1. UNIVERSITY OF MICHIGAN
COLLEGE OF ENGINEERING
DEPARTMENT OF AEROSPACE ENGINEERING
Structural Health Monitoring Using Electro
Mechanical Impedance Spectroscopy (EMIS) with
MFC Transducers
Author:
Yi YANG
Supervisor:
Prof. Carlos CESNIK
Dr. Yanfeng SHEN
December 20, 2015
3. Abstract
The topic of structural health monitoring (SHM) has become really popular nowadays among
automotive, aerospace, civil and naval engineering applications due to its growing demand. It is
typically a process of implementing a damage detection and characterization strategy for engineer-
ing structures. Here the damage is defined as changes to the material and/or geometric properties
of a structural system, including changes to the boundary conditions and system connectivity, which
adversely affect the system’s performance. Prof. Calos Cesnik is directing lots of research projects
related to this topic in the Active Aero-elasticity and Structure Research Laboratory. In this study,
We are focusing on using some particular actuators, for example Macroscopic Fiber Composite
(MFC), to detect the resonance spectrum of the structure. The paper covers one of the research
project which uses the impedance spectrum analysis. We compared the resonance spectrum of the
pristine case and the damaged case. The difference in the shifting of resonance frequency and the
amplitude variation carry the information of the damage. Both experiment and computer aided sim-
ulation are highly involved in the project. The precision impedance analyzer HP 4294A was used to
acquire the impedance spectrum of the specimen under different control conditions. Then the dam-
age index, which indicates the seriousness of the damage was calculated based on the difference of
the impedance spectrum between the damaged case and the pristine case. Meanwhile, ANSYS sim-
ulation were conducted to guide the experiment setup and to check result. At the end of the project,
a database was established for the specimen. Given the location/seriousness of the damage and
the sweep frequency of impedance analyzer, one may tell the seriousness/location of the damage by
referring to the database.
1 Introduction
The project is intending to use a Macroscopic Fiber Composite (MFC) to detect the seriousness and
location of damages on an aluminum plate. As mentioned in the abstract, we did both experiment
and software simulation to help us map out the relationship between the impedance spectrum and the
seriousness and location of the damage. The general idea involved in the process is called Electro-
Mechanical Impedance Spectroscopy (EMIS). Basic ideas of the method and corresponding properties
related to MFC transducer will be shown in the following sections. Later, Details about the experiment
set-up and result analysis will be covered. Then, The process and result of ANSYS simulation will be
given to compare with the experimental result. Finally, some conclusions will be drew based on my
research experience over the entire semester.
1.1 Basics of Impedance Method
The impedance method we talk about here in SHM says that we can predict some mechanical properties
of a structure by measuring the impedance of an active sensor that was set up on it. We somehow can use
a mathematical model to find the relationship between the impedance spectrum and the position, size or
seriousness of a damage on the structure.
1.2 Mechanism of EMIS for damage detection
The damage detection of EMIS method uses small-size piezoelectric active sensors intimately bonded
to an existing structure, or embedded into a new composite construction. Experimental demonstration
shows that the real part of the high-frequency impedance spectrum is directly affected by the presence
of damage or defects in the monitored structure.
Figure 1(a) shows the basic set up of the EMSI impedance experiment. An active sensor was set
somewhere on the detected board. The spectrum analyzer excites the sensor by sending a harmonic
voltage signal to its electrodes. This would lead to the axial and flexural vibration of the sensor itself,
which result in a wave propagation along a certain direction. The frequency of the signal varies from
very low frequency ( 40Hz) to very high frequency (200MHz), due to the resonance phenomenon, the
2
4. Figure 1: PZT wafer transducer acting as active sensor to monitor structural damage: (a) mounting of
the PZT wafer transducer on a damaged structure; (b) the change in EIM impedance due to the presence
of a crack. [Anderi N. Zagrai, Victor Giurgiutiu]
calculated impedance of the PZT sensor would reflect the mechanical properties of the structure. For
example, Figure 1 1(b) shows the spectrum researchers got from the former set-up. Despite the peak
that corresponds to the pristine natural frequency of the structure, there is a another unusual peak which
reveals the fact that something might happens to the mechanical structure of the board since the natural
frequency of a structure would not vary unless it is mechanically changed, for instance, there is a crack
in the way that the mechanical wave propagates. Based on this idea, people would be able to further
develop the way to measure the size of the crack and evaluate its seriousness to the system.
