Coupled model
Uncoupled model
30
25
-1
T= 70ºC
20
15
T (ºC)
 (GPa)
0,6
.
 = 0,04 s
0,4
0,2
10
5
0
.
 = 0,04 s
-1
-5
T= 70ºC
0,0
-10
0
1
2
3
4
5
6
7
8
-15
 (%)
0
2
4
6
8
10
12
14
16
cum. (%)
1,0
35
Shaw & Kyriakides (1995)
Coupled model
Uncoupled model
0,8
.
 = 0,004 s
Shaw & Kyriakides (1995)
Coupled model
Uncoupled model
30
25
-1
T= 70ºC
20
T (ºC)
 (GPa)
0,6
0,4
15
10
5
0
0,2
-5
.
 = 0,004 s
-1
-10
T= 70ºC
0,0
-15
0
1
2
3
4
5
6
7
8
0
2
4
6
 (%)
8
10
12
14
16
cum. (%)
Figure 6 – Thermomechanical coupling.
We are intending to extrapolate this constitutive model for three-dimensional media (Oliveira et al.,
2010)
Solid phase transformations occur in different physical phenomena as steel quenching. Prof. Pedro
Pacheco (CEFET/RJ) participated in this research together with E. Prieto Silva and Dr. Wendell Porto
de Oliveira. Resutls were published Oin several conferences and in journals: Journal of Strain Analysis
for Engineering Design, Archive of Applied Mechanics, International Journal of Solids and Structures
and Mechanics of Materials.
Finite Element Method
Finite element method is explored from the proposed constitutive model. Prof. P. Pacheco
(CEFET/RJ), Prof. Theodoro Antoun Netto (COPPE/UFRJ), Dr. P.C.C. Monteiro Jr, and M.Sc.
students C.A.P.L. La Cava and E.L. Bandeira participated in this research. Results were published in
conferences COBEM 2009 and CONEM 2008. Besides, journal papers were published in Smart
Materials & Structures and Archive of Applied Mechanics.
From principle of virtual work and the SMA constitutive model, Galerkin method is used using
Lagrange and Hermite shape functions, and the following discrete system is obtained:
K U  F  Fˆ 
e
e
e
 
e
e
where F̂ is related to nonlinear behavior of the SMA actuator. An iterative numerical procedure
based on operator split technique is employed to deal with nonlinearities of the formulation. Results
show the behavior of bars subjected to different thermomechanical loadings. Homogeneous behavior
is used to verify the model and then, nonhomogeneous behavior is investigated.
In order to illustrate the potential application of this procedure, Figure 7 shows a SMA truss subjected
to a shape memory effect thermomechanical loading. Note large displacements/rotations related to the
structure.
Figure 7 – SMA truss shape memory effect behavior.
Dynamics of Smart Systems
Smart systems have a increasing importance in mechanical sciences wit applications in areas varying
from robotics to bioengineering (Machado & Savi, 2003, 2002, Paiva & Savi, 2006). This research
Project performed an experimental analysis of SMA systems (Savi & Pacheco, 2002; Machado et al.,
2003, 2004). Prof. Alberto Paiva and the undergraduate student Milton A.N. Sá participated of this
effort. Besides, there is a international cooperation with Prof. Dimitris C. Lagoudas and Dr. Luciano
Machado of Texas A&M University.
Dynamical analysis started with an SMA one-degree of freedom oscillator and the main results were
published in COBEM 2005 and Chaos Solitons and Fractals and International Journal of Solids and
Structures. Numerical simulations are explored in these papers (Savi et al., 2005d,e). In general, SMA
systems have a rich dynamical response, presenting different kinds of responses that are temperature
dependent. Figure 8 shows a potential application of SMA dynamical system where temperature
variation can change oscillation position.
Figure 8  SMA system free vibration with temperature variations.
Figure 9 shows a chaotic response of this system, confirming results obtained with simpler models.
Figure 9  Chaotic response of an SMA oscillator.
In this point, it is important to highlight the novel procedure proposed to evaluate Lyapuniv exponents
in hysteretic systems (Machado et al., 2008). The procedure employs the classical algorithm due to
Wolf et al. (1995) but employs a state space split analyzing the hysteretic dissipation from an
equivalent viscous damping dissipation. This contribution was published in the International Journal of
Solids and Structures (Machado et al., 2009).
Experimental Analysis
Experimental analysis of smart systems used some nonlinear apparatus. Essencially, the resarch is
trying to assure numerically obtained results highlighting SMA systems (Savi et al., 2008) and other
results related to vibration reduction procedures (Santos & Savi, 2009; Sitnikova et al., 2010; Savi et
al., 2010; Machado et al., 2009).
Nonlinear pendulum analysis was developed with a PhD student, Aline Souza de Paula and Prof.
Wallace M. Bessa (UFRN). The main results were published in conferences COBEM 2009, CONEM
2008, CILAMCE 2009, DINAME 2009, DINCON 2009, CBA 2008 (De Paula et al., 2006, 2005a,b;
Pereira-Pinto et al., 2003, 2004a,b, 2005b,c). Besides, journal papers in Chaos Solitons & Fractals,
International Journal of Bifurcation and Chaos (Pereira-Pinto et al., 2004, 2005a), Journal of Sound
and Vibration and Shock and Vibration (De Paula et al., 2006; Savi et al., 2006a).
Experimental apparatus is shown in Figure 10. The pendulum consists of a disc excited by a motorspring system. Movement is measured by sensors and there is a magnetic device to control
dissipation.
Figure 10 – Experimental pendulum.
The nonlinear dynamics of this pendulum is very rich. The research treated the modeling and
simulation as well as the time series analysis. The model considers the dissipation as a combination of
linear viscous damping and dry friction. Chaos control is an important application of this research that
tries to mimic natural system behavior to mechanical system. The main idea is to give flexibility to the
mechanical system.
Free and forced vibrations are presented in Figure 11-12, respectively. Note the close agreement
between numerical and experimental results.
(b)  = /2.
(a)  = .
Figure 11  Free vibration.
Figure 12 – Chaotic response.
Chaos control methods exploit three characteristics of chaos: sensitivity to inirial condition, existence
of an infinite number of unstable periodic orbits (UPOs) embedded in chaotic attractor, and ergodicity.
These methods could be understood as a two stage technique. The learning stage, where UPOs are
identified and system aspects investigated. And the control stage wher UPOs are stabilized. The
pioneer OGY method is modified in order to treat system with high instability as the nonlinear
pendulum. Figure 13 shows UPOs embedded in chaotic attractor and the stabilized orbits using a
semi-continuous method. This research effort is related to several publication in conferences and in
journals as Chaos, Solitons and Fractals and Brazilian Journal of Physics.
Figure 13 – Chaos control.
Non-Smooth Systems
Mechanical systems with dry friction and impacts are examples of non-smooth systems. These
systems operate in different modes and their mathematical modeling are usually discontinuous.
Usually, the non-smooth model is related to differential equations with a kind of switch model.
This research dedicated a special effort to non-smooth systems. Dr. Luiz Fernando P. Franca, Prof.
Hans I. Weber (PUC/Rio) and students Sandor Divenyi and Steve F. Loureiro Maior were involved in
this effort. Results were published in conferences DINAME 2005 and COBEM 2005 (Franca et al.,
2005; Divenyi et al., 2005) and in journals: Journal of Sound and Vibration, Shock and Vibration and
Chaos, Solitons and Fractals (Savi et al., 2005b; Divenyi et al., 2005; Divenyi et al., 2008).
Basically, we investigated the mathematical modeling, the numerical simulation and experimental
analysis of this subject. The idea of the modeling is to split the state space in subspaces, defining a
transition between different parts. Figure 15 shows the discontinuous and the smoothed situations.
Figure 15 – Non-smooth systems.
As an application of the general formulation, a single degree of freedom oscillator with discontinuous
support is of concern. Figure 16 shows a schematic picture of the systems.
Figure 16  Non-smooth system.
This system has a rich dynamics. Figure 17 shows numerical and experimental results that present a
very good agreement.
Figure 17 – Non-smooth system: numerical and experimental results.
Chaotic response is a possibility of this kind of system. Figure 18 shows some chaotic attractor
obtained by both approaches.
Figure 18 – Numerical and experimental strange attractors of non-smooth systems.
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th
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Shibata, H. (1998), “Quantitative Characterization of Spatiotemporal Chaos”, Physica A, v.252,
pp.428-449.
Sitnikova, E., Pavlovskaia, E., Wiercigroch, M. & Savi, M.A. (2010), “Vibration Reduction of the Impact
System by an SMA Restraint: Numerical Studies”, International Journal of Non-linear Mechanics.
doi:10.1016/j.ijnonlinmec.2009.11.01
Umberger, D.K., Grebogi, C., Ott, E. & Afeyan, B. (1989), “Spatiotemporal Dynamics in a Dispersively
Coupled Chain of Nonlinear Oscillators”, Physical Review A, v.39, n.9, pp.4835-4842.
Wiercigroch, M. (2000), “Modelling of Dynamical Systems with Motion Dependent Discontinuities”,
Chaos, Solitons and Fractals, v.11, pp. 2429-2442.
Wiggins, S. (1990), “Introduction to Applied Nonlinear Dynamical Systems and Chaos”, SpringerVerlag, New York.
2.2 Robust Control and Power Harvesting using Smart Materials
Main technical-scientific results;
The technical report addresses two themes: Active Control of Non-Linear Mechanical Vibration and
Modeling of Smart Structure Systems and Methods for Energy Harvesting.
Methods for Energy Harvesting
Power harvesting is the process by which energy is derived from some external source (environmental
energy) and then converted into usable electrical energy. This environmental source is infinite and can
be obtained from mechanical vibrations, solar energy, from the gravitational field, the flow of fluids, the
pressure of acoustic sound, etc. There has been much research on this in recent years, due to the
development of wireless technology and low power electronic equipment.
There are numerous applications of power harvesting in the industrial, commercial and residential
areas. Undoubtedly, power harvesting applied to remote sensing stands out, which through this
technique, systems requiring a battery for its operation can self-replenish.
A power harvesting method obtains energy due to the vibration of a structure using piezoelectric
material. Piezoelectric material is a transducer that produces electricity in the presence of vibration.
This energy is stored in a battery or a super-capacitor for later use in electronic circuits.
The piezoelectric transducer converts the vibration produced by the structure into AC electrical energy.
The output of the piezoelectric transducer can be represented as a voltage source connected in series
to a capacitor. The AC current is converted into direct current through the AC/DC converter, then the
electricity is stored in a battery or a super capacitor, as shown in Figure 1.
Figure 1 – Basic electrical model of power harvesting
The major limitation is the power harvesting is the very low output power; therefore it is essential to
utilize all the energy converted.
One way to improve the efficiency of power harvesting is the use of electrical circuits to maximize the
amount of energy available. There are various circuits that can be used for this, such as DC-DC
converters, as shown in Figure 2
Figure 2 – Piezoelectric transducer, rectifier and DC-DC converter
Since the objective is decrease the voltage, some topologies can be used in order to decrease the
voltage, as for instance: Converter; Buck-boot Converter and Flyback Converter, Figure 3.
Figure 3 –Topologies of the DC-DC converters used
The power harvesting system can be divided into 3 parts: the energy source, the power extraction
circuit and the storage device. The piezoelectric material can be modeled in a simplified form, with a
voltage source, a resistor and a capacitor, as in Figure 4, where the resistance and capacitor are
internal parameters of the piezoelectric transducer.
Figure 4 – Electrical modeling
For the circuit extraction simulation to be as real as possible, it is necessary to obtain the output
voltage harmonics of the piezoelectric transducer. When the output waveform of the piezoelectric
transducer is known, the harmonics can be obtained through a computational tool. With these data, a
waveform that resembles the output of the piezoelectric transducer can be obtained in a simulation,
placing each harmonic as an electrical source and connecting them in series.
The power extraction system is composed of three parts: rectifier, power stage and control circuit, as
shown in Figure 5
Figure 5 – Diagram of the power harvesting system
The rectifier circuit is used to satisfactorily convert AC/DC. The rectifier may comprise diodes or a
MOS transistor. This circuit will rectify the AC signal from the transducer.
Simulations were performed in the PSpice software in order to observe the performance of the
configurations, of the rectifier, using diodes and MOS transistors. Simulations of half-wave rectifier,
full wave with a center tap and full-wave bridge transformer are shown below. The following
components were used for the simulation: a sinusoidal voltage with a peak of 2.5 V and a frequency of
10 Hz, BAT62 Schottky diode, ALD1107 transistor for NMOS and ALD1106 for PMOS, a 10 μF
capacitor for the output filter and a 10 KΩ charge.
Figure 6 – Half-wave diode rectifier
Figure 7 – Waveforms of half-wave diode rectifier
Figure 8 - Rectifier with half-wave MOS transistor
Figure 9 - Waveforms of the rectifier with half-wave MOS transistor
Figure 6 shows that the lowest output value for the half-wave diode rectifier was of 1.17 V, with a drop
of 1.33 V, as shown in Figure 7. For the rectifier with half-wave MOS transistor, shown in Figure 8, the
input voltage has the offset voltage of 1.5 V for the convergence of the MOS transistor, and the peak
voltage is of approximately 3.9 V, as shown Figure 9. The lowest voltage for the output was of 3.1 V,
thus the circuit had a voltage drop of 0.8 V.
Rechargeable batteries or super capacitors can be used to store energy in the power harvesting
system. Some examples of rechargeable batteries are: nickel-cadmium (NiCd), NiMH and lithium. The
super-capacitor is a frequently used energy storage alternative. The energy density of the supercapacitor is 10-100 times greater than that of traditional electrolytic capacitor (Guilar et al, 2009). To
determine which storage device is more appropriate, various parameters should be observed, such as:
the lifetime per cycle, energy capacity, energy density and energy efficiency.
Another important parameter is the lifetime of the storage device. Its lifetime depends on the number
of charge/discharge cycles. The NiMH battery varies from 300 to 500 cycles, the lithium battery varies
from 500 to 1000 cycles. Although the lithium battery has a longer cycle than the NiMH, its internal
resistance increases with time, which impairs its lifetime. The super-capacitor however, has more than
100,000 cycles.
The energy density is the charge accumulated on the device and depends on two measures: the
voltage and power capacity. Thus, the rechargeable battery holds 10 times more charge than the
super-capacitor. The values for the NiMH battery are around 60 to 80 Wh/kg, 120 to 140 Wh/kg for a
lithium battery and 1 to 10 Wh/kg for the super-capacitor. The lithium rechargeable battery has the
disadvantage of needing a charge protection circuit. However the rechargeable NiMH battery and
super capacitor do not need this.
Thus, there are several advantages and disadvantages to all storage devices. The best choice
depends on the application. For applications not requiring to store large amounts of energy, the best
choice is the super-capacitor. As for example, the remote sensors in which the energy density of the
super-capacitor is sufficient for its operation.
Another way to improve the power harvesting system is by optimizing the electromagnetic
piezoelectric transducer. This model determines the parameters of the piezoelectric transducer for its
proper performance. The ideal point where the sensor produces a maximum power of several
parameters, mechanical or electrical, is obtained through it. The electrical part is seen as an
equivalent resistance, and its optimum point is obtained by the following formula in Figure 10:
Figure 10 – Power produced by the Piezoelectric depending on the charge resistance
(Nakano et al, 2007)
Monitoring integrity in aircraft structures.
This part of the project presents the study and development of a technique for Structural Integrity
Monitoring (SHM) to identify and characterize structural damage through the methodology of Lamb
waves using piezoelectric materials (PZT) as sensors and actuators. Lamb waves are elastic forms of
disturbance that propagate between two free parallel surfaces. Lamb waves are formed when the
actuator excites the surface of the structure with a pulse after receiving a signal. When a wave
propagates on the surface of a plate, it comes in a PZT sensor by different routes. One route is when
the wave reaches the sensor directly, that is, without obstacles in the path in which it
propagates. Another possible route is when the wave reaches the sensor after it propagates on
existing discontinuities on the surface of the structure. With the various features of the signals
received, and using certain techniques of signal processing, these damages can be identified, hence
applying the correct action to prevent the structure‟s complete breakdown.
The aerospace industry has one of the highest SHM investments, since any sort of damage can lead
to catastrophic and costly failures, therefore the vehicles involved undergo regular
inspections. Currently, 27% of the cost for a mid-sized plane‟s life cycle is spent on inspection and
repair. This statistic excludes the cost associated with the time the airplane is iddle.
Therefore, experimental tests were performed on an aircraft structure (aircraft panel). Sensor networks
and piezoelectric actuators were attached onto the surface of this structure, in order to configurate the
Lamb waves. The PZTs actuators excited the structure in the frequency range of 0 to 30 kHz, with the
result analysis performed in the range of 11 to 16 kHz, the range in which the best signal coherency
was obtained. Structural faults were simulated by increasing the mass on the surface of the structure.
Figure 11 shows the configuration of PZTs formed on the outer surface of the panel. This
sensor/actuator system, formed on the surface of the panel, is known as Piezoelectric Wafer Active
Sensors - PWAS and has been very important in implementing and developing Structural Integrity
Monitoring systems.
Figure 11. Configuration of PZTs formed on the outer surface of the panel.
Different configurations of sensor/actuator pairs were used. The process of excitation and
measurement of the signals follows a fixed sequence. Table 1 shows the sequence of excitations, the
PZTs in each excitation and the paths from the different combinations of sensor/actuator pairs.
Table 1. Excitation sequence, PZTs involved and resulting paths
Excitation sequence
PZT actuator
PZT sensors
Paths
1st
5
1, 2, 3, 4, 6, 7 and 9
5-1, 5-2, 5-3, 5-4,5-6, 5-7 and 5-9
2nd
8
7, 9, 10, 11 and 12
8-7, 8-9, 8-10, 8-11 and 8-12
3rd
2
1, 3, 4 and 6
2-1, 2-3, 2-4 and 2-6
4th
4
1 and and 7
4-1 and 4-7
5th
6
3 and 9
6-3 and 6-9
6th
11
10 and 12
11-10 and 11-12
First, the tests were performed on the structure without faults (healthy structure), obtaining the
reference signals (baseline) for each path. After the baseline signals were taken, the tests were
performed on the structure, adding the simulated/coupled structural failures onto the surface of the
aircraft panel. The structural defects were simulated by additional masses affixed to the surface of the
structure.
To simulate a multiple failure, two failures (mass equal to 1g) were affixed to the surface of the
structure: One fault was affixed between path 5-3 and path 2-6 the other was affixed between PZT 4
and PZT 7 (figure (12)).
Figure 12. Position of faults on the structure‟s surface.
After the tests with the flaws coupled to the structure were conducted, the failure of the structure was
removed and the tests were performed again in order to simulate a repaired structure. It is expected
that the structure returns to the healthy structure condition, that is, that the indicators no longer
“evidence” a fault in the structure.
The fault detection is based on a comparison between the structure‟s Frequency Response Function
in healthy conditions and of the structure during normal operation (unknown condition). Four failure
indicators were used to detect the fault in the structure, they are: Root-Means-Square Deviation
(RMSD) Metric Failure Index (MFI) H2 Standard and Correlation Coefficient Deviation Mean (CCDM).
Figure 13 shows some examples of FRFs obtained from the tests for the structure without faults.
FRF - Baseline - Caminho 5-2
-20
-60
-100
-140
1.1
1.15
1.2
1.25
1.35
1.4
1.45
1.5
1.55
1.6
x 10
FRF - Caminho 2-1
-20
Magnitude (dB)
1.3
4
-60
-100
-140
1.1
1.15
1.2
1.25
1.3
1.35
1.4
1.45
1.5
1.55
FRF - Caminho 8-12
-20
1.6
x 10
4
-60
-100
-140
1.1
1.15
1.2
1.25
1.3
1.35
1.4
1.45
1.5
1.55
FRF - Estrutura Reparada - Caminho 11-12
-20
1.6
x 10
4
-60
-100
-140
1.1
1.15
1.2
1.25
1.3
1.35
1.4
Frequência (Hz)
1.45
1.5
1.55
1.6
x 10
4
Figure 13. Examples FRFs from the experiments.
With the FRF of the output signals obtained experimentally in each of the tests, the four fault indicators
were calculated for all paths and for each analyzed fault condition, including the repaired structure.
Figure 14 shows the fault indicators computed, showing the fault detection in the structure.
Norma H2
0.04
0.02
0
RMSD
1200
800
400
0
IFM
4
x 10
7
2
0
CCDM
0.06
0
5-1 5-2 5-3 5-4 5-6 5-7 5-9
8-7 8-9 8-10 8-11 8-12
2-1 2-3 2-4 2-6
4-1 4-7
6-3 6-9
11-1011-12
8-7 8-9 8-10 8-11 8-12
2-1 2-3 2-4 2-6
4-1 4-7
6-3 6-9
11-1011-12
Caminhos
Norma H2
(a)
0.04
0.02
0
RMSD
1200
800
400
0
IFM
4
x 10
7
2
0
CCDM
0.06
0
5-1 5-2 5-3 5-4 5-6 5-7 5-9
Caminhos
(b)
Figure 14. Fault indicators computed - Failure detection: (a) Condition unknown and (b)
structure repaired.
To detect and simultaneously locate the fault in the structure, just by looking at the figure with the
indicators, a new way of presenting the results was suggested: when the fault is detected, the
indicators are shown in the figure that represents the surface of the aircraft structure. Thus, the paths
were put in the figure in the same position they really are on the surface of the aeronautic panel. The
wave paths are in the abscissa axis of the figures, and the values obtained for each indicator analyzed
are in the coordinates axis. It can be observed that the position of the PZTs in the figures are exactly
the same positions of the PZTs affixed to the outer surface of the aeronautic panel. Therefore, it is
easy to recognize the position of the paths analyzed. Thus, figure 15 presents the results for Fault
Condition 1, clearly showing the detection and the fault location.
1
0
0
0.5
0.02
0.01
0
Norma H2
0.02
0.01
0
0
2-1
5-1 2-4
0
0.5
0.02
0.01
0
1
0.01
0
0.5
0.02
0.01
0
0
5-4
0.02
0.01
0
5-2
0
0.5
1
5-3 2-6
0
6-3
5-9
0
0.5
6-9
1
PZT 8
0.5
0
0.5
1
0.02
0.01
0
1
8-7
0
0.02
0.01
0
1
0
8-10
0
0.5
0.01
0
1
0
0.5
0.02
0.01
0
8-11
1
PZT 10 0.02
0.5
PZT 8
0.5
11-10
0
0.5
0
0.5
1000
500
0
0
0.5
1000
500
0
1
1000
500
0
4-7
1
2-1
5-12-4
1
0.5
0
4
2
0
1
0.5
0
0
0.5
x 10
1
7
4
2
0
4-1
PZT 4
0
0.5
x 10
1
4
2
0
7
4
2
0
4-7
PZT 7
0
4
2
0
0.5
1
4
2
0
4
2
0
1
0.5
0
PZT 10
0
0.5
1
4
2
0
x 10
2-1
0.01
0
1
x 10
7
5-1 2-4
x 10
0.5
x 10
1
7
4
2
0
1
0.5
0
1
PZT 5
0
0.5
1
4
2
0
7
8-7
x 10
1
0.5
0
7
4
2
0
8-10
x 10
4
2
0
7
5-7
x 10
4
2
0
7
5-4
x 10
4
2
0
PZT 2
0
4
2
0
0.5
x 10
11-10
PZT 11
0.5
0
0.5
1000
500
0
1
1000
500
0
5-7
0
0.5
1
1000
500
0
1
8-7
0
1000
500
0
PZT 8
0.5
0
0.5
8-12
1
PZT 12
0.5
0
0
11-12
0
0.5
8-10
5-32-6
0
PZT 3
0
5-9
0
PZT 6
0
0.5
1000
500
0
0
1
6-3
1
0.5
5-6
0.5
1000
500
0
1
6-9
PZT 9
0
0.5
1
8-9
1
0
0.5
1
500
0
1
x 10
7
2-3
x 10
7
5-3 2-6
x 10
x 10
0
1
7
7
0
4
2
0
1
0.5
0
PZT 6
0.5
x 10
0
4-1
PZT 9
0.5
0
0.5
0
0
0
4-7
1
0
0
0
0
1
4
2
0
0.5
Caminhos
0
11-12
1
PZT 12
0
0.5
0
1
5-3 2-6
1
0
0
5-7
0.5
0
1
0
0
PZT 8
0.5
0
0.5
PZT 6
5-6
0
0
0
8-11
1
0
0.5
1
0.05
5-9
0
6-9
PZT 9
0
0
0.5
1
8-9
0.05
0
0
0.5
8-12
1
0.05
PZT 11
0.5
11-10
1
1
0.05
8-10
0.5
6-3
1
0.05
1
8-7
PZT 10 0.05
0
PZT 3
0
0.5
0.05
0.05
0.5
0
1
0.05
1
7
1
0.5
0
1
2-3
0.05
0.05
0
0.5
1
0
7
0.5
PZT 12
0
0.5
8-12
x 10
0
0
5-2
PZT 5
0
0
0.5
1
0.05
1
5-4
11-12
PZT 7
8-9
x 10
0.5
0.05
5-1 2-4
1
0.5
0.05
PZT 2
0
0.5
1
1
0.05
0.5
1
2-1
0.05
0.05
5-9
0
0
1
7
0
0.5
500
0
Caminhos
0.5
PZT 4
0.5
0
1
0.05
1
0.05
0
6-3
0
0.5
0.05
1
1
0.5
0
7
5-9
x 10
4
2
0
0.5
PZT 1
0.5
PZT 3
0
7
5-6
x 10
1
1
0.5
0
0
8-12
PZT 11 1000
0.5
11-10
1000
500
0
8-11
1
PZT 10 1000
1
0.5
1000
500
0
0
4
2
0
8-11
0
5-2
PZT 5
1
7
7
1
0.5
0
1000
500
0
2-3
1
1000
500
0
PZT 8
0
0
1
0.5
0.5
8-9
0.02
0.01
0
7
1
0.5
0
1000
500
0
1
5-4
0.5
0
PZT 7
0.5
1
CCDM
Índice de Falha Métrica
4
2
0
PZT 1
0
0.5
Caminhos
1
0.5
0
0
1
PZT 2 1000
500
0.5
1
PZT 11 0.02
0.5
0
0
0.02
0.01
0
1
1
0
0
PZT 4
0.5
1000
500
0
0.02
0.01
0
0.5
4-1
1
PZT 6
0
0
5-6
0
0
1
1000
500
0
1
0.01
0
0.5
0.02
0.01
0
0.5
0.02
0.01
0
5-7
0
2-3
1
PZT 1 1000
500
0.5
0
PZT 7
0.5
PZT 3
0.5
0.01
0
1
PZT 5 0.02
0.5
0.02
0.01
0
4-7
1
0
1
PZT 4 0.02
1
PZT 2 0.02
0.5
0.01
0
1
4-1
1
0.5
0
1
PZT 1 0.02
RMSD
1
0.5
PZT 12
0.5
1
0
Caminhos
11-12
0
0
0.5
1
Figure 15. Computed fault indicators: Fault detection and location.
These figures show that paths 5-3, 2-6 and 4-7 were the most affected by the fault at all levels tested,
except for Standard H2. According to the path positions in the figure, the fault on the surface of the
structure can be located. The fault is located in the region that includes the affected paths, that is, near
the blue color (the bars/indicatos) is included (region represented by red). Figure 5 clearly shows that
two faults are identified: a fault in the region corresponding to the intersection of paths 5-3 and 2-6 and
another faults in the region between PZT 4 and PZT 7. For a better view of these regions, figure 16a
shows the faults identified and figure 16b shows the faults introduzed into the structure.
(a)
(b)
Figure 16. (a) Regions of the faults identified; (b) position of the faults, confirming the identified
region.
The configuration for the aircraft panel enabled the precise location of the fault on the surface of the
plate. Note that the simulated faults are located exactly in the regions identified by the methodology
presented. The results showed the feasibility of the Lamb waves method when using a Structural
Integrity Monitoring system applying smart materials as actuators and sensors.
Structural Fault Detection Based on Electromechanical Impedance
The purpose of this section is to present the theoretical and experimental results obtained using the
electromechanical impedance technique for fault detections in smart structures.
Introduction
The electromechanical impedance technique (E/M) is a nondestructive evaluation (NDE) based on the
of Frequency Response Function (FRF) which stands out for its simplicity and the use of low cost
piezoelectric transducers. These transducers, usually PZT ceramics (Lead Zirconate Titanate) are
bonded to the structure to be monitored using a high-hardness glue that can be a cyanoacrylate based
instant glue or epoxy resin. Due to the piezoelectric effect, a relationship between the mechanical
properties of the structure and the electrical impedance of the transducer is established. Thus, it is
possible to monitor the variations of these properties by measuring the electrical impedance
(CAWLEY, 1984). The transducer and the monitored structure can be represented by a mass-spring
electromechanical model, as illustrated in Figure 17.
Figure 17. PZT transducer and the monitored structure represented by a mass-spring
electromechanical model.
In Figure 17, M is the mass, k is the elastic constant of the spring and C is the damping
coefficient. The transducer is excited by a sinusoidal voltage source
U with amplitude U m and
angular frequency  which produces a current I with amplitude m and phase  . The solution for
this electromechanical model in terms of electrical impedance of the transducer is given, according to
LIANG, SUN and ROGERS (1994), by the following equation
I
E
U
1  T
Z ( )
Z E ( )  
d32x Y xx 
  33 
I
j a 
Z ( )  Z a ( )