1.3 Mechanisms of piezoelectric Macro Fiber Composites (MFC) for sensing and actu-
ation
Macro Fiber Composite (MFC) is the leading low-profile actuator and sensor offering high performance,
flexibility and reliability in a cost competitive device. The MFC consists of rectangular piezo ceramic
rods sandwiched between layers of adhesive, electrodes and polyimide film. The assembly is well
designed that enables in-plane poling, actuation and sensing in a sealed and durable, ready to use pack-
age. If voltage is applied, it will bend or distort materials, counteract vibrations or generate vibrations.
While if no voltage is applied it can work as a very sensitive strain gauge, sensing deformations, noise
and vibrations. The MFC is also an excellent device to harvest energy from vibrations. [www.smart-
material.com]
The MFC is available in d33 and d31 operational mode, a unique feature of the Macro Fiber Compos-
ite.MFC P1 type with d33 effect is called Elongator, while the P2 and P3 type with d31 effect is called
Contractor. The P1 type MFCs (See Fig. 3), including the F1 and S1 types are utilizing the d33 effect for
actuation and will elongate up to 1800ppm is operated at the maximum voltage rate of -500V to +1500V.
The P1 type MFCs are also very sensitive strain sensors. The P2, P3 type MFCs (Fig. 3) are utilizing
the d31 effect for actuation and will contract up tp 750 ppm if operated at the maximum voltage rate of
-60V to +360V. The P2 and P3 tyoe MFCs are mostly used for energy harvesting and as strain sensors.
[www.smart-material.com]
3
6. In our case, we are using the d33 effect of the MFC actuator. The following table (See Fig. 5) shows the
specifications of the MFC actuator we use in the lab.
Figure 5: Estimated Mechanical Properties of MFC Actuator
2 Experiment Setup
2.1 HP4294 A Impedance Analyzer
The impedance Method requires us to have a resonance spectrum of the structure, therefore, we need
to some powerful machine to measure the resonance amplitude and phase within the frequency domain.
HP 4294 A is able to help us accomplish the task. Fig. 6 shows our experiment Set-up.
Figure 6: Experiment Setup (Overview)
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7. As you you can see from the overview of our experiment setup, the Impedance Analyzer is connected
to two shielded wires, which were used to reduce the electromagnetic noise. We put all our sample test
specimen on the pink test platform, you may refer to the following picture (Fig. 7) to see more details
about it. In order to familiarize the operation method of the Impedance Analyzer, I tested several type
Figure 7: Experiment Setup (Test Platform)
of specimen at the beginning. They are Capacitor with a capacitance of 10000pF, a PZT transducer and
a beam with MFC sensor on it.
2.2 General Design of the Experiment
As is mentioned above, the purpose of the experiment is to investigate the influence of the coupled
”damage” on the amplitude and natural frequency of the aluminum board. To do so, we switch the test
sample above to be an aluminum board. Then, we first get the impedance spectrum of the pristine case
from the impedance analyzer and vary the position of the coupled magnets for the damaged cases. The
purpose of doing this is to compare the impedance spectrum between the pristine case and the damaged
case. However, more importantly, we are more interested in how this difference varies on the board as
we change the position of the coupled ”damage” (strong magnets). Fig. 8 is the set-up of this experiment.
Fig.8 shows all the places I plan to place the magnets. As indicated in the picture ( 9), I design the
experiment matrix as shown in Table.1. The positions shown in the table are represented in the polar
coordinates. I divided the phase angle from 0 deg to 90 deg by an increment of 10 deg. The distance
was settled from 3cm to 15 cm with an increment of 2cm. Since the board is symmetric with respect to
its geometric center, we can apply the principle of symmetry to predict the experiment result conducted
on the other three phases.
2.3 Data Acquisition System
Now,we are able to operate the impedance analyzer by carefully following the operation manual. How-
ever, we still need to figure out how to extract the data from the impedance analyzer to a computer, with
which we can use Matlab to better analyze the collected data. The following diagram (Fig. 10) shows
our data transfer schematic which might help students in the future get along with the analyzer much
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8. Figure 8: Experiment Setup for the Inspection of the Board
Figure 9: Test Positions of the Coupled Magnets (Damage)
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9. 3 5 7 9 11 13 15
A (3cm, 0 deg) (5cm,0 deg) (7cm, 0 deg) (9cm, 0 deg) (11cm, 0 deg) (13cm, 0 deg) (15cm, 0 deg)
B (3cm, 10 deg) (5cm,10 deg) (7cm, 10 deg) (9cm, 10 deg) (11cm, 10 deg) (13cm, 10 deg) (15cm, 10 deg)
C (3cm, 20 deg) (5cm,20 deg) (7cm, 20 deg) (9cm, 20 deg) (11cm, 20 deg) (13cm, 20 deg) (15cm, 20 deg)
D (3cm, 30 deg) (5cm,30 deg) (7cm, 30 deg) (9cm, 30 deg) (11cm, 30 deg) (13cm, 30 deg) (15cm, 30 deg)
E (3cm, 40 deg) (5cm,40 deg) (7cm, 40 deg) (9cm, 40 deg) (11cm, 40 deg) (13cm, 40 deg) (15cm, 40 deg)
F (3cm, 50 deg) (5cm,50 deg) (7cm, 50 deg) (9cm, 50 deg) (11cm, 50 deg) (13cm, 50 deg) (15cm, 50 deg)
G (3cm, 60 deg) (5cm,60 deg) (7cm, 60 deg) (9cm, 60 deg) (11cm, 60 deg) (13cm, 60 deg) (15cm, 60 deg)
H (3cm, 70 deg) (5cm,70 deg) (7cm, 70 deg) (9cm, 70 deg) (11cm, 70 deg) (13cm, 70 deg) (15cm, 70 deg)
I (3cm, 80 deg) (5cm,80 deg) (7cm, 80 deg) (9cm, 80 deg) (11cm, 80 deg) (13cm, 80 deg) (15cm, 80 deg)
J (3cm, 90 deg) (5cm,90 deg) (7cm, 90 deg) (9cm, 90 deg) (11cm, 90 deg) (13cm, 90 deg) (15cm, 90 deg)
Table 1: Experiment Matrix for the Position of the Coupled Damage (Strong Magnets)
more easier.
Figure 10: Data Acquisition System Schematic
The Data Acquisition System mentioned above makes it possible for me to analyze the data through
some Matlab tools. However, it still needs people to set the frequency domain manually, which is really
time consuming if you are interested in the spectrum of multiple frequency domains.What I expect future
students to do is designing a LabView code that could be able to set the frequency domain automatically,
which would promote the efficiency tremendously.
3 Experiment Result
Now, we are able to conduct the experiment after introducing the experiment set-up, Experiment Method
and the Data Acquisition System. The section starts from the test result of an aluminum beam. It
shows the general idea of how we approached to the problem. From the resultant impedance spectrum,
you would have an intuitive sense of how we analyze the influence of the damage on the specimen.
Later, result from the experiment conducted on the aluminum board will be given. By comparing the
impedance spectrum obtained under different circumstances, you might have a deeper understanding of
the influence created by the coupled ”damage”.
3.1 Sample Test Result
As mentioned above, some sample experiments were taken in order to make me familiarize how to use
the Impedance Analyzer.I want to show the one with the MFC actuator here to give you a big picture of
what we are going to do in the following several sections.
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10. First of all, we just test the spectrum for a free beam with no extra payload exerting on it. Then, we
used a small, square and very strong magnets to model the structure damage on the beam. Moreover, we
move the position of the magnets to see what the influence is of its positions on the spectrum. You may
refer to Fig. 11 to see more details.
Figure 11: Impedance Spectrum Experiment of a Beam
We vary the location of the magnets for 5 times. As you may see above, we set the coordinate at the
end of the MFC patch to be x=0, then we obtained five groups data at the positions of x = 1cm,x =
2cm,x = 3cm,x = 4cm,x = 5cm. The following picture (Fig. 12) shows our results.It shows the
impedance spectrum of different damage cases. Notice that the peak value in the red circle varies signif-
icantly when I move the position of the magnets. Fig. 13 shows more details within the red circle.
Fig. 13 shows that as we change the position of the magnets, the peak value and its corresponding
resonance frequency does change. However, its kind of hard for me to draw any conclusions for now.
We would have a more sensible result in the following sections.