j is the imaginary unit,
transducer,
(1)
Z E is the electrical impedance, Z a is the mechanical impedance of the
T
Z is the mechanical impedance of the monitored structure, a a geometric constant,  33
E
Y xx
the dielectric constant to a constant stress,
d3x
1
is Young's modulus to a constant electric field and
is the piezoelectric constant.
According to (1), any change to the mechanical impedance of the structure caused by a damage
implies a corresponding variation in the electrical impedance of the transducer. Therefore, the
impedance technique E/M allows for the integrity of the structure to be evaluated in a simple manner
by measuring the electrical impedance of the PZT transducer. The fault is identified by comparing the
electrical impedance of the transducer measured with the structure in an initial condition, considered
whole, to the impedance measured after the structure has undergone a possible damage. This
comparison is performed by metric fault indicators. One of the most commonly used indicators in the
literature is the RMSD (Root Mean Square Deviation). The RMSD index is based on the Euclidean
norm (GIURGIUTIU; ROGERS, 1998). Some changes in this index have been suggested by several
researchers, with one of the most widely used calculated by
N
 Z n ,d  Z n ,h 
n
Z n ,h 2
RMSD  
2
(2)
where
Z n,h
is the electrical impedance of the transducer with the whole structure and
impedance after the occurrence of possible faults, both measured the frequency n ;
number of samples.
Z n,d
the
N is the total
Results
Electrical Impedance Measurement System
Although the E/M impedance technique is simple and uses low-cost and compact transducers, most
universities and research centers use commercial tools (e.g., Hewlett-Packard HP4192A, HP4194A) to
measure the electrical impedance of PZT transducers . Though accurate, these instruments are
heavy, bulky, have many unnecessary functions for SHM applications (Structural Integrity Monitoring)
and often quite expensive; prohibitive prices.
In order to eliminate these problems, a simple, efficient and low-cost system for measuring electrical
impedance was developed by Baptista and Vieira Filho (2009a). Figure 18 shows the diagram of the
system.
Figure 18. Proposed impedance measurement system.
The basic operating principle is based on the mean FRF H [k ] obtained through the DFT of the
excitation signals x(t) and response y(t) of an auxiliary circuit used for connecting the PZT transducer.
From the FRF and considering in detail the circuit parameters, the impedance of the transducer is
accurately obtained. The system hardware consists of a low-cost National Instruments DAQ device
(Data Acquisition) Model USB-6211, essentially comprised of an analog-digital converter (ADC) and
an digital-analog converter (DAC), a simple current limiter resistor Rs and a personal computer (PC).
The control and operation software was developed in LabVIEW. The connection between the device
and the PC is via a USB (Universal Serial Bus), providing a better versatility to the system. From the
mean FRF
H [k ] , the electrical impedance of the transducer Z[k] can be accurately calculated by
Z [k ] =
H [k ]  RS  r + Zin [k ]
Zin [k] - H [k ]  RS + r + Zin [k]

(3)
Z
[k]
in
where
is the input impedance of the DAQ, and r is the resistance of the connecting
cables.
Several tests were performed on metal structures to assess and compare the proposed measuring
system with a commercial impedance analyzer HP4192A (Hewlett-Packard). The results obtained with
the proposed system were very close to those obtained with the commercial instrument, with the
discrepancies between the measurements less than 5%. Besides accurate, the proposed system
allows measuring the electrical impedance very quickly, enabling experiments on complex structures
with a many transducers.
The results indicate that the proposed system efficiently replaces and at lower costs, the
conventional impedance analyzers used by most universities and research centers.
Analysis of Transducer Charge Effect
A practical problem that has not been considered in applications of the E/M impedance technique is
the charge effect of the PZT transducer due to the propagation means, in other words, the monitored
structure. This effect is well known in the literature and has been investigated, for instance, in
piezoelectric transducers charged by means of supporters and electrodes or by the liquid in which they
operate.
Figure 19(a) shows the analysis of the charge effect of the PZT transducers in SHM systems that can
be conducted through the equivalent electromechanical circuit proposed by Baptista and Viera Filho
(2010).
Figure 19. (a) equivalent electromechanical Circuit to a PZT transducer and (b) the charge
effect for an excitation frequency of 10 kHz.
The circuit in Figure 19 (a) is valid for a side  square transducer, with static capacitance
C0
,
d31 , constant elasticity s11 , mechanical impedance ZT , electrical impedance Z E
Z
and wave number k. The term S represents the mechanical impedance of the monitored structure
dielectric constant
that is related to its dimensions, especially with its cross-sectional area.
The charge effect can be analyzed by observing the transducer‟s electrical impedance change due to
Z /Z
T , as shown in Figure 19 (b) for a transducer comprising a Piezo Systems
the impedance ratio S
PSI-5H4E ceramic of 20 x 20 x 0.267 mm operating at 10 kHz. According to Figure 19 (b), transducers
Z /Z
Z /Z
T ratio) or to very large structures (high
S
T ratio)
affixed to very small structures (low S
have small variation in the electrical impedance due to a change in the mechanical impedance of the
structure due to a fault. Therefore, under these conditions, the system should have small sensitivity
Z /Z
T ratios were carried out
for detection of structural damages. Tests on structures with various S
by Baptista and Viera Filho (2010a) and the experimental results confirm this hypothesis. Figure 20
shows the RMSD indicators calculated by equation (2) using the real part of electrical impedance for
structures designated 1, 2, 3, 4, 5 and 6 with
Z S / ZT ratios 8, 16, 31, 62, 78 and 623, respectively.
Figure 20. RMSD indexes obtained for structures with various
Z S / ZT ratios
Z /Z
T
According to Figure 20, there was a significant reduction in the RMSD indicator, while the S
ratio increased. Therefore, for the system to have a good sensitivity to detect structural damage, the
transducer must operate in a linear region of the curve shown in Figure 19 (b). The analysis of the
charge effect may be important to assist in the proper design of piezoelectric transducers applied to
detecting faults in large structures.
Selecting the Frequency Range
Selecting the correct frequency range for calculating the metric fault indicators is an important step in
SHM systems based on the of E/M impedance technique, especially in portable and wireless
systems. Generally, selecting the appropriate frequency range is done by trial and error or from the
statistical analysis of data measured in the structure of interest.
The methodology developed by Baptista and Vieira Filho (2010B) uses electromechanical circuit of
Figure 19 (a), enabling to analyze the frequency ranges in which the transducer has good
sensitivity. Figure 21 shows the theoretical sensitivity curve of a transducer consisting of a PZT PSI5H4E ceramic of 20 x 20 x 0.267 mm.
Figure 21. Sensitivity curve of a PZT transducer.
Z /Z
T ratio. Throughout the
Figure 21 shows that the sensitivity varies with the frequency and S
frequency range there are maximum points and minimum points. Thus, detecting the structural faults
should be more efficient in frequency ranges around the maximum points and inefficient in the ranges
round the minimum points.
Several tests were performed on aluminum structures and the results indicated that the sensitivity
analysis of the transducer can be a good reference for the correct selection of the frequency range in
which the metric fault indicators are calculated for detecting structural damages.
References
Baptista, F. G.; Vieira Filho, J. A New impedance measurement system for PZT based structural
health monitoring. IEEE Transactions on Instrumentation and Measurement, New York, v. 58, n. 10, p.
3602-3608, 2009a.
Baptista, F. G.; Vieira Filho, J. The influence of the structure area on the performance of SHM systems
based on E/M impedance. In: INTERNATIONAL WORKSHOP ON STRUCTURAL HEALTH
MONITORING, 7, 2009b, Stanford. Proceedings… Lancaster: DEStech Publications, 2009b. artigo n.
691.
Baptista, F. G.; Vieira Filho, J.; Turra, A.E; Lopes Júnior, V. Experimental analysis of the effect of the
structure area on the PZT-based SHM systems. In: CONFERENCE ON SMART MATERIALS,
ADAPTIVE STRUCTURES AND INTELLIGENT SYSTEMS, 2, 2009c, Oxnard. Proceedings…
Oxnard, 2009c. artigo n. 1270.
Baptista, F. G.; Vieira Filho, J. Transducer loading effect on the performance of PZT-based SHM
systems. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, New York, 2010?a
(aceito para publicação)
Baptista, F. G.; Vieira Filho, J. Optimal frequency range selection for PZT transducers in impedancebased SHM systems. IEEE Sensors Journal, New York, 2010?b (aceito para publicação).
BAPTISTA, F. G. Uma Contribuição aos Sistemas de Monitoramento de Integridade Estrutural
Baseados na Impedância Eletromecânica. 2010c. 91f. Tese (Doutorado)-Departamento de
Engenharia Elétrica, Universidade Estadual Paulista (UNESP), Ilha Solteira, 2010c.
CAWLEY, P. The impedance method of non-destructive inspection. NDT International, Ann Arbor, v.
17, p. 59-65, 1984.
Giurgiutiu, V.; Rogers, C. A. Recent advancements in the electro-mechanical (E/M) impedance
method for structural health monitoring and NDE. In: ANNUAL INTERNATIONAL SYMPOSIUM ON
SMART STRUCTURES AND MATERIALS, 5, 1998, San Diego. Proceedings… San Diego: SPIE,
1998. v. 3329. p. 536-547.
GUILAR, N. J.; AMIRTHARAJAH, R.; HURST, P. J., A Full-Wave Rectifier With Integrated Peak
Selection for Multiple Electrode Piezoelectric Energy Harvesters, IEEE Journal ff Solid-State Circuits,
Vol 44, nº 1, 2009
Liang, C.; Sun, F. P.; Rogers, C. A. Coupled electro-mechanical analysis of adaptive material
systems-determination of the actuator power consumption and system energy transfer. Journal of
Intelligent Material Systems and Structures, Thousand Oaks, v. 5, n. 1, p. 12-20, 1994.
NAKANO, K.; ELLIOTT, S. J.; RUSTIGHI, E., A unified approach to optimal conditions of power
harvesting using electromagnetic and piezoelectric transducers, IOP Publishing Smart Materials and
Structures, vol 16, nº 4, 2007.
FRANCO, V. R. Monitoramento da integridade em estruturas aeronáuticas. 2009. 202f. Dissertação
(Mestrado Engenharia Mecânica) – Faculdade de Engenharia, Universidade Estadual Paulista –
UNESP, Ilha Solteira, 2009.
2.3 Aeroelastic Active/Passive Control via Active Fiber Composites (AFCs)
Objective:
This research aims the development of technological innovations in active fiber composites (AFCs)
applied in aeroelastic problems. The work follows by four stages. In the first stage a mathematical
model of the mechanics of the AFC material will be developed and validated. The second stage is
carried out designing control laws for active aeroelastic wing in composite materials and embedded
AFCs. At this stage, models will use the technique of aeroelastic aeroelastic tailoring, which will allow
the design of a wing for wind tunnel testing. Then, experimental investigations of an aeroelastic wing
with AFCs will be held. The third stage is dedicated to the study of passive use of AFCs as modal
sensors applied to predict the flutter. Aeroelastic models with modal sensors will be developed based
computer in AFCs. The final stage of research concerns the design and implementation of tests of
flutter in the wind tunnel, in order to validate the application of modal sensors based on AFCs.
Introduction
The activities developed along the year of 2009 are reported here. In order to contextualize this report
inside to the original idea, the related research activities will be developed in terms of four steps,
according to the following methodology:
1) Development, validation and implementation of a model for material mechanics applied to
AFCs.
2) Application of AFCs in aeroelastic control.
3) Development and evaluation of a modal sensing system based in active fibers.
4) Application and validation of the sensing system applied to flutter.
st
So far the development is focused at 1 step. The following sections present the development and
reached results.
Piezoelectric-fiber composites have been widely studied due their capability of provide high design
requirements needed in aerospace industry. In this segment, Active Fiber Composites (AFC) can be
applied for several tasks such as structural health monitoring, control or suppression of undesired
vibrations, precision positioning, among others. Smart structures have been developed along the last
25 years but the recent development of piezoelectric materials as fibers brought a new approach for
this class of materials: composite structures with embedded piezoelectric fibers behaving as one
material. Such approach avoids bonding patches to the final structure and expands the design
possibilities, considering that piezoelectric fibers can be added to any composite layer according to
design needs.
Among the possibilities cited, aircraft engineering have developed two of them. The first consists in the
utilization of AFCs as sensors, monitoring the structural health of strategic points of the aircraft, as well
as monitoring repairs done along aircraft life. A second class of applications, more complex than first
one, consists in the utilization of AFCs as actuators over helicopters blades, aircraft wings, and others,
in such a way to vanish or decrease undesired vibrations generated by aerodynamic loading. The use
of AFCs as actuators depends on a control system fully integrated. The main goal of this work is the
use of AFC s as sensors to form a base from which the study of their use as actuators can be started.
Both uses need the development of calculation tools which provide a high level of reliability in the
prevision of AFCs behavior. The most popular tool for this purpose is the finite element method.
Nowadays, available commercial software present limited capability to deal with this problem. It is
possible the coupled solution for the piezoelectric and mechanical problem but this approach is not
available for multilayer elements used to simulate composite material behavior. The usual solution
consists in testing composite samples in order to obtain average parameters and apply them in the
numerical simulations considering the material as homogeneous. Because composite materials are
heterogeneous materials, it can be supposed that is a difficult task the evaluation of all material
parameters. A solution that have been applied is an initial micromechanical model or a representative
volume element with suitable boundary condition in order to represent the behavior of the whole active
composite; then the effective material parameters (including the electro-mechanical coupling effect)
can be estimated. From this point there is some divergence of opinions about modeling complex parts
with embedded PFC. Some researchers defends a full micro-mechanical approach, leading to huge
models, with a big computational effort. There are also researchers that defend a macro-mechanical
approach supported by as many experimental testing as necessary. The third option is to improve the
computational tools available in order to obtain better results and decrease the dependence on
experimental testing, but avoiding modeling complex parts with a full micro-mechanical approach.
The finite element code ABAQUS (R) accepts the implementation of user defined subroutines that can
be used to non-standard uses as to describe the behavior of new materials (UMAT – User Material)
and new elements formulation (UEL – User Element). It is planned to develop routines in order to
create a set of elements and materials that describes the electro mechanical coupling effect saving
computational effort when applied to complex models.
With the development of the purposed calculation methodology using finite element analysis to
support the design of piezoelectric composites the next step consists on testing and investigation of
possibilities and limitations of the developed models when applied to aircraft problems.
Objetives
In front of the presented goals, the focus of this research project is the development of computational
models that provide a reliable prevision of the behavior of AFC structures. In other words, the goal is
the first step of the research line coordinated by the present supervisor together with the INCT. In
order to achieve these results, the work is divided in six partial objectives, described below.






st
1 : study of analytical modeling theory applied to composites with piezoelectric fibers, as well
as finite element modeling of a representative volume element of the AFC. It consists in a
micromechanical approach.
2nd: expand mathematical models in order to incorporate piezoelectric effects in a general
way, considering not just the situation of bonded patches of piezoelectric composites, but also
embedded piezoelectric fibers in a determined composite ply. To reach this objective the tools
UMAT and UEL from ABAQUS® open the possibility to implement user defined FORTRAN
routines. The second step consist in a macro mechanical approach.
3rd: apply the model developed in previous step to simple structures in order to evaluate
model`s performance. The evaluated structures are bars and beams under different kind of
loading and constraints.
4th: Experimental testing of these elements under quasi static loading. Simple structures have
a predictable behavior that can be monitored in testing experiments validating the numerical
models.
5th: simple structures under dynamical loading to estimate piezoelectric behavior when
submitted to such conditions.
6th: preliminary investigation of use of finite element models integrated with computational
fluid dynamics models to the analysis of structures under aeroelastic loads.
Every experimental testing step along this project is supported by numerical simulations, providing a
better comprehension of the overall behavior and some orientation about data acquisition points.
At the end of the described steps, the developed models will be able to provide the behavior prevision
of complex structures under generic loading conditions.
The research group involved in the development of this work has been working to apply the developed
models in design and development of system of control to aircraft structures made with embedded
AFC under aeroelastic loading.
Development
The adopted methodology to the development of this work is summarized according to Figure 1. The
colors are related to the partial objectives, already described.
The work organization is divided in a first step where a bibliographic revision and study of main
approach techniques applied to piezoelectric composites (including analytical, numerical, experimental
or hybrid approaches) are carried out. Such works will be used as basis to the development of an AFC
micromechanical model. The first goal is reproduce similar works using the finite element method as
approach technique. Then the numerical simulation will be applied to the specific set fiber-matrix
chose to this work. The estimated parameters by the micromechanical model will give the effective
material properties of the AFC. Actually the composite is made of active and passive fibers, according
with the considered layer, each one with a given orientation following design requirements. In order to
properly describe the behavior it is necessary a macro-mechanical model when more general
geometries are analyzed. To deal with this problem, a reliable micro-mechanical model will provide
effective parameters to be used in the macro-mechanical model. The model validation will be done
based in suitable experimental testing, defined to each case. With these tests, parameters for
comparison with finite element analysis (FEA) can be obtained since the approach keeps focus in the
laminated parameters. Also parameters for the macro-mechanical model can be estimated, keeping
the focus in the composite‟s laminae. The relation between micro- and macro-mechanical is
represented at Figure 1 by the dashed line and the main focus of this work is presented in details in
Figure 2.
Once a reliable micromechanical model is reached, effective parameters for the AFC can be obtained.
The estimated values are directly input in the finite element software through a UMAT subroutine. It is
necessary to implement a layered element that accepts the electrical degree of freedom in addition to
the mechanical displacements for each layer. The target is to apply this element in generic problems,
where the user is able to chose active or regular fiber properties with user defined fiber orientation for
each layer.
The same kind of non-active composite proposed for this work was extensively studied by Tita (2003)
at the Katholieke Universiteit Leuven (Belgium) and the results will be used as reference to analyze
the properties of the composite in both, active and non-active built.
The workability of piezoelectric fibers, fragile components, is described in details in the work of High
and Wilkie (2003) that presents the procedure adopted by the Langley Research Center (LaRC) to
manufacture piezoelectric patches with MFC (macro Fiber Composites) fibers embedded in polymeric
TM
matrix and interdigitated electrodes included through thin poliamidy films (like DuPont „s Kapton®)
bonded at top and bottom faces. Ghasemi-Nejhad et al (2005) presents a procedure to join the
patches embedded to an structure made of non-active composites, producing a smart structure. The
objective of this work does not include manufacturing the piezoelectric patches, but a procedure
similar to the work of Ghasemi-Nejhad et al (2005). Nowadays piezoelectric patches are commercially
available, so it is possible to buy them from companies like the already cited Midé Technology
Corporation.
Figure 1.Work methodology scheme
Figure 2. Interface between micro- and macro-mechanical models
Steps under Development
Among the proposed activities those referent to the partial objective 1 are concluded, according to the
notation of Figure 1. With new researchers starting activities since the beginning of this year (2010)
the activities 2 and 4 started, running in parallel. The summary of the activity already finished is
presented below. The revision presents a brief introduction to basic concepts and then the results of
the unit cell implementation. Finally the scheduled further activities are presented.
Literature survey
Active fiber composites have been intensively studied along the past few years because their potential
use as sensor / actuator in smart structures. Several approaches have been developed, including
analytical techniques giving a homogenization of material properties, experimental techniques in order
to characterize the behavior of each material as well as the composite and numerical approaches,
applying mainly the finite element method. Such sort of analysis can be divided in micromechanical
analysis, where fiber and matrix are simulated as a unit cell with suitable boundary conditions to make
it representative of the whole composite and also macro-mechanical analysis, where, with the support
of experimental testing average properties can be estimated and applied to general structures. This
procedure treats a heterogeneous material as a homogeneous anisotropic material. Several authors
employ more than one of these approaches for comparison effect or apply hybrid procedures to full
characterization of the sample structure.
Piezoeletricity
Piezoelectricity coupling problems are those where an electrical potential gradient causes a
mechanical deformation and vice-versa. The coupling between mechanical and electrical fields is
represented by the piezoelectric coefficients and can be written as:
T ij = C ijkl S kl − e kij E k
Di = eikl S kl ε ik E k
(1)
where: Tij , Skl , Ek are, respectively, stress, strains and electrical fields, Di are the components of
electrical displacements. Cijkl is the 4th order elastic tensor, ik are the dielectric constants and eikl the
piezoelectric modulus.
The symmetry of the tensors [C], [T], [S] e [], makes possible to write:
{ }[
]{ }
[e ]
{T } = [ C ]
{S }
T
{D} [e ] − [ ε ] − {E }
(2)
where the super-index T indicates the transpose of the matrix.
Also, for transversely isotropic composites (with unidirectional aligned fibers in isotropic
matrix) the constitutive matrix (stiffness-piezoelectric-dielectric matrix) can be written in terms of 11
independent coefficients, as:
C eff
11
eff
C 12
C eff
13
0
0
0
0
0
eeff
13
C eff
12
eff
C 11
C eff
13
0
0
0
0
0
eeff
13
C eff
13
eff
C 13
C eff
33
0
0
0
0
0
eeff
33
0
0
0
C eff
66
0
0
0
0
0
0
0
0
0
C eff
44
0
0
eeff
15
0
eff
e15
eff
− ε 11
0
0
0
0
{ }[
T11
T22
T33
T12
T23 =
T31
1
D
2
D
3
D
0
0
0
0
0
0
0
0
0
0
C eff
44
eff
e 15
0
0
0
0
e eff
15
0
0
− ε eff
11
0
e eff
13
eff
e13
eeff
33
0
0
0
0
0
− ε eff
33
]{ }

S 11
22
S

S 33

S 12

S 23
31
S
1
−E
2
−E
(3)
3
−E
where the coefficients must be homogenized to the structure, so using effective values to the
constitutive matrix (represented by the eff index) and average values to [S], [E], [T] and [D]
(represented by an over-bar in the considered component).
In case of more than one fiber orientation, according to the considered layer, the constitutive
relation must be written for each ply, as function of the angle between the ply local system of
coordinates and the global system of coordinates (Torres and Mendonça, 2008). Scientific papers
about piezoelectric composites adopt the convention of fibers aligned with z axis (or 3) to the
development of equations.
Composites
Composite materials are widely applied in aircraft and aerospace industries, because the excellent
stiffness/weight ratio and the good response under dynamic loading. A composite is considered like a
multiphase material which exhibits a combination of properties to obtain a better performance of the
combined material that any of their individual components acting alone (Callister, 2007). The
components that made the composite can be classified as agglomerate or reinforcement. The first one
keeps the reinforcement together and these withstand the loading transmitted by the agglomerate. In
this work it will be studied structural composites reinforced with long fibers in polymeric matrix. Such
structures are formed by a stack of plies each one with different fiber orientation (Figure 3(a)). At each
ply there is a local system of coordinates based in the orthotropic axis (1,2,3), where direction 1 is
parallel to fiber, direction 2 is perpendicular to fiber and lies in the lamina plane (plane 1-2) and
direction 3 is also perpendicular to the fiber but normal to the plane 1-2 (Figure 3(b)).
The inherent anisotropy associated to this kind of composites makes possible the design of material
properties integrated to geometric and functional features, but, by other side, makes difficult the
prevision of the structure behavior, as well as the intra and inter laminar failure modes under dynamic
loading.
(a)
(b)
Figure 3. (a) Laminated; (b) Orthotropic lamina: global and local system of coordinates
Piezoelectric fibres in composites
The possibility of manufacturing composite materials with embedded active fibers and their use to
vibration response control introduces the concept of smart structures. A smart structure can be defined
as a structure that have embedded sensors and actuators, with structural functionality as well as a
logical control, signal conditioning and electronic power amplifier (Crawley, 1994).
Therefore the active fiber composite has integrated the physical elements that may work as sensors
and actuators, together with the common fibers. In theory, it is difficult to integrate the active fiber
composites, however it is difficulty to design the layout of actuators and sensors to meet the
requirements of each structural component. Figure 4 represents a composite designed with common
fibers and piezoelectric fibers integrated into its structure over the electrodes responsible for the
polarization of the piezoelectric fibers. In this figure are interdigital electrodes (interdigitated
electrodes), but can use other settings, each with positive and negative aspects that must be
considered in the design of piezoelectric composite. Despite the great possibilities that this type of
material presents, there is also a major difficulty in estimating the material behavior due to the inherent
anisotropy and due to the increased number of variables that must be included to characterize the
material and the difficulty in testing.
Figure 4. Representation of a composite including embedded active fibers
The connectivity between the two phases (fiber and matrix) is usually indicated by two numbers,
where the first indicates the number of directions of continuity of the fiber, while the second index
indicates the same condition for the array. Therefore, particles of PZT fibers matrix composites are an
example of 0-3. Continuous unidirectional fiber matrix composites receive the designation 1-3 (Bent,
1997). This nomenclature is common in the available references. A detailed review of basic concepts
employed in the technology of composite piezoelectric active fiber is presented by Bent (1994 and
1997). Different electrodes configurations have advantages and disadvantages. The use of interdigital
electrodes has as main advantage the direction of polarization preferentially aligned with the fiber
length. Such behavior is illustrated in Figure 5 (b). In Figure 5 (a) also shows the configuration where
the polarization is made towards the thickness of the active layer of the composite, where the effect
towards the secondary fiber is therefore not as efficient as the interdigital electrodes. Ideally, the
interdigital electrodes are better the lower width and increased their spacing, as this situation is
reflected in a pattern more homogeneous electric field oriented in the fiber. In practice, however, there
is a limitation that should be respected. The influence of interdigital pattern in the behavior of
piezoelectric composite is studied by Paradies and Melnykowycz (2007). A detailed procedure of
fabrication of composites using active piezoelectric macro-fiber developed and manufactured by NASA
Langley Research Center in is presented by High and Wilkie (2003). Patches made from piezoelectric
fibers are commercially available, as can be seen in the company Mide (MIDE Technology
Corporation. Engineering Smart Technologies. Available at <http://www.mide.com/>), whose patches
with interdigital electrodes can be purchased at various formats and are designated as "D33
Piezoelectric effect". These piezoelectric elements can be affixed to various surfaces through specific
TM
solutions available commercially (eg 3M Adhesive Transfer Tape, used in aerospace applications)
as well as be integrated into the structure of the composite not active according to procedure given by
Ghasemi-Nejhad et al . (2005).
(a)
(b)
Figure 5. Polarization of piezoelectric composites: (a) top and bottom electrodes; (b) interdigitated
electrodes (adapted from Wilkie et al., 2000)
Representative Volume Element
One of the numerical techniques to obtain effective properties of AFCs is based in a representative
volume element. This kind of model is used to determine a homogeneous medium equivalent to the
original composite. In the example of Figure 6(a), a unidirectional fiber composite with periodical fiber
arrangement (hexagonal) is showed. Several other fiber arrangements can be used, as discussed by
Kar-Gupta e Venkatesh (2007). The Figure 6(b) shows the correspondent unit cell that, with suitable
boundary conditions can represent the behavior of the whole composite considering that the
dimensions in all directions are significantly greater than the fiber diameter. This hypothesis considers
that the material have the same properties in the two coordinate directions perpendicular to the fiber
direction. By using FEA the unit cell can be modeled in details and using the properties of each
material individually, effective properties for the composite material can be estimated. The parameters
of the constitutive matrix (Eq.(3)) can be obtained by suitable combination of loads and boundary
conditions, providing even the electro-mechanical coupling parameters. In order to use the unit cell
approach, displacement compatibility equations related to the hypothetical adjacent cells must be
specified. As presented by Moreno et al (2010), such relations can be written as:
u1i − u 2i = u 3i − u 4i
ϕ −ϕ =ϕ −ϕ
1
2
3
(4)
4
(5)
where ui is the displacement field and φ is the electrical potential correspondent to the node indicated
by the super-index, according to the notation in Figure 7.
Such relation must be employed successively between correspondent nodes of opposite faces. In
Figure 7 example the relation is applied between the correspondent nodes of faces Y+ and Y- and
correspondent nodes of faces X+ and X-. it can be concluded that the finite element model of a unit
cell needs a correspondence between the mesh generated at opposite faces, in such a way that the
compatibility conditions can be correctly applied.
Figure 6. (a) Periodic composite representation; (b) Respective unit cell
Figure 7. Correspondence between nodes in opposite faces
User defined features
The ABAQUS (R) code allows some levels of interaction between solver and user, in order to
implement customized unavailable resources. Such interaction is done through user subroutines, and
in this work specifically the UMAT and UEL subroutines are intended. The programming language is
FORTRAN.
The UMAT subroutine (User MATerial) is used to define the constitutive behavior of a material and
once associated to an element, will be used to the calculation of state variables associated to each
integration point of every element at every analysis step. It allows also the interaction with other state
variables, giving the possibility of update and save them at each analysis step. It is mandatory that the
UMAT updates the stress and dependent state variables at the end of every increment as well as
provide the Jacobian material matrix to the constitutive model.
The UEL subroutine (User ELement) can be used to create usual finite elements that represent
geometrical parts of the model and also as feedback, providing forces in certain points as function of
displacement, velocity (and others) values applied in other points of the model. They can be used also
to solve equations in terms of non-standard degrees of freedom and, finally, can be linear or nonlinear. The main disadvantage is that there are limitations in the post-processing resources, especially
when using contours, so history variables must be saved in order to analyze data as graphs.
Approaches to piezoelectric composites characterization
Active fiber composites have been largely studied during the last years applied as actuator and/or
sensor in smart structures with large potential use in aerospace industry. Several approaches have
been studied in order to describe the electromechanical behavior of the piezoelectric coupling in
composite materials. These approaches are experimental, analytical, numerical or hybrid. Frequently,
authors apply more than one approach to obtain a better evaluation of the material coefficients and
electromechanical behavior. Several researches like described by Chan and Unsworth (1989) as well
as by Smith and Auld (1991) are based in analytical approaches that are limited in terms of loading
cases in which they can be applied. Researches like described by Dunn and Taya (1993) employs
micro-mechanical theory coupled to the electro-elastic solution study ellipsoidal inclusions into a
infinite piezoelectric medium. Bisegna and Luciano (1996 and 1997) generalize the Hashin-Shtrikman
principles in order to determine the limits of all piezoelectric properties of selected materials.
Rodriguez-Ramos et al. (2001) and Bravo-Castillero et al. (2001) apply the asymptotic homogenization
to composites (piezoelectric or not) with fibers in square arrangement. Guinovart-Díaz et al. (2001 and
2002) and Sevostianov (2001) also apply the asymptotic homogenization, but to models with
hexagonal symmetry of fibers and random distribution, respectively, both with good agreement.
Finite element techniques using a representative volume element (unit cell) were employed by
Gaudenzi (1997) to obtain the properties for piezo-composite patches applied on metallic plates. With
suitable simmetry conditions a good prediction of the material behavior analyzing an unit cell under
different loading conditions. Poizat and Sester (1999) show how to obtain two effective piezoelectric
coefficients (longitudinal and transverse). Teply and Dvorak (1988) developed unit cell models with
boundary conditions that were successfully in the prediction of the whole composite behavior.
Petterman and Suresh (2000) use unit cell models applied to 1-3 piezo-composites. Paradies and
Melnykowycz (2007) study the influence of interdigital electrodes over mechanical properties of PZT
fibers. The authors conclude that despite there are several works studying the determination of
electro-mechanical properties, there are still not suitable tools to correctly evaluate stresses in
piezoelectric elements, including non-homogeneous electric field conditions and eventual changes in
material properties.
Melnykowycz et al. (2006) characterize the performance of intelligent composite materials reinforced
with fiberglass and integrated PZT fibers. The research of Kar-Gupta and Venkatesh (2005, 2007a
and 2007b) is about the influence of fiber distribution in 1-3 piezoelectric composites considering both,
fiber and matrix, with piezoelectric properties. Analytical techniques discussed can not consider fiber
distribution. Therefore, finite element analysis are presented and discussed. Berger et al. (2005)
evaluate effective material properties of piezoelectric composites using analytical and numerical
techniques.
Azzouz et al. (2001) improve the properties of MIN6 element (three nodes aniso-parametric element)
TM
to take into account the modeling of AFC (active fiber composite) and MFC (macro fiber composite).
Tan and Vu-Quoc (2005) present a solid-shell element formulation to model active composite
structures considering large deformation and displacements. The element has displacement and
electrical degrees of freedom. The authors ensure the efficiency and precision in the analysis of
multilayer composite structures submitted to large deformation, including piezoelectric layers. Panda
and Ray (2006, 2008) include temperature dependence to the piezoelectric composite properties. The
studied structure is a composite plate with piezoelectric composite patches. Dent et al. (2005) identify
positive and negative characteristics of PZF fibers for use in piezoelectric composites through
extensive evaluation of commercially available fibers due to their morphology, micro-structure and
phase-composition. Paik et al. (2007) employ direct numerical simulation – a simulation using detailed
modeling, incorporating every micro-structure – justifying that unit cell models are limited to predict the
behavior of piezoelectric fiber composites.
Applications using composites and piezoelectric actuators
Among the applications for piezoelectric actuators using several of the works already discussed, it can
be founded one branch that applies the basic concepts to simple structures, verifying their functionality
in a model of easy analysis and interpretation and other branch with technological use in complex
parts, with suitable simplifying hypothesis and comparison with experimental testing in real parts.
Silva et al (1998) used unit cell models, changing their topology in order to develop an optimal design
methodology applied to piezo-composite microstructures in hydrophones and naval sonars.
The work of Ghasemi-Nejhad et al (2005) presents the experimental analysis of composite plates with
piezoelectric patches bonded, producing an active composite panel (ACP). As support to experimental
analysis, finite element models are also developed. Ghasemi-Nejhad et al (2006) study the
determination of optimal voltage to elimination of structural vibration to a wide range of frequencies
around a particular natural frequency considered. Numerical analyses were also performed, and the
ideal location of actuators as function of studied frequencies range and modal shape is discussed.
Ghiringhelli et al (2001) presents a procedure and tools to aeroelastic analysis of a helicopter rotor
with active twist. The AFC is used obtain induced anisotropic strains which act twisting the blade. A
unit cell is user to estimate homogeneous equivalent properties required by the rotor‟s blade section.
In the macro-mechanical model the blades are modeled as beams, under rotation and large
displacement condition.
Thakkar and Ganguli (2004) have developed control equations to the blades of a helicopter rotor with
piezoelectric ceramic pieces bonded at their surface. Park and Kim (2008) designed and analyzed an
advanced active twist rotor (AATR) incorporating an actuator single crystal Macro Fiber Composite
(single crystal MFC). Aeroelastic analysis are carried out and a numerical model was created to
evaluate the noise reduction capability of the AATR. The results permits the comparison between
active twist rotor blades using AFC and MFC elements.
Aeroelastic problem
Aeroelastic analysis can be done in two main forms: experimental or mathematical models.
Experimental aeroelasticity gives answers for aeroelastic analysis, however, both for the case of
aeroelastic models for testing in wind tunnels and in the flight tests, the difficulties are the large costs
required. Current methodologies for developing mathematical models for analysis of aeroelastic
problems are shortcomings mainly because they involve two different modes of dynamic behavior,
namely: (i) the elastic medium which corresponds to the structure, and (ii) the fluid medium
surrounding such a structure. Mathematical models for practical analysis in aeroelasticity (called
aeroelastic models) end up being the sum of two uncoupled models (Marques, 1997), and a law of
interaction between them. These models are the structural model, which translates the equations of
motion of the dynamic system involved, and the aerodynamic model, used to solve the load applied to
the structure.
The structural dynamic response provides the structure, or the modes of the structure. Arbitrary
deflections can then be described as a superposition of some of these structural modes (Dowell et al.
1995). The method used to account for the effects of structural dynamics in aeronautics has been the
finite element method. A varying number of commercial programs and current developments in
equipment performance computing have facilitated the application of finite element method both in
academia and in industrial environment. For aeroelastic analysis, the model structure must be such as
to ensure high fidelity of the structure behavior.
In the context of aeroelastic problems, the greatest difficulty in developing mathematical models still
lies in the determination of aerodynamic behavior. This difficulty is understandable when one
examines the basic equations involved in this problem (Fox and McDonald, 1992; Anderson, 1995).
The physical aspects of any flow are defined by three fundamental principles: conservation of mass,
Newton's second law and conservation of energy. However, the analytical investigation of these
equations of fluid mechanics has not yet produced results that could significantly influence their
implementation. This has motivated many studies to determine alternative mathematical and statistical
methods based on experimental data and other forms of modeling the behavior of fluid dynamics, such
as the use of functional (Marques, 1997). Among the problems related to these methodologies are:
losses in the analysis of physical phenomena and little flexibility to evaluate different flow regimes with
the same model. Such issues may be decisive in studies of the interaction between fluid and elastic
bodies. In many cases, such as methodologies for predicting flutter, the models are specific to the
problem considered. The methods of computational fluid dynamics already reached an acceptable
level of maturity for the case of aerodynamic stationary or steady state (Anderson, 1995). However, in
many problems we are interested in aerodynamic models that compute the non stationary behavior, ie
in the time domain. Thus, the effects of motion boundaries of separation and shock waves, for
example, can be booked in aeroelastic models (Marques, 1997).
Piezoelectric composites in the context of aeroelastic problems, can act as sensors suitable for
producing the electrical signals needed to close a control loop active, or to a method of identification.
Because of AFCs can be built in arbitrary ways and to incorporate the structures of non intrusive way,
there is a high possibility of using them for modal sensing, or could be used to directly relate the
measurements of dynamic structural responses with its vibration modes, which would facilitate the use
of reduced models for complex structures, as well as the development of identification methods in
terms of models in modal variables. Thus, work on numerical modeling of such composites provides
basic design parameters for its application to aeroelastic problems.
Implementation of micro-mechanical numerical models
The micromechanical models implementation developed by this group along the year of 2009 were
published in the papers: Moreno, Tita and Marques (2009) and Moreno, Tita and Marques (2010). It
was studied a logical sequence of numerical analysis in order to get the effective material parameters,
the influence of different fiber arrangements inside the composite structure keeping a constant the
fiber volume fraction. Also the sensitivity of the results as function of the boundary conditions in unit
cell models was studied. The results were compared with analytical and numerical results provided by
other authors.
Fiber and matrix properties as used in the numerical models are presented in Table 1. The fiber
corresponds to PZT5H and the matrix to typical epoxy resin properties. The fiber cross section was
considered as circular.
Table 1. Material Properties for fiber and matrix and fiber volume fraction
C11
C12
10
x 10
Fiber
12.1
Matrix 0.386
C13
C33
C44
C66
Pa
e13
C/m
e15
e33
2
11
33
-9
x 10 F / m
7.54
7.52
11.1
2.11
2.28
-5.4
12.3
15.8
8.11
7.35
0.257
0.257
0.386
0.064
0.064
-
-
-
0.0797
0.0797
Fiber volume fraction: 55.5%
Several models were developed in order to analyze different fiber arrangements (square and
hexagonal). Considering the need of correspondence between nodes in opposite faces, discussed at
section 1.4, it is necessary to use 3 different models to carry out the analysis of hexagonal fiber
arrangement. Such models are presented in Figure 8.
(a)
(b)
(c)
(d)
Figure 8. FE models: (a) square; (b) hexagonal; (c) hexagonal shear XY; (d) hexagonal shear YZ
Considering the equations and unit cell models previously presented, the Table 2 summarizes the
proposed analysis procedure to obtain the effective coefficients. The procedure is based in six
numerical analysis correspondent to each row of the table. The material coefficients evaluated at each
analysis are presented in column 2, followed by the respective equation at column 3 (according to
Eq.(3) of this report). In columns 4 to 6 are indicated the applied loads (displacements, forces or
potential difference), considering the unit cell faces as regions of loading. Along the development the
fiber was considered always aligned with Z direction. The two following columns (7 and 8) present the
applied boundary conditions. The last column indicates the necessity of additional constraint equations
to force displacement compatibility when shear loading is applied.
The results patterns of the unit cell models were presented by Moreno, Tita e Marques (2009). From
these results, average values can be estimated by element results weighted by respective elementary
volume which makes possible the use of Eq. (3) to estimate effective properties values. Analytical
models (asymptotic homogenization) available in Berger et al (2005) were used to validate the
developed numerical models. The paper of Berger et al (2005) also presents numerical results that are
reproduced in Table 3 together with results obtained by Moreno, Tita and Marques (2009).
New numerical simulations have been carried with the objective of decrease the observed difference
between analytical and numerical results. Actually some of the coefficient differences have been
reduced to about 5%, as, for example, the e15 with the use of second order elements (element
SOLID226 of ANSYS®). The authors have concluded that the piezoelectric coefficient is strongly
dependent of the electric field that corresponds to a gradient of the electrical potential which is better
evaluated by high order element. The last results are being prepared to submission to an important
periodic in this area.
Table 2. Loading and boundary conditions
Equatio Prescribed
Prescribed
(a)
n
displacemen force field [N]
t field [m]
C1
st
1 line
C3 3rd line
3
1.
Prescribe Displacemen Electric
d electric t BCs [m]
Potential
potential
BCs [V]
field [V]
2.
(b)
positive uz /
face Z+
-
Zero normal
displacemen
Zero /
ts /
faces
all faces
X+, X-, Y+,
Y-, Z-
-
positive
voltage /
face Z+
Zero normal
Zero /
displacemen
face Zts / all faces
-
positive ux /
face X+
-
Zero normal
displacemen
Zero /
ts / faces Xall faces
, Y+, Y-, Z+,
Z-
-
-
-
positive
voltage /
face X+
Zero normal
Zero /
displacemen
face Xts / all faces
-
-
+Fy and -Fy /
faces X+ and
X+Fx and -Fx /
faces Y+ and
Y-
Zero normal
displacemen Zero /
ts /
faces all faces
Z+, Z-
between
pairs
of
faces X+,
X- and Y+,
Y-
3
e13 st
1 line
e33 rd
3 line
3 th
9 line
Additional
constraint
equations
-
-
3
C1
st
1 line
C1 2nd line
1
3.
2
1
4.
th
7 line
1
C6
5.
(c)
6
th
4 line
+Fy and -Fy /
faces Z+ and
Zero normal
C4 th
Z6.
5 line
displacemen Zero /
(c)
th
4
+Fz and -Fz /
8 line
ts /
faces all faces
e15
faces Y+ and
X+, XY(a)
: Lines number referred to Eq. (3);
(b)
: According to Eq. (4) and Eq. (5);
(c)
: Convenient restrictions to avoid rigid body movement are also added.
between
faces Z+,
Z- and Y+,
Y-
Next Steps
The research line can be divided in two branches, numerical and experimental. The targets for the
numerical branch are:
 Convert micromechanical models from ANSYS to ABAQUS;
 Study of simplified models, simulating piezoelectric actuators or piezoelectric patches applied
over non-active composite material;