3.2 Test Result of the Aluminum Board
Similarly as what we did for the aluminum beam, we also obtained the impedance spectrum of the
aluminum plate for both pristine and damaged case. The following picture (Fig. 14)shows a particular
case where the coupled damaged was put at position A3. The blue curves represents the pristine spectrum
while the red curve stands for the damaged curve.
As you can see from the plot above, the amplitude and the resonant frequency do change when we
couple an extra mass on the specimen. However, it should be noted that such kind of variation between
the pristine and damaged case varies with respect to the excitation frequency. Therefore, in order to
obtain most valuable result, we need to zoom into a particular domain where the variation is amplified.
Further discussion will be addressed in the Result Analysis Section.
4 Result Analysis
In this section, I will talk about what information can we extract from the experiment result. First of
all, we keep saying that we need to compare the impedance spectrum between the pristine and damaged
9
11. Figure 12: The Impedance Spectrum of a Beam
Figure 13: The Impedance of a Beam (Continued)
10
13. case. However, we need to quantify such difference through a mathematical tool which is called Damage
Index. Then, we tried to map the sensitivity of the MFC actuator to location of the damage. It is
reasonable because we’ve already got a database by conducting experiment on the entire board. What
we have to do then is calculate the Damage Index for each location, and provide a contour plot that
shows the distribution of the MFC sensitivity. Later, I will briefly talk about the potential help that we
can utilize from the computational simulation.
4.1 Analysis of the Impedance Spectrum
The term I am going to introduce here is called Damage Index. It is defined by the following equation.
DI = N [Re(Zi) − Re(Z0
i )]2
N [Re(Z0
i )]2
(1)
Damage Index can be really useful in two ways. Firstly, by computing the DI with different frequencies,
we will be able to know which excitation frequency is more sensitive to the coupled damage. For
example, I divided the current frequency domain into 10 sub-pieces and calculate the DI within each
sub-domain. The following picture shows the result of the calculation.
Figure 15: Damage Index on Each Sub-domains for Real Part Signal at Position J1
Clearly, as shown in Fig. 15 and Fig. 16,DI varies between each sub-domain. It tells us that for each
location on the board, we have different damage index under different excitation frequencies. Moreover,
DI also provides us spacial information. That is for a given sweep frequency, the value of DI changes
as we move the position of the coupled magnets. Fig. 15 shows the change of the DI along the Fiber
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14. Figure 16: Damage Index on Each Sub-domains for Imaginary Part Signal at Position J1
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15. Figure 17: The change of the Damage Index along the Axial Direction when the Sweep Frequency is set
from 60 kHz to 70 kHz
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16. (Axial) direction as we change the position of the coupled magnets. The red and blue curve represent
the DI computed from the real part and imaginary signal respectively. Although the plot doesn’t reveal
any distinguishable tendency of both two curves, it gives us an intuition of how the whole system works.
4.2 Database of the Damage Index Distribution
With the techniques introduced in the previous sections, we are now able to give a contour plot to show
the distribution of the sensitivity of the MFC actuator in terms of Damage Index. Fig. 19 - Fig. 28 show
the analysis result on each 10kHz domain from 60 kHz to 70 kHz. As a matter of fact, the information
we’ve collected till now is really important. It essentially creates a database to which we can refer to
find the location of the damage. Fig. 18 shows the flow chart of the idea.
Figure 18: Computational Flowchart of Damage Localization
Briefly speaking, if we are given a specific Damage Index and corresponding sweep frequency, we
would be able to predict the location of the damage by referring to the Database of the Damage Index
Distribution.
5 ANSYS Simulation
Another approach to the problem is running a computational simulation. We are looking for the relation-
ship between the damage seriousness and the location of them. However, we are not able to model the
damage seriousness directly from any kind of software. Instead, what we could report is the stress inten-
sity, for instance the Von Mises Stress distribution of the system with respect to the external excitation
vibration caused by the coupled actuator. Then, we are able to tell the anisotropic property of the MFC
actuator by investigating the Von Mises Stress contour plot. For example, if point A has a very large
stress intensity under the excitation frequency of f1. Then we might expect a large damage seriousness if
Figure 19: Damage Index Distribution when the fre-
quency is set from 60 kHz to 61 kHz
Figure 20: Damage Index Distribution when the fre-
quency is set from 61 kHz to 62 kHz
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17. Figure 21: Damage Index Distribution when the fre-
quency is set from 62 kHz to 63 kHz
Figure 22: Damage Index Distribution when the fre-
quency is set from 63 kHz to 64 kHz
Figure 23: Damage Index Distribution when the fre-
quency is set from 64 kHz to 65 kHz
Figure 24: Damage Index Distribution when the fre-
quency is set from 65 kHz to 66 kHz
Figure 25: Damage Index Distribution when the fre-
quency is set from 66 kHz to 67 kHz
Figure 26: Damage Index Distribution when the fre-
quency is set from 67 kHz to 68 kHz
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18. Figure 27: Damage Index Distribution when the fre-
quency is set from 68 kHz to 69 kHz
Figure 28: Damage Index Distribution when the fre-
quency is set from 69 kHz to 70 kHz
we couple an artificial ”damage” at point A, and sweep the frequency very near that particular frequency.