Start the implementation of user specified elements in ABAQUS: implementation of layered
shell element with option of electrical degree of freedom in order to simulate piezoelectric
behavior;
Development of models to macro-mechanical study cases.
Table 3. Analytical and numerical results comparison
Coefficient Units
(1)
(2)
(3)
(4)
0.95
1.10
1.088
1.068
Difference
(a)
[%]
15.8
C12
0.56
0.48
0.465
0.522
14.3
17.1
6.8
C13
0.60
0.60
0.604
0.619
0.0
0.7
3.2
C33
3.50
3.50
3.525
3.521
0.0
0.7
0.6
C44
0.22
0.18
0.215
0.195
18.2
2.3
11.4
C66
0.20
0.16
0.154
0.181
20.0
23.1
9.5
e13
-0.26
-0.26
-0.258
-0.269
0.0
0.7
3.5
e15
0.02
0.018
0.0241
0.0164
10.0
20.5
18.0
e33
11.0
11.0
10.86
10.86
0.0
1.3
1.3
11
0.28
0.29
0.284
0.303
3.6
1.4
8.2
33
4.20
4.20
4.27
4.27
0.0
1.6
1.6
C11
10
x
10
Pa
Difference
(b)
[%]
14.5
Difference
(c)
[%]
12.4
(1) BERGER et al. (2005) analytical results (estimated from graphs);
(2) BERGER et al. (2005) numerical results with square fiber arrangement (estimated from
graphs);
(3) MORENO et al. (2009) – square fiber arrangement;
(4) MORENO et al. (2009) – hexagonal fiber arrangement.
(a)
: Comparing (1) and (2);
(b)
: Comparing (1) and (3);
(c)
: Comparing (1) and (4).
The experimental branch has the following targets:
 Manufacturing of non-active composite samples in order to characterize the non piezoelectric
medium;
 Definition of active testing samples shape and dimensions including piezoelectric patches
positioning;
 Definition of relevant loading cases and parameters to be measured and analyzed in
numerical simulations.
Both branches will run in parallel, with intense information exchange. Basic cases will provide data for
the numerical models which allow the starting of dimensioning of geometry and loading for more
complex experimental testing.
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Torres, D.A.; Mendonça, P.T.R. Análise de placas laminadas compostas piezelétricas com o método
de elementos finitos generalizados. In: XXIX CILAMCE, 16pp. 2008.
Wilkie, W.K.; Bryant, R.G.; High, J.W.; Fox, R.L.;Little, B.D.; Mirick, P.H.; Hellbaum, R.F.; Jalink, A.
NASA-Langley Research Center Macro-Fiber Composite actuator (LaRC-MFC): technical
overview. Langley Research Center presentation. 2000.
2.4 Multifunctional Structures for Unmanned Air Vehicles
Introduction
Multifunctional structures are pointed out as a future breakthrough technology for Micro Air Vehicles
(MAVs) and Unmanned Air Vehicles (UAVs) design (Pines e Bohorquez, 2006). An additional task to
the primary load-bearing function of these aircraft structures is to provide an additional source of
electrical energy by converting the vibrations available in their environment to electricity through the
concept of vibration energy harvesting (Erturk et al., 2009a, Anton e Inman, 2008; De Marqui et al.,
2009a). A possible source of energy for UAVs and MAVs is the mechanical vibration energy due to
unsteady aerodynamic loads during the flight (Anton e Inman, 2008) or due to ground excitation in
perching (Magoteaux et al., 2008; Erturk et al., 2009b). Although other transduction mechanisms exist,
piezoelectric transduction has received the most attention for vibration-based energy harvesting and
several review articles have appeared in the last four years (Sodano et al, 2004; Priya, 2007; Anton e
Sodano, 2007; Cook-Chennault et al, 2008).
The literature of piezoaeroelasticity or active aeroelasticity includes the use of smart materials
(piezoelectric materials are of particular interest in this work) as sensors or actuators. Researchers
have also used piezoelectric materials as actuators for morphing wings or morphing aircraft (Bilgen,
2007). Piezoelectric materials (piezoceramics or piezo-fiber-composites) can also be added into a
structure for energy harvesting. Generating usable electrical energy during the mission of a UAV can
relieve the auxiliary power drains or provide the power required by its sensors. Recently the concept of
self-charging structures Anton et al. (2009) has been introduced to improve multifunctionality in UAVs.
The proposed multilayer structure is composed of piezoceramic layers for vibration-to-electric energy
conversion, thin-film battery layers for storing the generated energy and a metallic substructure layer
as the original load-bearing layer.
Piezoelectric power generators can harvest electrical energy from mechanical vibrations based on the
direct piezoelectric effect. These harvesters are cantilevered beams or plates with one substructure
layer completely or partially covered with piezoceramic layers. The piezoceramic layer (which is poled
in the thickness direction) is covered by continuous electrodes (which are assumed to be perfectly
conductive) with negligible thickness. In general, a resistive electrical load is considered in the
electrical domain, in agreement with the simplified analyses followed by others.
The literature of piezoelectric sensing and actuation includes finite element (FE) models for plates with
piezoceramic materials. Although these FE models have not been used to study the energy harvesting
problem, they provide the basis for modeling of a piezoelectric energy harvester. As far as the
literature of FE modeling is considered, it can be observed that some of these FE models do not
account for the presence of conductive electrodes bracketing the piezoceramic layer (Tzou e Tzeng,
1990); although, in practice, piezoceramic layers usually come with highly conductive electrode layers
from the manufacturer. If the presence of the conductive electrodes is not taken into consideration, a
space- dependent electric potential distribution is obtained throughout the surface of the piezoceramic,
yielding a different electric potential term (i.e., electrical degree of freedom) for each finite element.
Some authors have considered the presence of the electrodes in the electromechanical problem
(Hwang e Park, 1991; Detwiler et al., 1995) and obtained one voltage output (i.e., potential difference)
between the electrode pair covering the piezoceramic. However, regardless of this electrode-based
consideration, most of these models in the literature have focused on structural actuation and damping
and plate-type formulation has not been considered in the literature of energy harvesting.
Electromechanically Coupled Finite Element Model
An electromechanically coupled FE model based on Kirchhoff assumptions was recently presented for
energy harvesting (De Marqui, Erturk and Inman, 2009a). A resistive electrical load is considered in
the electrical domain, in agreement with the simplified analyses followed by others (Roundy et al.,
2003; Sodano et al., 2004; duToit et al., 2005; Erturk and Inman, 2008a). The FE model was
successfully verified against the analytical results obtained from the closed-form solution for a
unimorph harvester under base excitation (Erturk e Inman, 2008a). The moduli of the power FRFs
obtained from the FE model (thinner lines) for five different values of load resistance are plotted in Fig.
1. These FRFs are in good agreement with the analytically obtained curves (thicker lines).
a)
b)
Figure 1 – a) Power FRFs for five different values of load resistance with the enlarged view of mode1
and b) Relative tip motion FRFs for five different values of load resistance with the enlarged view of
mode1 (De Marqui et al, 2009a).
The results obtained from the electromechanical FE model for a cantilevered bimorph with a tip mass
under base excitation (Fig. 2) are compared with the single-mode analytical predictions of the closedform solution and experimental results presented by (Erturk e Inman, 2009a). The bimorph harvester
configuration has a brass substructure bracketed by two PZT-5A layers. The piezoceramic layers are
poled in the opposite directions and therefore the combination of the layers to the electrical load is the
series connection case. The voltage FRF is defined here as the voltage output per base acceleration
2
(in terms of the gravitational acceleration, g = 9.81 m/s ) to be in agreement with the experimental and
analytical voltage FRFs given by Erturk e Inman (2009a). The voltage FRFs for the first mode of this
harvester obtained from the FE model are plotted in Fig. 3a along with the analytical solution and
experimental results for eight different values of load resistance (1, 6.7, 11.8, 22, 33, 47, 100, 470
k  ). A similar monotonic behavior of voltage output with increasing load resistance is observed for all
excitation frequencies according to the numerical (FE model), analytical and experimental results. The
experimental short circuit and open circuit resonance frequencies for the harvester are 45.6 and 48.4
Hz, respectively. The analytical model predicts these frequencies as 45.7 and 48.2 Hz, respectively.
The FE model predictions of the short circuit and open circuit resonance frequencies are 45.7 and
48.3 Hz, respectively. The mechanical vibration FRFs of the bimorph piezoelectric energy harvester
obtained from the FE model, analytical model and experimental tests are presented in Fig. 3b. The tip
velocity FRF is defined as the ratio of the amplitude of velocity at the tip of the beam (relative to the
fixed frame) to the gravitational acceleration as it is measured by a laser vibrometer located on the
fixed ground. It is observed in Fig. 3b that the mechanical FRFs obtained from the FE model are in
agreement with the analytical and experimental results. The vibration amplitude at the short circuit
resonance frequency is attenuated as the load resistance is increased up to 100 k  . Approximately
after this value of load resistance, increasing load resistance amplifies the vibration amplitude at the
open circuit resonance frequency and the vibration amplitude at the short circuit resonance frequency
is no longer attenuated.
Figure 2 – Bimorph harvester with tip mass under base excitation (series connection).
a)
b)
Figure 3 – a) Analytical, FE and experimental voltage FRFs for eight different values of load resistance
and b) Analytical, FE and experimental tip velocity FRFs for eight different values of load resistance.
(De Marqui et al, 2009a).
Time Domain Piezoaeroelastic Model
However the destructive nature of most aeroelastic phenomena the conversion of aeroelastic
vibrations into electrical energy is an interesting opportunity for energy harvesting. The interaction of
piezoelectric energy harvesting and an aeroelastic structure (resulting in a piezoaeroelastic structure)
can have interesting aspects for energy conversion and also for aeroelastic vibrations control.
Recently, time-domain piezoaeroelastic modeling of a piezoelectric generator wing with embedded
piezoceramics has been presented in the literature (De Marqui et al., 2009b). The model is obtained
from the combination of an electromechanically coupled finite element (FE) model (De Marqui et al.,
2009a) with an unsteady vortex lattice model. The conversion of aeroelastic vibrations into electrical
energy is investigated at several airflow speeds for a set of electrical load resistances.
The aeroelastic behavior, and consequently the power generated, is dependent on aerodynamic
damping which is modified with increasing airflow speed. At the flutter speed (which depends on the
external load resistance), the aerodynamic damping vanishes and the oscillations are persistent.
Although this condition is usually avoided in a real aircraft, it is the simplest case for the concept
demonstration of a generator wing using the linear piezoaeroelastic model. The response history with
 104  in Fig. 5a) shows a decaying
behavior which is due to the shunt damping effect of power generation. However, if Rl is increased to
the largest instantaneous power output at the flutter speed ( Rl
105  , the generator wing becomes unstable. In addition to the power generation the aeroelastic
behavior can be modified. Therefore, the power harvesting elements (load resistance in the electrical
domain in this case) could be switched turning the energy conversion on (adding electrical damping)
and off (removing electrical damping and allowing vibrations to increase).
The effect of using segmented electrodes on the piezoaeroelastic response of the same generator
wing and the same set of load resistances has also been investigated (De Marqui et al. 2009c). The
electrodes are segmented on the center line (mid-chord position) and properly combined to the
electrical load to avoid the cancelation of the potential electrical output of the torsion-dominated
modes (which is strongly cancelled when continuous electrodes are used). As in the continuouselectrode case, the value of load resistance
Rl  104  provides the maximum power output among
the set of load resistance values considered here. It is important to note that the peak power obtained
for the segmented electrodes case (Fig. 5b) is larger than the peak power obtained for the continuouselectrode case for all values of load resistance (Fig. 5a). In general, torsional modes are excited during
the coupled flutter motions. Therefore the shunt damping effect can be strongly improved by using
segmented electrodes in piezoaeroelastic problems. As a consequence of the improved
electromechanical coupling, better power generation and shunt damping effects are obtained for the
aeroelastic behavior since the piezoelectric reaction of the torsional modes in the coupled aeroelastic
motions of flutter are taken into account with the segmented-electrode configuration.
a)
b)
Figure 4 – a) Thin cantilevered wing with embedded piezoceramic layers and its cross-section and b)
Thin cantilevered wing with embedded piezoceramic layers with segmented eletrodes and its crosssection. (De Marqui et al, 2009c).
a)
b)
Figure 5 – a) Power output for the continuous-electrode configuration and b) Power output for the
segmented–electrode configuration (five different values of load resistance at the short-circuit flutter
speed of the continuous-electrode configuration). (De Marqui et al, 2009c).
Frequency Domain Piezoaeroelastic Model
The cancelation of the electrical output when continuous electrodes are used could be also
investigated with a frequency domain piezoaerelastic model (Vieira et al., 2010). The piezo-aeroelastic model is obtained by combining the doublet lattice method and the electromechanically coupled
FE model previously discussed. Piezoaeroelastically coupled FRFs are defined by combining the base
excitation condition in the piezoaeroelastic problem.
The relative tip motion FRF and the electrical power output FRF are presented for several airflow
speed [from the no flow condition (V=0m/s) to the flutter speed] in Figs. 6. The peaks relative to the
first bending and second bending modes are observed for the no flow condition. As discussed in this
work and in the literature (Erturk e Inman, 2009a)the forcing term in the base excitation problem is
related to the inertia of the structure in the direction of base motion (z-direction in this work). For the
symmetric structures (as the generator wing with symmetric mass distribution used here), one cannot
observe the peaks related to pure torsional modes in the electromechanical FRFs for the base
excitation condition without unsteady aerodynamic influence (V=0 m/s). For instance, the resonance
frequency for the first torsional mode of the wing is 16.6 Hz and no peak is observed for this frequency
in Figs. 6 (a) and (b) when V=0 m/s. In typical aeroelastic response, modes are coupled with
increasing airflow speed. Therefore a peak is observed around 16 Hz for the airflow speed of 20 m/s in
Fig 6 (a). However, this peak is not observed in the power FRF (Fig. 6b). At this airflow speed this is a
bending-torsion coupled mode dominated by torsional motion. The electrical output from torsional
vibrations is canceled when continuous electrodes are covering the piezoceramic layers of the
generator wing. At the airflow speed of 35 m/s this peak is shifted for 13 Hz and still represents a
bending torsion mode. However, at this airflow speed it is dominated by bending motion. As a result,
one can observe a peak at this frequency in the power FRF of Fig. 6b (no cancellation). At the flutter
speed (40 m/s), aerodynamic damping is zero and modes are coupled at the flutter frequency (11.5
Hz) and maximum tip displacement and power output are achieved. Power could be optimized if
segmented electrodes were used to avoid the cancelation of electrical outputs from torsional motions
at the coupled bending torsion motions of flutter.
a)
b)
Figure 6 – (a) Relative tip motion FRF for several airflow speed and Rl  100 and (b) Power FRF for
several airflow speed and Rl  100 (Vieira et al. 2010).
The optimum load resistance for maximum power output at the flutter speed is also determined using
the piezoaeroelastically FRFs. The cantilevered end of the generator wing is excited at the short circuit
flutter frequency (determined in Fig. 6) and the maximum power output can be obtained for a certain
load resistance. The variation of power output with load resistance at the short circuit flutter frequency
(11.5 Hz) and V=40 m/s is presented in Fig. 7. The maximum power output is observed for
Rl  15.8k  .
Figure 7 – Variation of electrical power output with load resistance at flutter conditions.
The electrical power output and relative tip motion FRF at the flutter speed are presented in Figs. 8 (a)
and (b) for two values of load resistance. The first load resistance is
Rl  100
(short circuit
condition) and the second one is the optimum load resistance for maximum power. Power amplitude is
larger for the optimum load resistance over the entire range of frequencies considered. The system is
vibrating at slightly different frequencies at the short circuit condition and the optimum load condition, a
typical behavior due to the electromechanical coupling. The strong shunt damping effect of resistive
power dissipation is observed in the relative tip motion FRF.
a)
b)
Figure 8 – (a) Power FRF and (b) relative tip motion FRF at the flutter speed for the short circuit
condition and using the optimum load resistance for maximum power output.
The piezoaeroelastic behavior of the wing is also investigated when a resistor and an inductor
connected in series in the electrical domain. Increased power output and increased flutter speed (due
to increased shunt damping effect of the resonant circuit) are expected by adjusting the inductor to the
target frequency (short-circuit flutter frequency) and searching for the optimum load resistance for the
maximum power. The flutter frequency of 11.47 Hz (determined close to the short-circuit condition of
the resistive case) is the target frequency to calculate the inductance of the series connection
resistive-inductive generator circuit. It is straightforward to verify that the required inductance for the
flutter frequency is 194 H and the optimum load resistance is determined as 2.2k . Usually,
synthetic inductance or impedance circuits are employed to realize such large values of inductance.
The piezoaeroelastically coupled FRFs for the series connection resistive-inductive case are
compared to the FRFs obtained in the previous case study for the optimum load resistance
( Rl  15.8k  ) at the short-circuit flutter speed (40 m/s). Close to the short-circuit flutter frequency the
power generated from aeroelastic vibrations in the resistive-inductive configuration is 335 % larger
than the power generated when only a load resistance is considered in the electrical domain (Figs. 9a
e b). The strong shunt damping effect of resistive inductive power generation is observed around the
short-circuit flutter frequency in the relative tip motion FRF (Fig. 9b).
a)
b)
Figure 9 – (a) Power FRF and (b) relative tip motion FRF at the short-circuit flutter speed for the
optimum load resistance for maximum power output and for the resistive-inductive case.
The resistive-inductive shunt damping effect is clearly observed comparing damping of first torsion
mode in Fig. 10a and b. The evolution of damping with airflow speed (Fig. 10b) shows the flutter
instability for the resistive-inductive in series condition at 46 m/s (40 m/s was obtained for when the
optimum load resistance was used in the electrical domain) and flutter frequency of 8.3 Hz (second
bending mode).
a)
b)
Figure 10 –Damping evolution with increasing airflow speed. a) optimum load resistance and
b) resistive-inductive case.
Piezoaeroelastic Typical Section
An experimentally validated piezoaeroelastic lumped-parameter wing-section model with a focus on
the generated electrical power and its effect on the aeroelastic response is also presented. The
experiments are given for a modified typical section and the discussion is limited to the self-sustained
oscillations for the sake of completeness.
Consider the piezoaeroelastic airfoil section under airflow excitation shown in Fig. 11. After introducing
piezoelectric coupling to the plunge DOF in addition to two structural damping coefficients and
considering a resistive load in the electrical domain, the lumped-parameter aeroelastic equations are,
 m  m  h  mx b  d h  k h   v  L