To do so, we can model a metal board as our specimen and put a piezoelectric FEM model on the
center of it as our actuator. The whole simulation should follow the procedure as follows. First off,
we need to pre-process our model, which includes mesh refinement, boundary conditions constraint and
load application. Then, we do the simulation for both pristine case and damaged case. For the pristine
one, what we test is the natural response of the specimen relative to the excitation signal applied by
the actuator. Later, we conduct the simulation for the damaged case in which we add some coupled
”damage” to the pre-processing part. At the end, we should compare the simulation result, for example,
Von Mises Stress Distribution and Impedance Spectrum between the pristine case and damaged case.
The comparison is really meaningful since it gives us guidance for the actual experiment. I will show
how it works in the following sections.
5.1 Pre-processing
The pre-processing of our model is pretty simple, what we need is a flat aluminum board with a piezo-
electric actuator located at the center of it. As you can see from Fig. 29 which is the volume plot of the
model.
The red part shows shows the aluminum board specimen, while the blue part shows the piezoelectric
model which used to model our actuator. Then, Fig. 30 shows the element plot of the model which
is carefully meshed with three element per centimeters on the edge. As you can see in the middle of
the board, I put a harmonic voltage with amplitude of 1 Volts on the piezoelectric model. It creates a
expansion-contraction effect during the simulation process which models the actual actuator.
Later, we need to account for the existence of the coupled artificial damage. To do so, I model an extra
aluminum block on the axial direction of the board. The following element plot shows the detail. As
you can see from Fig. 30, we mesh the block with the same density as we meshed the block and the
actuator. The purpose to do so is to ensure the perfect coupling effect between the ”damage” and the
board. Ideally, we need to model the effect of the ”damage” on the entire board as what we did for the
experimental part. Nevertheless, I only did one sample here due to the limitation of time. But anyway,
It gives me a sense of how it looks like.
5.2 Post-processing
As we will stress later, our analysis is based on the comparison between the pristine case and the dam-
aged case. In order to obtain the guidance for both scenarios, we need to model both of them. I will
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19. Figure 29: Volume Plot of the Model
Figure 30: Element Plot of the Model
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20. Figure 31: Element Plot for the Damaged Case
illustrate the basic idea of the simulation through the modeling of the pristine model. Then further
comparison will be given between the pristine model and the damaged model.
5.2.1 Simulation of Pristine Model
With the simulation model settled, we did our computation for 300 steps within the frequency range from
60 kHz to 70 kHz. The following groups of pictures shows the stress intensity distribution for some of
them. As you can see from Fig. 32 which shows the simulation result when the input signal has a
frequency of f = 60.5kHz. The Von Mises Stress distribution has a uniform patter on the diagonal line
of the board, where the stress intensity is clearly higher on the other part of the board. Well, such kind
of pattern changes as we vary the frequency of the input electric signal. Fig. 33 shows more interesting
effect when we change the frequency of the input signal to f = 62.5 kHz. As you can see, the stress
intensity is much more stronger along the axial (fiber) direction than that along the flexural(horizontal)
direction. It is because, unlike the traditional PZT actuators, MFC actuator has different properties in
those two directions. Such anisotropic property leads to different actuation effects, therefore creates
different stress intensities along those two directions. The following picture shows more clearly about
this effect. This time we change the input signal frequency to f = 70 kHz. Similarly, we got quite
different response along both axial(fiber) and flexural (horizontal) directions. Compared with the effect
shown in Fig. 34, this time we got tremendously more stress along the fiber direction. It means that the
current excitation frequency is probably closer to the natural frequency of the system. We should pay
more attention to this frequency especially the behavior of the specimen along the axial (fiber) direction.