f
h
(1)
h
mx bh  I p  d  k  M
C eq v  v / R   h  0
p
(2)
(3)
l
where h is the plunge displacement (translation),  is the pitch displacement (rotation), m is the
airfoil mass per length (in the span direction), m f accounts for the fixture mass in the experiments
( m f  0 in the ideal representation given by Fig. 1), I p is the moment of inertia per length about the
b is the semi-chord length, x is the dimensionless chordwise offset of the centroid (point C) from the reference point, k h is the stiffness in the plunge DOF, k
reference point P where h is measured,
is the stiffness in the pitch DOF, L is the aerodynamic lift per length, M is the aerodynamic pitching
moment per length, d h and d , respectively, are the structural damping coefficients in the plunge and
Rl is the load resistance, v is the voltage across the resistive load, C peq
is the equivalent capacitance of the piezoceramic layers,  is the electromechanical coupling term
the pitch degrees of freedom,
and an over-dot represents differentiation with respect to time.
Figure 11 - Schematic of a piezoaeroelastic section under uniform airflow.
Assuming harmonic response at frequency

(i.e.
h  he jt ,    e jt , v  ve jt , L  Le jt ,
M  Me jt where j  1 ) leads to the following complex eigenvalue problem for the steady-state
plunge and pitch displacements:
     h /    ( )   2 1  j h   
  h  0 
 x   /  


   
2
2

 


x

m
/

r

m
/


r
1

j


0 
 h 


    


(4)
  , mh and m ) are taken from Theodorsen‟s unsteady thin
airfoil theory (Theodorsen, 1934) and are functions of the reduced frequency ( k  b / U where U is
where the aerodynamic loads (  h ,
the airflow speed) and the geometric parameters. It is important to note that, in this linear model, the
harmonic response assumption holds for the condition of neutral stability only (i.e. Eq. (4) is valid for
2
the flutter response only). The dimensionless terms are the complex eigenvalue,   ( /  ) , the
frequency ratio,
gyration,
  h / 
(where
h  kh / m
and
  k / I p
), the dimensionless radius of
r  I p / mb 2 , the airfoil – to – affected air mass ratio,   m / b2 (where  is the free-
stream air mass density), and a mass ratio for the presence of a fixture mass,
  (m  m f ) / m . In
most theoretical representations as well as in Fig. 1,   1 since only the airfoil mass contributes to
the inertia that is in equilibrium with the aerodynamic lift. However, usually there is an additional fixture
in the typical section experiments which makes
  1.
The loss factors in Eq. (4) are assumed to
   d / k and they are identified at zero airflow speed.
The dimensionless term  ( ) in Eq. (4) is due to eliminating the voltage term using Eq. (3) in
Eq. (1) and it depends on the eigenvalue  since it is a function of frequency:
obey
 h   d h / kh
 ( ) 
and
1
j 2
jC peq  1/ Rl 

m
(5)
Hence an iterative solution procedure is required where the frequency to be used in  ( ) is obtained
from the eigenvalue that becomes unstable with increasing airflow speed. The convergence of the
iterative eigensolution is extremely fast if one starts with the solution of the piezoelectrically uncoupled
aeroelastic problem (  ( )  0 ). Once the eigenvector relationship between
v is obtained from
h and  is obtained,
v   j  jC peq  1/ Rl  h
1
(6)
Expectedly, the airflow speed of neutral stability depends on the electrical load resistance. Hence the
airflow speed that makes the imaginary part of the respective eigenvalue branch zero is the flutter
speed ( U
 U c ) and the piezoaeroelastic eigenvector h 
v  is obtained using this eigenvalue
T
at this particular speed. Note that, for an electrical circuit of different linear elements, the admittance
1/ Rl can be replaced by the respective circuit admittance to investigate other piezoaeroelastic
phenomena.
Figure 12 shows the experimental setup used for investigating the piezoaeroelastic response of a
typical airfoil section. The system parameters are x  0.26 , r  0.504 ,   2.597 ,   3.33 ,
  29.6 , b  0.125 m and   15.4 rad/s. The loss factors identified for the plunge and the pitch
degrees of freedom at zero airflow speed are  h  0.007 and    0.12 . A geometric parameter
15,16
required for the Theodorsen function
is the relative location of the reference point with respect to
the mid-chord and it is a  0.5 for this setup. The plunge stiffness of the airfoil is due to four steel
beams connecting the airfoil to the ground from the reference point. Two PZT-5A piezoceramics
(QP10N from Midé Technology Corporation) are attached at the roots of two of these beams
symmetrically and their electrodes are combined in parallel. The beams providing the plunge stiffness
are in clamped-clamped end conditions and the piezoceramic patches cover approximately 20 % at
the root (close-up view in Fig. 12). The electromechanical coupling term is obtained based on
distributed-parameter modeling (Elvin e Elvin, 2009) as   1.55 mN/V and the published equivalent
capacitance of C p  120 nF is used in the model. In the experiments, for each resistive load (among
eq
a set ranging from 100  to 1M  ), the airflow speed is increased from zero until a self-sustained
piezoaeroelastic response is obtained.
Piezoceramic
patch
Airfoil
Blower tunnel
Figure 12 - Experimental setup showing a typical aeroelastic section with piezoceramics attached onto
the plunge stiffness members.
For an electrical boundary condition close to short-circuit conditions ( Rl
 0 ), the flutter speed is
measured as 8.85 m/s (the short-circuit flutter speed). Figure 13 shows the steady-state pitch
displacement, plunge displacement and the voltage time histories for an electrical load resistance of
100 k  with persistent oscillations at the flutter speed of 9.30 m/s. Among the set of resistors used in
the experiments, this is the electrical load that gives the maximum power output (10.7 mW). As can be
expected from the complex eigenvalue problem described previously, there is a relative phase
difference between the response histories in Fig. 13. For this electrical load, the absolute value of the
piezoaeroelastic
eigenvector
is
obtained
from
the
model
as
h

v

T
 1 mm 0.56 deg./mm 4.68 V/mm at the flutter speed of 9.32 m/s. The
T
experimental response amplitudes in Fig. 13 are h  7.65 mm,
  4.18 deg.
Hence the experimental pitch-to-plunge displacement amplitude ratio (
and v  32.7 V.
 / h  4.18 / 7.65  0.55
deg./mm) and the experimental voltage-to-plunge amplitude ratio ( v / h  32.7 / 7.65  4.27 V/mm)
exhibit good agreement with the model.
Figure 13 - Experimental piezoaeroelastic response showing the plunge displacement, pitch
displacement and the voltage output (for Rl  100 k  , U c  9.30 m/s).
Figure 14a shows the variation of the voltage – to – plunge displacement amplitude ratio while Fig.
14b shows the pitch – to – plunge displacement amplitude ratio for the set of resistors used in the
experiment along with the theoretical predictions. The voltage – to – plunge displacement versus load
resistance curve exhibits linear asymptotes similar to the trend in the harmonic base excitation of
piezoelectric energy harvesters whereas the variation of the pitch-to-plunge displacement amplitude is
considerably insensitive to the changing load resistance. It should be highlighted that these theoretical
curves and the experimental data points are given for the flutter velocity that corresponds to the
respective load resistance. For instance, in the experiments, for
  2.82 deg.
and
Rl  10 k  , h  5.15 mm,
v  2.42 V whereas for Rl  1 M  , h  7.95 mm,   4.40 deg. and
v  83.1 V. Hence the maximum plunge and pitch amplitudes differ and it is their ratio that remains
similar (  / h  2.82 / 5.15  4.40 / 7.95  0.55 ).
a)
b)
Figure 14 - Theoretical and experimental (a) voltage output – to – plunge displacement and (b) pitch
displacement – to – plunge displacement ratios versus load resistance.
The electrical power – to – plunge displacement ratio versus load resistance curve is shown in Fig.
15a. The optimal load that gives the maximum power output causes the maximum increase in the
flutter speed due to the shunt damping effect of piezoelectric power generation. The experimental
increase in the flutter speed (with respect to the short-circuit flutter speed) is 5.1 % and the model
predicts this increase as 4.3 % (Fig. 15b). Therefore, piezoelectric energy harvesting has the favorable
effect of increasing the flutter speed of the piezoaeroelastic system.
a)
b)
Figure15 - Theoretical and experimental variations of (a) the normalized power and (b) the percentage
increase in the flutter speed with load resistance.
Morphing Airfoil using MFCs as actuators
Conceptual Project
Macro-Fiber Composites reveal a superior means of airfoil actuation, allowing continuous camber
variation, improving aerodynamic and structural characteristics. The present work employs two metal
sheets in the bimorph configuration, attached to a fixed leading edge. Voltage input induces airfoil
actuation. The symmetric NACA 0012 profile is used for the morphing airfoil. The deformations
induced by the piezoelectric allow a wide, bi-directional actuation, while a cinematic mechanism allows
a shear-like motion during actuation, increasing its amplitude. Bilgen (2009) proposed a four-bar
mechanism (Fig. 16) in order to guarantee this degree of freedom. The compliant box mechanism was
designed as a series of simple piano hinges.
Figure 16 – Four-bar mechanism allows shear-like motion for trailing edge actuation. Bilgen, 2009.
In this work, a new mechanism is presented to guarantee only horizontal motion along the actuation,
guaranteeing a smaller discontinuity between leading and trailing edge, improving aerodynamic
efficiency. The upper surface moves horizontally above a fixed support. The preliminary CAD drawing
is presented in Figs. 17a and b. The airfoil chord is 168mm, while the obtained wing span is 150mm.
These dimensions were designed so as to allow two MFCs laminated laterally on each side of the
trailing edge sheets. The project will employ 8 MFCs M8587 P1. The lower surface is clamped in a
fixed support (Fig. 17a), which is connected to the leading edge. The upper surface is clamped to a
sliding element that moves horizontally over the same support. Five 5/32W screws were positioned so
as to allow the sliding element to move horizontally within longitudinal seats and to limit the
displacement. This system also permits to change the friction between the parts, by simply adjusting
the screws (Fig. 17b). The discontinuity between leading and trailing edge is covered by flexible tape
for smooth transition between the surfaces.
Sliding plate
5/32 W Screws
a)
Support fixed to the leading edge
b)
Figure 17 – a) Isometric view of morphing airfoil; b) Top view of the airfoil.
The conceptual project developed here has the advantage of simple construction and reduced friction
when compared to others found in the literature. The authors believe that this work also increases the
applicability in aircraft, since the fixed support may act as a wing spar itself.
Preliminary experimental airfoil
The components were machined in SAE 6351 aluminum. The first prototype (without the MFCs), was
assembled in order to check its feasibility. Figure 18a shows the fixed support where the lower surface
will be clamped and where the sliding plate will be connected. The sliding element is observed in
Figure 18b.
a)
b)
Figure 18 – a) Fixed support where the lower surface is clamped and the sliding element is connected to; b)
Sliding element which allows the horizontal motion.
The leading edge was manufactured in balsa wood, maintaining the original geometry of the NACA
0012. The final assembly may be verified in Figure 19. The mechanism is efficient and actuates as
predicted during the project. The trailing edge displacement is presented in Figures 20 a, b and c. It is
important to emphasize that the trailing edge surfaces, besides very thin (approximately 50μm) will
have their stiffness significantly increased after MFCs lamination. This configuration, as demonstrated
by Bilgen (2009), can withstand airflow speeds up to approximately 30m/s, sufficiently higher than the
speeds at which most UAVs and MAVs operate.
Figure 19 – First prototype of the morphing airfoil.
a)
b)
c)
Figure 20 – a) No camber airfoil; b) Negative camber actuation; c) Positive camber actuation.
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2.5 Active and Passive Structural Vibration Control Using Smart Materials
Line of research 1 – Modeling of laminated structures containing piezoelectric materials
connected to shunt circuits
Activity 1.1 - Extension of already developed models. Extension of the plate model already developed
to include variation of the actuation mode of piezoelectric materials, through its polarization, for the
maximization of its electromechanical coupling when inserted into a laminated composite plate;
Results obtained – A simplified model of laminated plates with piezoelectric layers was developed
using an equivalent single layer theory combined with third order shear deformation theory.
Electromechanical coupling is written in terms of electric charge, as opposed to the electric potential
which is traditionally used, to facilitate the coupling of piezoelectric sensors / actuators with shunt
circuits. The model discretization was carried out by the finite element method with particular attention
to post-processing of electrical parameters and their connection to shunt circuits consisting of
resistance, inductance and voltage source. The first results show that the formulation and
implementation are sufficiently precise and, in particular, independent of the number of existing layers.
For the study of poling direction of piezoceramic patches integrated into a laminated composite plate,
two extreme cases were studied considering patches poled in the thickness direction (31 mode) and in
the longitudinal direction (15 or 35). For the structure considered, the performance of the 31 mode
was significantly higher than the one of the 15 mode. Therefore, comparative analysis and
combination of the two modes in the same set of sensors was not justified. One of the great difficulties
encountered was the high computational cost of the analyses and that is the main reason why we
seek to build a high performance computing cluster to allow the study of more complex structures.
This computational difficulty has limited the number of structures considered in the calculations and,
thus, it was chosen to study the implementation of the active, passive and active-passive vibration
control methodology for the laminate plate instead of applying the model for more complex structures
[C6]. However, the aim is still to continue this study to other structures of interest for which a
combination of modes 31 and 15 may be more interesting.
Line of research 2 – Active, passive and semi-active vibration control techniques using
piezoelectric materials
Activity 2.1 - Control design and optimization. In the first stage, various configurations of coupling
between shunt circuit and controller (simultaneously or separately) will be studied. A parametric study
and optimization of the geometric properties (position and dimensions of transducers) and topological
(number of transducers and polarization) of the structure will be carried out.
Results achieved - Using models of sandwich beams and laminated plates with piezoelectric patches
connected to active-passive shunt circuits (APPN, Active-Passive Piezoelectric Networks) previously
developed, several performance analyses of passive, active and active-passive control promoted by
APPN in sandwich beams and laminated plates of interest were developed. In the case of sandwich
beams, the focus has been put on the design configuration of the beams considering the 31 and 15
actuation modes of piezoelectric patches and on the analysis of parametric uncertainties of the
passive elements of electrical circuits. It was shown that the 15 mode is more effective in the coupling
of passive and active mechanisms since the piezoelectric patch has a higher coupling factor in this
case, however, for the same reason, this actuation mode is also more sensitive to variations in circuit
parameters [C3, C5]. In the case of laminated composite plates, the focus was put on the optimization
of the positioning, along the three axes, of a series of piezoelectric patches connected to independent
active-passive circuits. On one hand, it was shown to be possible to use groups of independent pairs
of patches-circuits for the vibration control of a set of modes of interest [C6]. Furthermore, a study of
the effects that different pairs of patches-circuits present in the structure have on each other when the
structure is active-passively driven was performed [P3]. It was shown to be possible to provide an
active-passive control for a number of vibration modes of interest, independently, provided the mutual
effects are taken into account. These studies, both for beams and plates, should be continued for
integrated optimization of geometrical, electrical and control parameters.
Line of research 3 – Development of modal sensors using piezoelectric materials for
application in passive and active vibration control
Activity 3.1 – Topology optimization of sensors networks. Survey of the various techniques available
for optimizing, via software, the weighted sum of signals from a network of piezoelectric sensors to
isolate the response of certain vibration modes of interest. Optimization of the placement of
piezoelectric sensors in a metallic plate to provide the better isolation along a given frequency range.
Results achieved – An optimization strategy was developed using a combination of finite element
modeling, via ANSYS, for a plate containing a network of piezoelectric sensors bonded to it, and
topology optimization, via MATLAB, of the network of sensors to maximize the performance of the
resulting modal filters. For a case study, it proved to be possible, on one hand, to enlarge the
frequency range of a modal filter using weighted sums of the signal of network of sensors by up to
50% for a given number of sensors considered in the network or, on the other hand, reduce by 25%
the number of sensors required for an adequate modal filtering in a pre-defined frequency range [P2,
C2, C4, M1]. In a later study, the sensitivity of the performance of modal filters, based on optimal
topologies, when subject to uncertainties in the positioning of sensors and the weightings of the
signals from each sensor was analyzed. It was shown that realistic variations in the weighting
coefficients do not affect significantly the performance of the modal filter obtained [C1]. On the other
hand, uncertainties in the positioning of sensors can instead have a significant effect on filter
performance. The latter analysis is still in process considering that in the absence of a greater CPU
power, the calculations required for the analysis of variations in the positioning need about 15 days of
dedicated CPU.
Line of research 4 – Design and optimization of autonomous piezoelectric sensors
Activity 4.1 – Quantification and optimization of electromechanical coupling. Quantitative analysis of
electromechanical coupling and determination of the key design parameters to maximize the energy
absorbed by the transducer, with the purpose of proposing alternative arrangements and
configurations of transducers and their integration into flexible structures.
Results achieved - An analysis of the "electromechanical efficiency" of piezoelectric transducers in its
various applications such as actuators and / or sensors showed that there are two key factors to
optimize the electromechanical coupling: i) the electromechanical coupling coefficient of the
piezoelectric material in its main actuation mode, and ii) the mechanical coupling between the
structure and the transducer [P1]. This result is currently being applied to the geometric optimization of
a network of piezoelectric sensors integrated into a plate to maximize the electromechanical coupling
factor and quantification of the electricity generated by the device.
2.6 Smart Material Application in Aeroelastic Control
Introduction
This document presents a partial report of the activity carried out under the project INCT Smart
Structures in Engineering, sub-project "8.6 - Applications of Smart Materials in aeroelastic control."
Project INCT Project- Smart Structures for Innovation in Engineering related to the area of
aeroelasticity rotary and fixed-wing aircraft. Particularly the project focus the development of
aeroelastic systems mathematical models including control system design based on smart materials
technology, such as shape memory alloys, magnetorheological fluids and piezoelectric active fiber
composite materials.
The research is not based only on the employment of smart materials in aeroelastic control, but also
the understanding of aeroelastic phenomena and the dynamics of these systems since often are
nonlinear systems. For this, it is expected to meet the need of treatment of mathematical models
under the non-linear point of view. Among the nonlinear phenomena to be investigated, special
emphasis will be given in the use of smart materials for control of nonlinear aeroelastic systems,
especially those whose behavior is associated with large displacement, rotary effects and strong nonlinear characteristics of smart materials under investigation.
Besides the physical and mathematical characterization, it shall be provided for this research activity
the opportunity of experimental validation. Following this direction, the development and construction
of aeroelastic models for low speed wind tunnel testing is predicted for the desired mathematical
models validation purposes, as well as the knowledge on how feasible is the aeroelastic control based
on smart materials based actuator systems. The tests shall serve to evaluate the performance of the
designed controllers in the light of the technology under investigation.
The work developed is divided in two main research lines, the development of theoretical models of
aeroelastic systems using smart materials and design, construction, modeling and wind tunnel testing
on aeroelastic smart wings.
The first research line the theoretical developments included in this sub-project is divided into four
research areas as follows:
Line 1: Dynamics and Control of a nonlinear aeroelastic structure under the effect of
magnetorheological fluids;
Line 2: Dynamics and Control of a nonlinear aeroelastic structure modeled with Shape Memory Alloys;
Line 3: Methods of nonlinear aeroelasticity applied to the study of structures subjected to large
displacements;
Line 4: Aeroservoelastic Control of Single Rotorcraft Blade for Preventing Blade Sailing Phenomenon
in Permanent Flow
The goal of the first and second line of research is the study of systems with lumped parameters
through aeroelastic models of typical wing sections. The typical section consists of a two-dimensional
airfoil which moves in only two degrees of freedom, pitch and translation. In fact the dynamic system is
subjected to air flow. From the interaction of inertial, elastic and aerodynamic loading attributed to the
system is that it behaves aeroelastically. The smart materials will be added to these systems for
controlling aeroelastic system stability and response at chosen degrees of freedom. A presentation of
the methodologies to be employed in the work is presented in reference CASTAO et al (2009), paper
presented at DINCON 2009.
The third research area includes the study of nonlinear aeroelasticity, with emphasis on highly flexible,
composite materials based aeroelastic structures. This line of research merges with the objectives
presented in the sub-projects 8.3 and 8.4. These subprojects have as common objectives the
application of piezoelectric active fiber, both to aeroelastic control aeroelastic and energy harvesting.
The contribution the current subproject shall be the development of aeroelastic wing models based on
metallic and composite materials based light structures.
The experimental research area included in the subproject is work is considered as an approach for
completeness of the development numerical modeling activities. Aeroelastic models development and
construction included were mainly based on flexible wing aeroelastic models. The experimental setup
considered since conceptual design to wind tunnel setup and tests. Furthermore, lumped parameter
aeroelastic systems are considered as candidate aeroelastic plants to be controlled by the
aforementioned smart material based lumped devices. These tests are predicted mainly for the use of
shape memory and magneto rheological based devices, such as springs and dampers respectively.
The goal is to employ the same typical section model for wind tunnel tests built at the Laboratory of
Aeroelasticity EESC / USP, presented by De Marqui and Tavares (2008).
Developed Activities
The work developed so far are divided basically into two lines of action, development of theoretical
models of aeroelastic systems using smart materials and design, construction, modeling and wind
tunnel testing of aeroelastic wings. The first line consists of theoretical developments in this subproject
are divided into four research areas presented below.
Theoretical Developments
Dynamics and Control of a nonlinear aeroelastic structure under the effect of
magnetorheological fluids.
During 2009 studies were conducted concerning the application of (magnetorheological-MR) devices
for controlling aeroelastic phenomena such as Limit Cycle Oscillations (LCO) and gust loading, leading
to important results obtained. The aim of the studies of magnetorheological materials in aeroelasticity
is focused on control of damping associated to typical wing section degrees of freedom.
The reference (CASTAO et al. 2009) shows the first steps of modeling a damper using
magnetorheological fluids in a typical section. Were sources of nonlinearity in these
magnetorheological fluid dampers, resulting in the appearance of LCO.
In the reference CASTAO et al, 2010, are presented some mathematical models under evaluation
during the activities predicted for the doctoral student dissertation, Mr. Kleber Castao. These models
show a good agreement with the mathematical models presented in the literature. The first simulation
results got from the mathematical models obtained showed the feasibility of an open loop control as
well as its application to aeroelastic control. In subsequent steps, it shall be anticipated that the a goal
of the doctoral research the closed loop control laws synthesis and analysis, aiming the use of
magnetorheological dampers as proof of concept of this class of intelligent material in aeronautical
applications. Furthermore, it is predicted for the first half of 2010, research of other class of
mathematical models for the completeness of the physical aeroelastic behavior investigation.
Dynamics of a nonlinear aeroelastic structure controlled Shape Memory Alloys.
The research associated with this topic consists in the dynamic modeling of shape memory based
devices. The mathematical for shape memory material phased transition is based on the theory of
Devonshire for temperature induced first order phase transition combined with hysteretic behavior.
The approach lead to a polynomial free energy model, given by a function of temperature. The
associated derivative with respect to deformation to calculate the voltage is sufficient to derive free
energy with respect to deformation. This allows having the constitutive law based on the theory of
Devonshire. The use of shape memory alloys is idealized by modeling systems that incorporate
elements of aeroelastic stiffness composed of these alloys. The shape memory alloy mathematical
model used is the same presented in (Savi and Braga, 1993).
Two types of aeroelastic models were treated, namely: a rigid blade of a helicopter rotor, and a typical
aeroelastic section. In the first case by a spring league is considered the degree of freedom to beat
the blade of the helicopter, designed this study as hard. For the typical section, the shape memory
alloy is associated with the degree of freedom of the pitch section. The proposal of the two studies is
to understand the effects of this material, this first phase of a semi-active in the case of a helicopter
blade and parametric varying stiffness as a function of temperature of the alloy in the case of typical
section.
The results of this first phase of investigation, provided in accordance with planning the activities of
this subproject showed that the nonlinear models arising from inclusion of this class of intelligent
material leads to nonlinear aeroelastic models. Nonlinearities such as specific studies investigated
through bifurcation diagrams. It was observed that the system has periodic motions, quasi-periodic or
chaotic (Piccirillo et al, 2010).
The goals of understanding of aeroelastic models in the case of typical section and in the case of the
phenomenon of "blade sailing" were achieved, and their combination with shape memory alloys
according to the models chosen for this phase of preliminary studies.
Methods of nonlinear aeroelasticity applied to the study of structures subjected to large
displacements.
The activities undertaken in 2009 regarding this line of research were concentrated on developing
models based on aeroelastic methods of non-stationary panels, in particular the implementation of the
Doublet-Lattice method for calculating the unsteady loading. Models of aircraft structures in composite
materials were also investigated a priori using commercial numerical tools (and ZAERO NASTRAN),
aiming to understand the effect of orientation of fibers in the composite material in the stability
characteristics of an aeroelastic wing (de Souza et al , 2009). These are the first steps to establish a
better understanding of the physical effect known as aeroelastic tailoring.
Composites usually have nonlinear mechanical properties and are often applied to build lightweight
structures for aeronautical applications. Also, lightweight composite material structures are subjected
to large displacements, leading to nonlinear stiffness behavior, for example, in these situations. For
this reason, it is objective of this research to increase the structural models for design conditions which
attend criteria of lightness and strength simultaneously
The study of this class of structural models points out to the use of smart composite materials such as
piezo-active fibers combined with conventional composite materials. This research approach
interfaces with the another subproject of the INCT-EIE. Among the applications of intelligent materials
in aeroelastic structures, one can list the suppression of flutter, LCO, improving static aeroelastic
stability (divergence), vibration reduction and improved aerodynamic efficiency.
The current developments include aeroelastic analysis methods in state space which have been
implemented as a tool for supporting the aeroelastic stability and response of structures. Flat plate
type wing models built using fiberglass and epoxy resin matrix were manufactured. Wind tunnel tests
are planned throughout the development of student work Carlos Eduardo de Souza, with the support
of master's thesis by student recently accepted to the masters program in mechanical and
aeronautical engineering from ITA, André Balbi Aguiar. The results of these wind tunnel tests will
support validation procedures for the theoretical models under development. The goals of these
numerical models are to characterize the linear flutter and LCO simulation at the same conditions of
the aeroelastic tests. The subsequent nonlinear aeroelastic response to gust loads shall be
investigated based on the improvement of the numerical models develop under this research.
Individual Helicopter Blade Aeroservoelastic Control of Helicopter Blade Sailing phenomenon
in Permanent Flow
The simulation results of the "blade sailing" phenomenon indicate that the individual state feedback
control proposed, named as “D-IBRC” has good performance in typical conditions of steady flow. The
role of the control is to avoid the blades impacting in the fuselage, as well as reduce “blade up” large
deflections. The control system is designed looking for avoiding actuators, saturation, set as a design
condition. The use of D-IBRC strategy for enhancing the flapping mode damping can suppress about
20% of reduction in the deflections of the blade downward, avoiding fuselage impacts under severe
crosswind floe conditions. D-IBRC strategy proposal also allows a reduction of approximately 35% in
upward deflections, which might be severe in the structural integrity point of view. These investigations
are summarized in Ramos et al, (2009) and Ramos et al. (2009A).
Experimental Developments
High Aspect Ratio Flexible Wings
The development of aeroelastic models for low speed wing tunnel testing were based on the work of
Tang and Dowell (2001), from Duke University, USA. The hi=gh aspect ratio wing under experimental
investigation was chosen to understand fluid-structure interaction mechanisms associated with nonlinear aeroelastic stability and response.
The built model aimed a simple construction philosophy, and its aeroelastic characteristics were
adjusted to show the most interesting aeroelastic phenomenon, flutter, in a low speed range between
20 to 40 m/s. This speed range allows wind tunnel testing in open and closed test sections, which
facilitates the assembly of the constraining and measurement apparatus and minimizes the effects of
wall aerodynamic interference as well. The design of the wing employed a different material from
reference wing (Dowell and Tang, 2001) including the ballast inertia properties. These aeroelastic
(stiffness, inertial and aerodynamic) properties were adjusted to have aeroelastic instabilities at flow
velocities compatible with the available wind tunnel power. As preliminary steps of investigation, it was
quantified based on linear modal analysis the structural dynamic properties differences from the
present wing and the reference wing ( Dowell & Tang 2001).
Since the designed aeroelastic system becomes interesting concerning the phenomena at low speeds
point of view, the resulting test beds are suitable for active aeroelastic control applications without the
concern of the energy required for the suppression of instabilities or control the dynamic response of
structure. The proposed aeroelastic development of these models is to prove the concept of use of
smart materials applied to aeroelastic systems seeking as a first step the proof of concept,
disregarding the power requirements since the containing goal is to have low energy aeroelastic
coupling mechanisms, turning smart material application a feasible approach in the context of this
research.
As the first step, it is planned to control the flexible wing aeroelastic phenomena using piezoelectric
materials, since sensors to actuators. For such activities were selected and admitted to the master's
program in Aerospace and Mechanical Engineering students André Balbi and Alexandre Carvalho
Sergio. First student will develop an aeroelastic model of composite material for the use of
piezoelectric active fiber. This study supports the anticipated developments in doctoral student work,
Carlos Eduardo de Souza. It was already built fiberglass wing models, simplified as a flat plate type
wing. There was chosen different composite fibers orientation orientations tailored at 90 and 45
degrees with reference to wing‟s elastic axes. The proposal is initially to investigate the passive control
through fiber redirectioning, approach known as aeroelastic tailoring technology. The are schedules a
set of experiments during 2010 to validate the mathematical models developed in the doctoral student
Carlos Eduardo de Souza. Once known the ability of passive control of aeroelastic stability and
response, it starts for jobs in composites based on fiber piezo-active. The later approach look for
strategies not only for controlling aeroelastic stability and response, but also as a energy harvesting
device as stated in the subproject 8.3.
The second student Alexandre Carvalho Sergio will focus on a complementary model of hight aspect
ratio (slender) wing, metal-based structure including a model of the piezoelectric ceramic material is
compatible with the device to be installed in the wings already tested in wind tunnels. The
aeroservoelastic models will be developed based on the work of masters student Michelle Fernandino
Westin. (Westin et al. 2009)
Support for this work will be performed by scholarship students in scientific research. The assignments
will be the construction of additional wings and installation of piezoelectric materials for testing in wind
tunnels to the open loop and closed loop later. At this stage closed-loop control will be done by
distortions imposed by piezo-electric actuators. Such deformations will interfere in wing bending mode
to control flutter, for example, for a range of known flutter speeds.
The models to be developed, based on typical sections will be the object of application of shape
memory alloys and magneto rheological fluids. An typical section aeroelastic wind tunnel model,
developed in the Aeroelasticity Laboratory (EESC-USP) shall be the reference test bed for lumped
parameter system testing. Work in aeroelastic control using piezoelectric materials has been the line
of research of Prof. Carlos Demarqui EESC / USP. In 2009 a Master's thesis dealing with the typical
section model to be controlled by smart materials was presented. The test bed developed under
supervision of Prof. Demarqui provide the interaction between two INCT associated laboratories,
LEICA and EESC/USP Aeroelasticity Laboratory.
It should also be provided action aiming the portability of the experimental devices, fpr testing in the
wind tunnel of the EESC / USP and Laboratório Feng ITA / IEA. This portability will guarantee
availability of tunnels for testing, as well as inter-laboratory aspect desirable for experiments in wind
tunnels.
Design and modeling of an aeroelastic wing
The conceptual design of the wing was developed, respecting the characteristics of wind tunnels to be
used in testing, as well as the availability of materials used in construction of prototypes. The design of
the model, as well aeroelastic analysis in state space are presented in the graduate work of João
Otavio Falcão Arantes Filho (Arantes Filho, 2009). The idea of modeling the wing as an aeroelastic
system in state space, is to provide a reasonable way to incorporate control laws to be projected in
subsequent work in this subproject.
In the materials selection phase, it was predicted that the wing should provide conditions for using
smart materials. This approach indicated as a design philosophy, the building of simplified aeroelastic
wings, from the constructive point of view. For example, the first models consist of a plate-like spar
that will resist all efforts, made of aluminum 2024-T3 plate. The coating of made by depron foam as to
be elements responsible for the aerodynamic shape (NACA 0012 profile). Balsa ribs were laser-cutted
as NACA 0012 sections rto be a reference for bonding depron plates to be shapes as the selected
sections. The wing was divided in sections glued over the plate-like spar sufficiently separated to
ensure the free deformation of the beam without the contribution of the foam stiffness. The resulting
flexible high aspect ratio structure provide interesting aeroelastic behavior since findings on
aeroelastic instability at low dynamic pressures, in other words, low energy conditions.
A series of design iterations were carried out to obtain flutter speeds within the wind tunnel operating
range available for the experiments (it was established that flutter should occur near 30m/s.
Furthermore, the other worry regarding the flutter mechanism, strongly energetic flutter coupling
mechanisms to avoid model and wind tunnel damage. The procedure for determining the modes, the
frequencies modal analyses were carried out using NASTRAN software which provides a modal space
dynamic model to interact with unsteady aerodynamic modeled by ZAERO aeroelastic solver. Modal
analysis results are documented in the graduate work Arantes Filho, 2001. This model was tested by
a ground vibration test (GVT) to determine the vibration modes and frequencies in order to validate the
results obtained from the NASTRAN qualitative point of view only by comparing the natural
frequencies of the numerical model and the actual experiment.
The tests form the basis of the models part of the work of master‟s student Michelle Fernandino
Westin, currently being finalized with the defense scheduled for April 2010. The model was tested in
the wind tunnel TA3 Institute of Aeronautics and Space Administration to validate the flutter speed
obtained ZAERO software through an aeroelastic stability analysis, assuming a priori a linear model.
As preliminary wind tunnel results it was observed a reasonable agreement on the flutter speeds
between the numerical and experimental models. However, during the wind tunnel tests it was also
noted non-linear behavior of the model because, among other causes such as flexibility of the
restraining system, there is a coupling of three modes composing the flutter mechanism, including the
lead lag wing displacement. In an attempt to reduce the influence of the first order lead-lag behavior of
flutter, it was decided to reduce the mass concentrated at the tip of the wing. It was tried to what would
be the smallest mass possible to still get flutter.
To perform data acquisition during testing in wind tunnels ICP accelerometers were used installed
near wing root to minimize their influence on natural modes of the structure. In tests of the first model
was used only one accelerometer was placed near the wing root, allowing the identification of fluttre
speed from the accelerometer Power Spectrum Density analyses. This approach was selected since
the nature of the flutter mechanism is the flow energy extraction. In this situation a sudden increase of
the PSD function is observed at a gives flow speed.
References
Savi, M., and Braga, A.M.B., 1993, “Chaotic Vibrations of an Oscillator with Shape Memory”, Journal
of the Brazilian Society of Mechanical Sciences and Engineering, Vol. XV, pp. 1 – 20.
De Marqui, Jr., C.; Tavares, E.J. . 2008, Simulação Numérica e Experimental de Flutter. In: V
Congresso Nacional de Engenharia Mecânica, 2008, Salvador. Anais do V Congresso Nacional de
Engenharia Mecânica.
DOWELL, E.H.; TANG, D., 2001, Experimental and Theoretical Study on Aeroelastic Response for
High-Aspect-Ratio Wings. AIAA Journal, v. 39, n. 8, p. 1430-1441.
NAM, C.; KIM, Y.; WEISSHAAR, T.A., 2001, Computational Aids in Aeroservoelastic Analysis
Using MATLAB. 175 p.
WEISSHAAR, T.A., 1995, Aircraft Aeroelastic Design and Analysis. West Lafayette: Purdue
University, 1995. p. 122-129.
ZONA Technology, 2007. ZAERO Version 8.1- Theorical Manual. p. 3.1-3.27.
2.7 Structural Health Monitoring of Composite Structures
Introduction
Concerning this subproject, one presents next the fundamentals for the use of impedance-based
techniques for structural health monitoring, thus representing the focus of our research effort during
this first stage of the Institute.
Smart Structures and Materials
In the context of this Report, Structural Systems may be understood as being those which seek to
perform a function in the context of engineering, such as those found in engineering constructions,
bridges, ships and airplanes. The elements that compose these structures, such as airplane wings or
even the helicopter‟s propeller blades may be considered as structural elements as well, once they
also have a specific function in the system they belong to.
Due to special design needs in engineering, along with the development of new materials, new
devices and materials were created, which have been successfully incorporated to structural
elements, such as sensors and actuators. In the case of piezoelectric materials, they behave
simultaneously as sensors and actuators. Based on physical and operational characteristics of these
materials, sophisticated control systems can be implemented, replacing, in many cases,
servomechanisms that came to be traditionally used. These new structures, named as “smart
structures”, are served by those new materials, named “smart materials”, which have gained
recognition and has recently found applications in the industry. Scientific and technological
investigations made in research centers worldwide have accomplished new paradigms in the design of
structural systems and promised new applications in many engineering areas.
Clearly, the term “smart” (specialist, skilful, insightful, wise, cleaver, etc…) is not suited at first sight in
the structural engineering context. Thus, the engineering community adopted the wording “ Smart
Structures” along the last decade and, currently, this means the extraordinary ability of some
structures or structural components to modify their properties. Smartness, in this context implies: (a)
the ability of structural components to feel, diagnose and actuate in such a manner to keep their
functionality; (b) a project that improves the structural integrity by means of the monitoring of a
variable, such as temperature , pressure, stress, etc, allowing to diagnose the nature and size of the
problem, so that some control action is adopted and also; besides the system permits storing the
information that leads the system to “learn” from previous experiences so that it will be able to act if
similar situations happen in the future.
Some attributes of this “intelligence” would be the self-diagnosis, the healing, the functional recover
and the learning. Then, smart materials aim at attending to one of the critical requisites of any
structure, i.e., its preservation or even the improvement of the corresponding monitoring conditions. In
this sense, such characteristics may be observed by the extension of structure‟s life and by the
prognosis possibilities. Consequently, the present topic represents an interdisciplinary issue, including
many areas of interest, for instance: materials science, applied mechanics (vibration, fracture
mechanics, elasticity, aerodynamics), electronic (sensors, actuators, controls), photonics (optical
fiber), production (process, microstructure) and biomimics (devices that use the same strategies as
those used by structures found in the nature). The sensors are to be bonded on the surface or
embedded into the structure, besides they have to be chosen in such a way that they do not influence
significantly the dynamic behavior of the system. Similarly to the sensors, ideal actuators should have
a minimum weight (negligible with respect to structure) and also a small effect over the dynamics of
the system. At last, the actuators should present fast dynamic responses in such a way they are not
influenced by waiting times, which have a destabilizing effect over the system. In general, either the
sensors or the actuators must be able to work in extreme environment. Another characteristic is that
these actuators must be flexible in such a way they may be used in a variety of places and
configurations on the structure.
Among the materials employed to form smart structures, the most used are the following: piezoelectric
ceramics, electrostrictive and magnetostrictive materials, electrorheological and magnetorheological
fluids and solids, shape memory alloys and optical fibers. The properties of these materials are
already known but only recently they have been refined for applications in smart structures. Anyway,
the use of these materials as components, such as sensors and actuators in a smart system is quite
new and their applications are still under intense investigation, with many interesting perspectives and
some successful experiences already confirmed.
Piezoelectric Materials
The piezoelectric materials come from a class of dielectric materials which presents electric stresses
in response to a deformation imposed (direct effect), as well as they strain in response to applied
electric stresses (inverse effect). The piezoelectric sensors and actuators are built by the polarization
of the material, which, when applied to high electric fields and subjected to high temperatures they
exhibit piezoelectric characteristics.
It is important to stand out that the direct effect of the piezo is used it behaves as a sensor. On the
contrary, the inverse effect is responsible for the actuator effect. Thus, it is possible to realize the
capacity of these materials in applications related to fault detection and control by using a single
sensor-actuator device. Besides, this device is insensitive to temperature variations, providing that the
temperature is below the so-called Curie temperature above which the material would lose its
piezoelectric properties.
An advantage that may be observed from these elements is their flexibility to various real world
situations. There is a number of materials that can be polarized in order to acquire piezoelectric
properties. Among the most used materials, the lead-zirconate-titanate (PZT), a piezoceramic, and the
polyvinylidene fluoride (PVDF), a piezopolymer, should be mentioned.
As the PZT is a ceramics, the stiffness of the PZT patch is generally higher than the structure on which
it is bonded to, leading to an efficient electromechanical conversion. Consequently, this material is
very efficient in applications where actuator behavior is required. Its use in controlling tasks has found
many applications due to the efficiency of the PZT over high frequency ranges. The PZT patch is also
recommended as a self-sensitive actuator, particularly in control and damage detection. It is worth
mentioning the MFC (micro-fiber composite), which is an interesting alternative in applications where
the surface on which the material is to be applied is curved or waved because the MFC is very flexible
as compared to the PZT.
The use of PVDF films as actuators is not recommended, since their coefficient of electromechanical
coupling is far lower than the one of the PZT patch. On the other hand, the dielectric potential of the
PVDF film is about twenty times higher than the PZT‟s, i.e., they can be exposed to higher electric
fields.
Some advantages of piezoelectric elements can be mentioned, such as: relative insensitivity to
temperature change, linear response for low level of excitation, low weight and great flexibility both as
sensors and actuators, besides showing a wide band frequency response function. Some possible
disadvantages of these elements are the hystereses that appear under high electric fields, machining
difficulties due to their ceramics‟ characteristics, weak electromechanical coupling (for the PVDF films)
and, eventually, the possible decrease of the polarization characteristics of the piezoelectric elements,
thus reducing their performance as sensor-actuators.
Electromechanical Impedance
Mechanical impedance
One may define mechanical impedance as being the quotient between the harmonic force applied to a
given point of the system and the velocity developed by this same point as in the Eq. (1).
Zm 
F
v
(1)
where Zm represents the mechanical impedance, F is the force applied and v is the velocity.
Physically, the mechanical impedance represents how much can a structure resist to movement when
a given force is applied. It is a complex value, since both the force and the velocity are vector
quantities (with modulus and phase angle).
The mechanical impedance is intimately related to many parameters of the mechanical systems, being
the frequency an important parameter to be studied. Other elements related to impedance are listed
below:
 Mechanical Damping (Rm): parameter associated to the real part of the complex mechanical
impedance, representing the agent that dissipates mechanical energy that is given to the
system. A mechanical device acts as a mechanical damper when it obeys the Eq. (2).
F  t   Rmv  t 
(2)
In the International System (SI), mechanical damping is given by N.s/m.
 Mechanical Mass (Mm): parameter associated to the positive imaginary part of the complex
impedance. Thus, for a mechanical device to be considered as a mechanical mass, a force
applied to this device shall result in an acceleration that is directly proportional to the force
applied, Eq.(3).
F t   M m
dv  t 
dt
(3)
The mass is expressed in the International System (SI) in kg
 Mechanical Compliance (Cm): associated to the negative imaginary part of the complex
impedance. A mechanical device behaves like a mechanical compliance when, once it is driven
by a force, the corresponding displacement is proportional to the force, Eq. (4).
x  t   Cm F  t 
(4)
By convention, however, one prefers not to work with flexibility, using otherwise its inverse, i.e., the
stiffness. Thus, one defines stiffness as being the inverse of the mechanical flexibility, as follows.
K
1
Cm
(5)
Electric impedance
Electric impedance can be defined as being the resistance that an element of an electric circuit offers
to the transit of alternated electric current, according to Eq.(6):
Z t  
V
I
(6)
being Z the electrical impedance, V is the alternated electrical voltage and I is the resulting current.
The electrical impedance is of complex nature, and, therefore, it represents not only the magnitude
values, so as values of relative phase between the electrical voltage and the resulting current. The
electrical impedance is given in Ohms (Ω).
The complex value of the electrical impedance can be separated in two distinct parts: the real part
(also named electric resistance) and the imaginary part (known as electric reactance).
The electric resistance behaves in a similar manner either in alternated current circuits or continuous
current, always assuming positive values in Ohms. For a purely resistive electric circuit, the electric
current augments as the resistance present in the circuit is reduced, thus obeying the Ohm‟s Law.
The reactance, which exists only in alternate current circuits, may assume either positive or negative
values. By convention, one names inductive reactance the non-negative values found in the imaginary
part of the electrical impedance, and capacitive reactance the corresponding non-positive values.
Thus, the inductive (XL) and capacitive (XC) reactances are expressed in ohms by Equations (7) and
(8), respectively:
X L  2  fL
XC 
1
2  fC
(7)
(8)
where L is the inductance given in Henries, C is the capacitance given in Farads and f is the frequency
of excitation in Hertz of the alternate current circuit considered.
Eventually, when one obtains null values of reactance, the impedance is called “purely resistive”, and
the inverse value of the electrical Impedance is named electrical admittance, given in Siemens.
Measurement of electromechanical impedance
The impedance signals are generally obtained from an impedance analyzer. Concerning the
Laboratory of Structural Mechanics Professor José Eduardo Tannús Reis, (FEMEC-UFU), this
equipment is represented by the impedance analyzer HP 4194A (Fig.1), which has eleven functions of
impedance measurement and covers a frequency range from 100Hz to 40MHz.
Figure 1 – Impedance Analyzer HP 4194A.
The output levels are from 10mV to 1Vrms. According to the equipment‟s user‟s manual, more than
401 points can be selected for special applications. The basic measurements have a precision of
0,17% for the impedance measurements. Other parameters have to be adjusted. The integration time
(INTEG TIME) is used to choose the digital integration, which may be SHORT, MED or LONG. The
MED and long integration times are selected to minimize the noise in the signal. SHORT is chosen to
initialize the process. The integration time may be changed anytime even during the measurement
phase. Another parameter to configure is the average (named, AVERAGING), which is used to alter
the number of measurements by point being 1 (one) the default value. This average is used to
eliminate the noise effects in the signal. It is more adequate to select small values for this average in
applications where the test is performed in real time. Thus, when small values are chosen the time of
response is much faster than when higher values are selected. For a good quality sign, one may
choose the value 256, that is, the highest available value for adjustment. Another parameter that can
be altered in the impedance analyzer is the DELAY TIME, through which one can establish the
excitation time before proceeding to the measurements. According to Fig.2, the DELAY TIME assume
values from 0 to 3600 seconds.
Figure 2 – DELAY TIME funtion of the impedance analyzer HP 4194A.
The data acquired by the impedance analyzer are transferred to a personal computer for later analysis
and evaluation. The disadvantages of this procedure is that the impedance analyser is not portable
and is quite expensive. Another important aspect is that only a few of its resources are used in
electromechanical impedance testing. Thus, as an alternative, an impedance measurement device of
low cost was developed by using the software LabView, resulting a low cost and low weight
equipment. In Fig.3 the architecture of the alternative impedance measurement system is shown.
Figure 3 – Basic arquitecture of the alternative impedance measurement device.
Structural Health Monitoring
Damage which normally occur in industrial equipments and in structures in general are associated to
different factors such as friction, stress, impact, stress concentration, crack growth, among another
reasons. For real operating conditions, the damage must be precisely determined with respect to its
position, and timely repaired. One of the most ambicious processes of current engineering is the
monitoring of structural health in real time of high cost components or of great responsibility to the
system considered.
Structural health monitoring, or SHM , is the process of damage detection in the context of
applications that points out to various engineering fields, such as aerospace, civil and, mechanical.
One of the most important goals of SHM is to predict and increase the lifetime of an engineering
system. In this regard, the creation or improvement of techniques that increase the precision,
robustness and reliability of monitoring processes are highly desirable, being the reason of many
studies both in the industrial environment and in the academy. Therefore, the objective is to increase
safety and reliability of engineering structures provided that operational and maintenance costs are
reduced. The essence of SHM is to develop self-sufficient systems for continuous monitoring,
inspection and detection of damage in structures demanding minimum human intervention. There are
different techniques devoted to monitoring the occurrence and propagation of damage in the
structures. One of these techniques is the electromechanical impedancance based structural health
monitoring.
Structural health monitoring based on the electromechanical impedance
The structural health monitoring technique based on impedance signals has been developed as a
promising tool for the identification of structural failure and is considered as a new method for nondestructive evaluation.
This technique is based on the piezoelectric property of materials so as to obtain an electrical
impedance, which value is directely related to the mechanical impedance of the structure on which the
PZT patch is bonded or inserted. For this reason it is named electromechanical impedance.
Particularly, the electromechanical impedance value is easier to obtain than the value of the
mechanical impedance itself, since it requires simply an equipment that is able to measure the
electrical impedance. Thus, one monitors the variations of impedance values caused by possible
damage found in the structure. Obviously, one considers that the piezoelectric element used as
impedance sensor as well as the adesive employed remain both unaffected during the whole period of
investigation.
To ilustrate the measurement process, one presents in Fig.4 a single-degree-of-freedom model for
which it is considered that the axial PZT actuator is placed at one end of the system, while the other is
fixed.
Figure 4 – One-dimensional model of electromechanical coupling used by the impedance method
Therefore, it is possible to demonstrate that the admitance Y(ω) of the PZT actuator can be written as
a combined function of the mechanical impedance of the PZT actuator, Za(ω), and from the structure,
Zs(ω), according to Eq. (9):
 T