5.2.2 Simulation of the Damaged Model
Similarly as what we did for the pristine case, we are also interested in the Von Mises Stress distribution
for the damaged case. Out of curiosity, I did a particular test by setting the excitation frequency to
be f = 70kHz.(See. Fig. 34) The comparison between the pristine case and the damaged case is
19
21. Figure 32: Von Mises Stess Distribution at f = 60.5kHz
Figure 33: Von Mises Stress Distribution at f = 62.5kHz
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22. Figure 34: Von Mises Stress Distribution at f = 70kHz
Figure 35: Von Mises Stress Distribution of the Damaged Case at f = 70kHz
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23. obvious. By coupling an artificial damage on the board, we manually changes the natural frequency
of the system. It leads to a different Von Mises Stress Distribution at a particular excitation frequency.
However,another piece of information we can obtain from the simulation is the impedance spectrum
along the sweep frequency region. As mentioned above, I did the simulation for 300 steps between
f = 60 kHz and f = 70 kHz. Therefore, we could get 300 current output with corresponding voltage
input. Then, we calculate the impedance from Ohm’s Law. The following picture (Fig. 36) shows how
the impedance spectrum changes between the pristine case and the damaged case.
Figure 36: Impedance Spectrum Comparison from ANSYS
6 Conclusion
To conclude the project, I want to review the whole research process and give my comments on some
specific key steps. As listed in the research objective table, I first learned the basic idea of EMIS method.
It gave me an overview of the project, which helps me to better design the experiment procedures. At the
meantime, I also did some literature reviews on the working mechanism of MFC and other piezoelec-
tric actuators. It turns out that EMIS method has a large comparative advantage over other inspection
method because such transducers would become fairly cheap once they were manufactured in a large
scale of amount.
Later, I move on to the experiment part. It is the part from which I learn most over the entire semester.
First off, Dr. Shen and I figured out how to use the HP 4294A impedance analyzer. More importantly,
we found a new way to export the experiment data from the analyzer to a personal computer, which is
definitely faster and easier to operate than the old way. Future student may refer to Fig. 10 for instruc-
tion. As mentioned in Section.4, we created a database of damage index distribution over the sweep
frequency from 60kHz to 70kHz. Although the current database only contains 70 data points, it is good
demonstration of the idea.
22
24. Then, I started my FEM simulation under the instruction of Dr. Shen. The first thing I did was to famil-
iarize the operation system of ANSYS by trying out multiple typical input files as learning examples.
With enough practice, I started to model our experiment independently. The most critical part of doing
simulation is to figure out how to couple a piezoelectric ”actuator” on the aluminum plate to model the
actual MFC transducer. Fortunately, there is available material online that I can refer to.2 At the end
of the day, I obtained the impedance spectrum for both pristine case and the damaged case. 36 shows
the comparison between them. Although it is a very rudimentary approach to the problem, we still got a
lot of guidance from it. For example, by doing simulation, we can zoom in our sweep frequency to the
range where the significant shift of resonant phenomenon appears.
Last but not least, I think the result of this research project can be refined in the future by carefully
focusing on the following two points. First off, as mentioned above, the current database contains 70
data points. To obtained more accurate and precise prediction, more data should be collected and ana-
lyzed. The data collection process is not hard as long as future researchers refer to my weekly reports.
Secondly, the same amount of data points should also be collected via ANSYS simulation. Due to the
limit of time, I only did the simulation for one particular location. However, it is necessary to do all of
them as what we did in the real experiment. Then, a damage index distribution comparison need to be
done between the simulated result and the experiment result.
Finally, I’d like to thank Prof. Cesnik and Dr. Shen for your kind and patient instruction to me over the
entire semester. I really appreciate it.
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25. References
[1] Caio dos Santos Guimaraes and Flavio Luiz de Silva Bussamra and Valerie Pommier-Budinger
and Joes Antonio Hernanes. Insituto Tecnologico de Aeronautica - ITA, Praca Marechal Eduardo
Gomes, Unicersite de Toulouse - ISAE. Asociacion Argentina de Mecanica Computatonal, Vol
XXIX pages 8263 - 8279, 15-18, November 2010.
[2] SMART-MATERIAL, Inc. MFC Datasheet
http://www.smart-material.com Accessed October 28th, 2015
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