Z s  
2
Y ( )  ia  33 1  i  
d 3 x YˆxxE 
Z s    Z a  


(9)
where:
Y is the electrical admittance;
Za is the mechanical impedance of the PZT;
Zs is the mechanical impedance of the structure;
E is the Young‟s complex modulus of the PZT for null electric field;
Ŷ xx
d3x is the coupling constant of the PZT along the x direction for null deformation;
 33T
is the dielectric constant for null deformation;
δ is the factor of dielectric loss of the PZT;
a
is a geometric constant of the PZT.
Assuming that the electromechanical characteristics of the PZT patch do not change along the
monitoring time, Eq. (9) shows that the electrical impedance of the PZT (or its inverse, the admittance)
is directly related to the mechanical impedance of the structure. This way, the electrical impedance
signal can be used for monitoring the structural health of the structure.
Consequently, the technique consists basically in obtaining the curves which represent the impedance
along a band of frequencies previously chosen, and further evaluating the modifications of these
signals that are periodically observed with respect to a baseline. A change in this curve indicates a
structural modification and, therefore, a failure. Fig. 5(b) presents an example of the signal obtained
from a riveted aluminium beam (Fig.5(a)) (the blue line represents the riveted structure and the red
line stands for the structure without the rivet).
Medições com HP4194A
1400
Baseline
Com dano
1200
Impedância [ohm]
1000
800
600
400
200
0
a) Riveted beam
3
3.1
3.2
3.3
3.4
3.5
Freqüência [Hz]
3.6
3.7
3.8
4
x 10
b) Impedance signals
Figure 5 – Example of the signals obtained with the method of electromechanical impedance
Bonding the PZT patch to the structure
The bonding of piezoelectric ceramics on a flexible structure is made by following the steps below:

Mechanical cleaning of the surface in order to take off residuals and dust (Fig. 6).
Sandpaper
Clean surface
Figure 6 – Mechanical cleaning of the surface

Chemical cleaning the surface with solvent (for instance: isotropic alcohol) to take off wax,
fats and oils (Fig.7).
Acetone
Clean surface
Figure 7 – Chemical cleaning of the surface

TM
Bond the copper tape 3M (3M EMI Copper Foil Shielding Tape 1181) on the surface of
the PZT patch that will be in contact with the surface of the (Fig.8).
Copper tape 3M 1181
PZT surface in contact
with the structure
Figure 8 – Copper tape to access both sides of the PZT patch for polarization.

Mark the ceramics perimeter with a pencil on the structure‟s surface at the position one
wishes to bond the ceramics as shown in Fig. 9.
Figure 9 – Perimeter definition for the PZT patch

Use a bonding tape to separate the area external to the PZT patch perimeter (Fig.10).
Figure 10 – Isolating the area on which the PZT patch will be fixed

Spread along the bounded surface a thin and uniform layer of adhesive (for instance the
Adhesive Epoxy Araldite Professional or Loctite 401). The procedure is illustrated in the
Fig. 11.
Figure 11 – Adhesives for bonding the PZT patch

Place the ceramics over the bounded surface and use a piece of isolating material to
press the ceramics to the structure until the piezoelectric material is fixed (Fig. 12).
Figure 12 – Positioning the PZT patch

Wait for the curing time of the adhesive and proceed to the final cleaning of the ensemble
formed by the structure and the piezoelectric ceramics (Fig.13).
Figure 13 – Pressure with a load on PZT tablet for a better mechanical coupling

Weld the cables for the polarization of the piezoelectric patch as shown in Fig.14.
Figure 14 – Welding the polarization cables
The following points deserve attention regarding the bonding process and the characteristics
of the piezoelectric sensors:



The piezoelectric element presents a typical side ranging from 15 and 25mm.
Despite there are no instructions concerning ideal dimensions of he PZT patch for SHM
applications, the configurations mentioned above lead to satisfactory results.
The adhesives which better worked in the experiments done so far, were those based on
epoxy resin.
Despite the piezoelectric sensors of PZT in general present good results, they represent a
relatively high cost and some installation complexity as compared to other piezoelectric
sensors. Thus, alternative sensors have been studied, such as the so-called buzzer.
These sensors are much cheaper as compared to the PZT sensors; however, they
present a lower coupling factor, resulting in signals of limited quality. The use of buzzer
sensors limits the frequency range of analysis and also the amplitudes of the acquired
signals. Consequently, this option should be carefully analyzed. Figure 15 illustrates a
typical buzzer.
Figure 15 – Buzzer sensor.
Obs 1 – In order to bond the piezoelectric tablets in the vertical position (for instance, in some region
of the fuselage of a aircraft) there are two basic procedures, which are: i) use a fast drying adhesive,
which is the case of the ones known as superbonder; ii) use some mechanical device to allow the PZT
adherence during the time of fixation of the glue.
Obs 2 – The lifetime of piezoelectric sensors was not determined in current work. Obviously, one
considers that their use in systematic and continuous way shall permit the survey of parameters
associated to their lifetime.
Parameters for impedance tests
Initial frequency
The sensitivity of the technique in finding structural damages is related to the frequency band selected.
A very small damage in the structure doesn‟t make significant changes in properties of rigidity, mass
and damping of the structure. Therefore, it‟s necessary a sufficiently short wavelength which is able to
detect the damage. According to the literature, the band of frequency typically used in the impedance
method is from 30kHz to 250kHz.
Band of frequency
The band of frequency to be studied depends on how the structure responds to excitation. This way, it
is generally determined by a trial and error method where many ranges are candidates. There are
several desirable characteristics of a frequency band of analysis: great density of peaks, low variation
of the curve in sequential measures without damage and high sensitivity to damage occurrence.
Though it is a quite effective method, Moura and Steffen (2004) still present a statistical proceeding
which may be used to obtain better configurations for the tests of electromechanical impedance. In the
method based on impedance bands of frequency containing from 20 to 30 peaks are generally
chosen, for the number of peaks implies in a more significant dynamic response along the frequency
band.
For instance, one may observe in Fig.16, which presents the dynamic response in the frequency band
between 10kHz and 250kHz taken for a aluminium beam. One notes two bands where the larger
number of peaks is verified (10 kHz to 45 kHz and 100 kHz to 175 kHz).
First frequency band
(10 kHz to 40 kHz)
Second frequency band
(100 kHz to 175 kHz)
Figure 16 – Impedance as a function of frequency
A range surrounding a high value of frequency (150 kHz) is favorable to detect the position, whilst at a
lower frequency band (70 kHz), one detects only the areas where damages are found. The measures
of electrical impedance may not confuse both types of peaks which appear in the frequency spectrum:
one of them has to do with the resonance frequencies of the structure; another type is found for the
resonance frequency of PZT patch. For light structures it‟s better to avoid the resonance of PZT patch,
when one selects the range of frequency. This is because the magnitude of response is much higher
when compared to the resonance of the structure.
It‟s worth standing out that the frequencies to be chosen for analysis, and consequently their
wavelength, influence directly the size of damage that can be observed. Thus, higher frequencies are
more sensitive to damages of lower extension. So, the frequencies inside the audible spectrum (below
20kHz) must be avoided for being little sensitive to minute damages.
Signal acquisition
The impedance of PZT element is mainly capacitive, according to what is showed by the complex part
of the impedance signal. This term is much more sensitive to temperature variations when compared
to the real part of the signal, according to literature. Thus, the real part of the signal is generally used
in most of the applications.
A good form to acquire the impedance signal may be done through the impedance analyzer HP,
model 4194A. The configurations to be set for acquisition in this equipment are presented in the
following table.
Parameter
FREQ. START
FREQ. STOP
Value
Determined
according
to
methodology of choice of
frequencies band.
1V
SHORT
8
R+jZ
OSC LVL
INTEG TIMER
AVERAGING
Kind of measurement
the
the
Damage metrics
The higher frequencies used by the impedance method make it difficult to predict the exact measure of
impedance of the piezoelectric sensor-actuator. The signals measured may have variations related to
the environment and not to the damage itself. Thus, it is convenient to use statistical techniques to
evaluate the impedance measure, which is obtained by the use of the named damage metrics.
In order to establish a methodology capable of quantifying the structural modifications studied, one
must define a reference for damage metrics, corresponding to the structure without failure. Thus, one
can make comparisons involving the metrics values for the structure with and without damage. These
comparisons enable to indicate the presence of damage in the structure. That is, the general aim of
damage metrics is to quantify the difference among impedance measures when compared to data
obtained for the structure without damage (so-named baseline condition).
The statistical model most used in literature is the root mean squared deviation, being its formal
definition described as follows.
 
2

  Re Z1,i  Re  Z 2 ,i   
RMSD   

n
i 1 



n
(10)
where Re(Z1,i) is the real part of the impedance of the measurement without damage (baseline) in a
frequency i, Re(Z2,i) is the real part of the impedance at a frequency i for a new configuration of the
structure, and n is the number of frequency points used in the comparison. The calculation is made
inside a frequency band previously defined. As a first alternative to this metrics, one suggests to
replace the denominator by the real part of the reference impedance, that is, of the structure without
damage.

  
2 

 Re Z1,i  Re  Z 2 ,i  
RMSD1   

2

i 1 
Re
Z


1,i



n
(11)
The root mean squared deviation given by Eq.(11) is named RMSD1. In this case, the level of
impedance measurement does not affect qualitatively the metrics, though the result obtained is
modified with the number of points taken in the comparison.
Another definition of root mean squared deviation, RMSD2, is described in Eq.(12), where one may
observe that the sums are computed independently in the numerator and in the denominator.
  Re  Z1,i   Re  Z2 ,i  
n
RMSD2  i 1
2
n
 Re  Z1,i 
(12)
2
i 1
Another possibility to use the root mean squared deviation is:
RMSD3 
n
 Re  Z1,i   Re  Z2 ,i  
i 1
Re  Z1,i 
2

(13)
2
Another modification in the root mean squared deviation, RMSD4, is proposed according to next
equation:


RMDS 4   
i 1 


n
 
 Re  Z
1,i
  Re  Z1    Re  Z 2 ,i   Re  Z 2 
2
n






(14)
 
where Re Z1 e Re Z2 , are the measurements means for both conditions analyzed. These means
were included in Eq.(14) to eleminate the effect of small variations over the value of the metrics,
resulting from changes of temperature or possible electric resistances of connecting cables from
sensors to the impedance analyzer, as one may observe in Fig.(17), where are illustrated the
measures taken in a aluminum beam keeping the same conditions (without damage).
Figura 17 – Example of the amplitude variations for the structure without damage.
To determine the reference (baseline), that is, the measure for a structure without damage one uses
an average of many measures done with the healthy structure. With this average and the standard
deviation calculated for each point, one has, according to Eq.(15), as a new definition of the root
squared mean deviation
  Re  Z   Re  Z  2
1 ,i
2 ,i



n 
S z ,i


RMSD5   
n
i 1 











(15)
where one includes the standard deviation of each point of the reference sign,
S Z1 ,i , with the purpose
of making the metrics less sensitive to changes in the environment (and not properly associated to
some form of damage).
The damage metrics related to the deviation of the correlation coefficient is used to interpret and
quantify the information contained in two sets of data. Eq.(16), involves the difference between one
and the correlation coefficient between a measure and the reference.
CCD = 1 – CC,
(16)
where CCD is the deviation of the correlation coefficient and CC is the coefficient of correlation given
by Eq.(17).
CC 
being


1 n Re  Z1 ,i   Re  Z1  Re  Z 2 ,i   Re  Z 2 

n i 1
SZ1 SZ2

(17)
S Z1 the standard deviation of the reference impedance signal and S Z2 is the standard deviation
of the impedance sign to be compared. When the correlation coefficient is equal to 1, the signs have
complete correlation. The higher the difference among signs, the less is the CC value. The value of
CC is also used to compare and quantify the admittance signals.
The mean squared difference is another of the metrics used by the method of electromechanical
impedance to quantify the damage, being its mathematical formulation given by Eq.(18).

n

ASD    Re  Z1 ,i   Re  Z 2 ,i    
i 1
2
(18)
where δ is the difference of the averages of each one of the signs according to Eq.(19)
  Re  Z1   Re  Z2 
(19)
With the use of this damage metrics, one searches also to eliminate the effect of the amplitude
variations due to changes in the environment.
Still another metric used by the method of electromechanical impedance is the percentage deviation of
absolute average.
n
MAPD  
i 1
Re  Z1 ,i   Re  Z 2 ,i 
Re  Z1 ,i 
x100
(20)
One observes that the MAPD, is similar to the squared root mean deviation given by RMSD3, since
both evaluate the differences of the signals at each point of the measurement data.
As the last metric one has the simple sum of the mean difference among signs. This damage metric
uses no relation among values, being implemented as shown given by Eq.(21)
n

M   Re  Z1 ,i   Re  Z 2 ,i 
i 1

2
(21)
Example
In order to illustrate the method of structural health monitoring based on the electromechanical
impedance, we consider a beam illustrated in Fig.(18) with a rivet on its central part. The main goal of
the experiments done with the aluminum beam is to evidence the presence of the rivet in a simplified
context, through the technique of electromechanical impedance.
Figure 18 – Beam used
The beam, having 4mm thickness, was mounted according to Fig.(18), and its geometry is shown in
Fig.(19), being also depicted two PZT patches bonded to its extremities. At the centre it was inserted a
rivet of 3mm of diameter. The structure was kept suspended by rubbers, in order to configurate free
boundary conditions.
Rivet
Figure 19 – Structure‟s geometry.
As the structure has a single rivet, this was removed to characterize the damage simulation in the
structure. It was used a impedance analyser HP4194A configured for a band of impedance
observation of both PZT‟s between 40kHz and 50kHz, osc level in 1V and eight averages for each
data acquired. Both PZT patches were used, but, considering the fact that PZT2 had bonding
problems, the corresponding data shall not be presented.
Besides, seeking for higher reliability for data obtained, twenty repetitions were done. This quantity
was defined by considering the time involved in the experiment and also the need of a significant
amount of samples for statistic tests to be accomplished.
Thus, data were taken according to what was previously explained, representing a set of samples to
be statistically analysed in this section.
Aiming at illustrating the variations of the impedance signals acquired, Fig.20 shows the data for a
condition with rivet (or, baseline) and with a damage caused by the rivet loss. One notices a significant
difference between signals corresponding to both situations.
Figure 20 – Example of signal variation obtained by the electromechanical impedance.
In order to quantify data showed above, RMSD damage metrics were calculated, resulting in the
values presented in Fig.21 below.
Riveted
Without the rivet
Figure 21 – Average and standard deviation for the RMSD taken in PZT1.
By analyzing the graphics of Fig.21, one may conclude that the technique has good sensio loss of the
clinch, once it‟s evident the difference in metrics values between healthy states and the state without
clinch, for one can easily separate both sets with an imaginary line.
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Materials, 2009, Porto. Proceedings of the IV ECCOMAS Thematic Conference on Smart Structures
and Materials, 2009.
SANTOS, H.F.L. ; TRINDADE, M. A. . Stochastic modeling of active-passive piezoelectric networks for
structural vibration control. In: IV ECCOMAS Thematic Conference on Smart Structures and Materials,
2009, Porto. Proceedings of the IV ECCOMAS Thematic Conference on Smart Structures and
Materials, 2009.
PAGANI JÚNIOR, C.C. ; TRINDADE, M. A. . Design of adaptive modal filters using piezoelectric
sensor arrays. In: XIII International Symposium on Dynamic Problems of Mechanics (DINAME 2009),
2009, Angra dos Reis. Proceedings of the XIII International Symposium on Dynamic Problems of
Mechanics (DINAME 2009). Rio de Janeiro : ABCM, 2009.
SANTOS, H.F.L. ; TRINDADE, M. A. . Vibration control using extension and shear active-passive
piezoelectric networks subject to parametric uncertainties. In: XIII International Symposium on
Dynamic Problems of Mechanics (DINAME 2009), 2009, Angra dos Reis. Proceedings of the XIII
International Symposium on Dynamic Problems of Mechanics (DINAME 2009). Rio de Janeiro :
ABCM, 2009.
GODOY, T.C. ; TRINDADE, M. A. . Modeling of laminate composite plates with embedded
piezoelectric sensors connected to resonant shunt circuits. In: XIII International Symposium on
Dynamic Problems of Mechanics (DINAME 2009), 2009, Angra dos Reis. Proceedings of the XIII
International Symposium on Dynamic Problems of Mechanics (DINAME 2009). Rio de Janeiro :
ABCM, 2009.
Lobato, Fran Sérgio; Steffen Junior, Valder; BACTERIAL FORAGING OPTIMIZATION ALGORITHM
APPLIED TO ENGINEERING SYSTEM DESIGN, Proceedings of 20th International Congress of
Mechanical Engineering, Gramado, Brazil, Nov. 15-20, 2009
Leucas, Leonardo de Freitas; Abrahão, Rodrigo Rebello Ribeiro; Steffen Jr, Valder; Moura, Jr, José
dos Reis Vieira; A COMPARATIVE ANALYSIS BETWEEN LAMB WAVE AND IMPEDANCE BASED
SHM METHODS APPLIED IN RIVETED STRUCTURES, Proceedings of 20th International Congress
of Mechanical Engineering, Gramado, Brazil, Nov. 15-20, 2009
Moura Jr, Jose dos Reis Vieira; Tsuruta, Karina Mayumi; Palomino, Lizeth Vargas; Rade, Domingos
Alves; Steffen Jr, Valder; Inman, Daniel J; IMPEDANCE-BASED STRUCTURAL HEALTH
MONITORING WEB SYSTEM FOR TESTS IN GROUND, Proceedings of 20th International Congress
of Mechanical Engineering, Gramado, Brazil, Nov. 15-20, 2009
Morais, Tobias Souza; Steffen Jr, Valder; Mahfoud, Jarir; Der Hagopian, Johan, MONITORING
CRACKED SHAFT BY USING ACTIVE ELECTRO-MAGNETIC ACTUATOR - NUMERICAL
SIMULATION, Proceedings of 20th International Congress of Mechanical Engineering, Gramado,
Brazil, Nov. 15-20, 2009
Tsutura, Karina Mayumi; Moura Junior, José Vieira de Moura; Steffen Jr, Valder; Rade, Raquel Santini
Leandro; Rade, Domingos Alves; Palomino, Lizeth Vargas, EVALUATION OF THE INFLUENCE OF
ELECTROMAGNETIC RADIATION ON THE STRUCTURAL HEALTH MONITORING METHOD
BASED ON ELECTROMECHANICAL IMPEDANCE MEASUREMENTS; Gramado, Brazil, Nov. 15-20,
2009
Silva Neto, Antônio; Lobato, Fran Sergio; Steffen Jr., Valder; SELF-ADAPTIVE DIFFERENTIAL
EVOLUTION BASED ON THE CONCEPT OF POPULATION DIVERSITY APPLIED TO
SIMULTANEOUS ESTIMATION OF RADIATION PHASE FUNCTION, ALBEDO AND OPTICAL
THICKNESS; Proceedings of 20th International Congress of Mechanical Engineering; Gramado,
Brazil, Nov. 15-20, 2009
Borges, Romes Antonio; De Lima, Antonio Marcos Gonçalves; Steffen Júnior, Valder; MODELING OF
DAMPED NONLINEAR DYNAMIC VIBRATION ABSORBERS BY USING BESSEL FUNCTIONS AND
PERTURBATION METHODS; Proceedings of 20th International Congress of Mechanical Engineering,
Gramado, Brazil, Nov. 15-20, 2009.
Silva, Alice Rosa da; Lima, Antônio Marcos Gonçalves de; Silveira-Neto, Aristeu; Francis, Ricardo,
APPLICATION OF THE IMMERSED BOUNDARY METHOD IN SIMULATIONS OF FLOWS AROUND
A PAIR OF CYLINDERS WITH FLUID AND STRUCTURE INTERACTION; Proceedings of 20th
International Congress of Mechanical Engineering; Gramado, Brazil, Nov. 15-20, 2009.
De Cazenove, Jean; Gonçalves de Lima, Antônio Marcos; Alves Rade, Domingos; NUMERICAL
ANALYSIS OF SELF-HEATING EFFECTS IN VISCOELASTIC DAMPERS; Proceedings of 20th
International Congress of Mechanical Engineering; Gramado, Brazil, Nov. 15-20, 2009.
Barros, Murilo Borges; Sales, Ricardo Gonçalves; Pillet, Emmanuel; Rade, Domingos Alves; Baars,
Edmar; OPTIMAL DESIGN OF A MULTIMODAL DYNAMIC VIBRATION ABSORBER IN THE
PRESENCE OF UNCERTAINTIES; Proceedings of 20th International Congress of Mechanical
Engineering; Gramado, Brazil, Nov. 15-20, 2009.
Borges, Adailton Silva; Paulo, Wellington Luziano; Silveira Neto, Aristeu; Rade, Domingos Alves; A
METHODOLOGY FOR MODELING SUBSEA RISERS BASED ON COSSERAT THEORY; Gramado,
Brazil, Nov. 15-20, 2009.
Avila, Edson Borges; Sales, Thiago de Paula; Rade, Domingos Alves; Lacerda, Helder Barbieri;
ASSESSMENT OF FRACTIONAL-ORDER CONTROLLERS FOR ACTIVE VIBRATION CONTROL.
Proceedings of 20th International Congress of Mechanical Engineering; Gramado, Brazil, Nov. 15-20,
2009.
PALOMINO, L.V.; MOURA Jr, J.R.V.; TSURUTA, K.M.; RADE, D.A.; STEFFEN Jr, V., “Impedancebased Health Monitoring and Mechanical Testing of Structures”, Proc. of the IMAC-XXVII Conference
& Exposition on Structural Dynamics, Orlando, USA, February 9-12,2009.
PALOMINO, L.V.; STEFFEN Jr, V.; MOURA Jr, J.R.V., “Electromechanical Impedance Technique for
Evaluating Cracks in Test Samples Subjected to Fatigue”; Proc. of the International Symposium on
Dynamic Problems of Mechanics – XIII DINAME, Angra dos Reis, Brazil, March 2.6, 2009.
LOBATO, F.S.; STEFFEN Jr, V., “Adaptive Differential Evolution Algorithm and Differential Index
Reduction Strategy Applied to the Solution of Optimal Control Problems”; Proceedings of the 8th
Brazilian Conference on Dynamics, Control and Applications (DINCON 2009), Arquimedes Series Vol 8, Bauru – SP, Brazil, May 18-22, 2009
LOBATO, F.S.; STEFFEN Jr, V., SILVA NETO, A.J., “Solution of the Coupled Inverse ConductionRadiation Problem using Multi-objective Optimization Differential Evolution”; Proc. of the 8th World
Congress on Structural and Multidisciplinary Optimization, Lisbon, Portugal, June 1-5, 2009.
PALOMINO, L.V.; MOURA Jr, J.R.V.; TSURUTA, K.M.; RADE, D.A.; STEFFEN Jr, V., “Impedancebased Health Monitoring and Mechanical Testing of Structures”, Proc. of the IMAC-XXVII Conference
& Exposition on Structural Dynamics, Orlando, USA, February 9-12,2009.
PALOMINO, L.V.; STEFFEN Jr, V.; MOURA Jr, J.R.V., “Electromechanical Impedance Technique for
Evaluating Cracks in Test Samples Subjected to Fatigue”; Proc. of the International Symposium on
Dynamic Problems of Mechanics – XIII DINAME, Angra dos Reis, Brazil, March 2-6, 2009.
LOBATO, F.S.; STEFFEN Jr, V., “Adaptive Differential Evolution Algorithm and Differential Index
Reduction Strategy Applied to the Solution of Optimal Control Problems”; Proceedings of the 8th
Brazilian Conference on Dynamics, Control and Applications (DINCON 2009), Arquimedes Series Vol 8, Bauru – SP, Brazil, May 18-22, 2009
LOBATO, F.S.; STEFFEN Jr, V., SILVA NETO, A.J., “Solution of the Coupled Inverse ConductionRadiation Problem using Multi-objective Optimization Differential Evolution”; Proc. of the 8th World
Congress on Structural and Multidisciplinary Optimization, Lisbon, Portugal, June 1-5, 2009.
4- Graduate courses organized
In the Graduate School of Mechanical Engineering of the University of São Paulo in São Carlos two
new courses have been organized and offered, namely: Piezoelectric energy generators –
applications to aeronautics; Intelligent Materials and Aeroelastic Control).
In the Graduate School of Mechanical Engineering of the Federal Univerity of Uberlândia a new
course has been organized and offered, namely: Intelligent Materials and Structures.
5- Symposium organization
rd
3 Symposium on Intelligent Materials and Control – SIMC: was held in Ilha Solteira, S.P., Brazil in the
period 12-13 August 2009.
Another symposium is being organized to be included in the technical program of the National
Congress of Mechanical Engineering in August 2010.
6 – Graduate Students Supervision
At UFCG: two MSc students graduated in the period. Also post-doctoral internship was concluded.
At EESC-USP: two MSc students are working in the topic related to the INCT-EIE. One MSc student
graduated.
At UFU: Three MSc students graduated. Also post-doctoral internship was concluded.
At UNESP-IS: A PhD student graduated.
At COPPE-UFRJ: A PhD student and a MSc student graduated.
At ITA: Seven MSc students graduated.
7- Perspectives and further developments
After the first year of the INCT-EIE the team has acquired more consciousness regarding the
challenges that we are facing in the field of smart materials and structures.
In terms of perspectives, the following are to be considered:
- Significant improvement in the infrastructure of the participating laboratories;
- Increase in the number of publications and innovation projects;
- Education of young researchers devoted to different topics associated to the Institute;
- Greater interaction among the various partners that encompass the Institute and also with the
international partners;
- The partial results presented in this report testify about the fulfillment of the prescribed goals.
As for further developments, the team intends to respond to the challenge of satisfying the necessities
of technology and innovation in smart materials and structures together with related areas in Brazil.