shm of composite plates: vibration based method by using pzt...
TRANSCRIPT
SHM of composite plates: Vibration based method by using PZT sensors
R. de Medeiros1,2, M. Sartorato1, D. Vandepitte2, V. Tita1 1 São Carlos School of Engineering, University of São Paulo, Department of Aeronautical Engineering
Av. João Dagnone 1100, 13563-120, São Carlos, São Paulo, Brazil
e-mail: [email protected]
2 KU Leuven, Department of Mechanical Engineering
Celestijnenlaan 300 B, B-3001, Heverlee, Belgium
Abstract This study presents experimental and numerical analyses about health monitoring metrics using vibration-
based method for damage detection in composite plates. Three composite plates, made of carbon fibre and
epoxy resin, were considered in this study, one intact, other damaged by manufacturing, i.e. a centre hole
(controlled damage) and the other damaged by low-velocity impact loading (uncontrolled damage).
Experimental and numerical analysis consists of vibration tests. In order to produce the excitation on the
structures, an impact hammer was used. Accelerometers and, in a second stage, piezoelectric transducers
were used for data acquisition. Firstly, the Frequencies Response Functions (FRFs) were obtained using
accelerometers. Then, secondly, piezoelectric transducers were used. Numerical analyses were carried out
through finite element modelling, considering the simulation of the piezoelectric transducers. Finally,
FRFs were analysed using appropriate metrics, which were compared in terms of their capability for
damage identification.
1 Introduction
Aircraft are composed by different complex systems, for example: structural, hydraulic, propulsion,
electronic and avionic elements. Damage detection on aircraft composite structures has been one of the
major concerns of operators during the last two decades. Vibration-based methods by using piezoelectric
sensors and/or actuators incorporated into composite structures offer a promising option to fulfil such
requirements and needs. These methods can use finite element analysis combined to experimental results
in order to detect damage. Thus, it is possible to identify, locate and estimate the damage events,
comparing dynamic responses between damaged and health structures. The basic idea of the vibration-
based damage detection method consists on assuming that damage is a combination of different failure
modes, which affect the local stiffness of the structure, and this modifies the dynamic characteristics of the
structure, i.e., the modal frequencies, mode shapes and modal damping values. Structural Health
Monitoring (SHM) can provide, all the time, during the aircraft life, a diagnosis of the material state and
the structure situation, as well as a prognostic like the residual strength of the structure. Thus, SHM can
reduce the maintenance costs, avoiding useless inspections.
Literature on vibration based method can been found in many conferences and journals. Salawu [1]
discussed the use of natural frequency as a diagnostic parameter in structural assessment procedures using
vibration monitoring. Doebling et al. [2] presented an overview of methods to detect, locate, and
characterize damage in structural and mechanical system by examining changes in measured vibration
response. Zou et al. [3] reviewed the model-based delamination detection methods for composite
structures using vibrations. Firstly, it describes the most commonly, model-based methods for damage
detection, used structural modelling techniques for delamination and the effects of delamination on
dynamic parameters. Then it focuses on the application of vibration-based model-dependent damage
3751
detection methods in composite structures. Finally, the review is devoted to the development of methods
with incorporated piezoelectric sensors and actuators for on-line delamination detection for composite
structures. Carden and Fanning [4] reviewed the state of the art in vibration-based conditioning monitoring
with particular emphasis on structural engineering applications. The review identified several different
approaches and categorized them. Montalvão et al. [5] reviewed the advances in structural health
monitoring and damage detection, with emphasis on composite structures. Ciang et al. [6] presented many
SHM methods for damage detection in a wind turbine system. Worden et al. [7] presented a review of
examples from nonlinear dynamical system theory and from nonlinear system identification techniques,
which are used for the feature-extraction portion of the damage detection process. It provides a number of
illustrations of complimentary approaches where damage-sensitive data features are based on nonlinear
system response. These features, in turn, can either be used as a direct diagnosis of damage or as input to
statistical damage classifier. Huang et al. [8] presented a review of the development of analytical,
numerical and hybrid approaches for modelling of the coupled piezo-elastodynamic behaviour in order to
use as a structural health monitoring system. Fan and Qiao [9] showed a review in order to identify
starting points for research in vibration-based damage identification and structural health monitoring.
Also, they guided researchers in better implementing available damage identification algorithms and
signal processing methods for beam- or plate-type structures. The review is organized by the classification
using the features extracted for damage identification methods. Pérez et al. [10] presented the results of an
experimental campaign conducted to investigate the feasibility of using vibration-based methods to
identify damages sustained by composite laminated due to low-velocity impacts. The experimental
programme include an evaluation of impact damage resistance and tolerance according to ASTM test
methods, characterization of damage by ultrasonic testing and quantification of the effects on the vibration
response. The experimental results indicate that impact-induced damages result in detectable changes in
the vibration response of coupons. Medeiros et al. [11-14] presented experimental and numerical results in
vibration-based damage detection and structural health monitoring for beam- cylinder- plate- or bonded
joints. The results demonstrated the potentiality of this technique in detecting damage.
Regarding numerical approaches, in general, the problem is to model correctly structures with
piezoelectric transducers, either attached or embedded [15]. In general, the results for different models of
finite elements can be used to identify damage by using electro-magnetic coupling of piezoelectric
sensors. Several theoretical models exist in the literature. However the mostly common used commercial
finite element packages contain only solid finite elements with piezoelectric capabilities [16]. Hence,
simulations of complex shell or large structures become computationally unfeasible, especially for thin or
curved structures, in which shell elements would be preferred. Also, for curved structures, some effects
are more important than for quasi-planar structures, such as the non-linear shearing relative distortions
terms on the normal strains and the electrical field-strain coupling [17]. Usually, the existing studies
propose ways to include higher order shell theories [18] or a lagrangean solution to the non-linear
geometric problem by including Green strains or von Karman strains [19]. In particular, Gabbert et al. [20]
and Nasser et al. [21] created non-linear models, which characterize better the electrical field-strain
coupling by using a first order electrical field solution that naturally fulfils Gauss’ Law. Moreover, most of
the works existing in the literature model the electrical-mechanical coupling innate via the first order
electrical field theories, which uses the continuous electrodes constitutive equations and Faraday induction
law solution.
In practical, for the large and complex structures, as well as for structures with hard access, it is very
difficult to detect damage by using local damage detection methods (e.g. ultrasonic), because this type of
methodology can be only used to inspect accessible components of a structure. In order to detect damage
throughout the whole structure, especially some large structure, a methodology, which uses global
vibration based, has been more adequate. Recently, this type of methodology has been used for composite
structures. Therefore, this present study shows experimental and numerical analyses about health
monitoring metrics by using vibration-based method for damage detection in composite plates. Three
composite plates, made of carbon fibre and epoxy resin, were considered in this study, one intact, other
damaged by manufacturing, i.e. a centre hole (controlled damage) and the other damaged by low-velocity
impact loading (uncontrolled damage). Experimental and numerical analysis consist of performed
vibration tests. In order to produce the excitation on the structures, an impact hammer was used.
Accelerometers and, after that, piezoelectric transducers were used for data acquisition. Firstly, the
3752 PROCEEDINGS OF ISMA2014 INCLUDING USD2014
Frequencies Response Functions (FRFs) were obtained by using accelerometers. Then, secondly, by using
piezoelectric transducers. Numerical analyses were carried out via Finite Element Method, considering the
simulation of the piezoelectric transducers. Regarding the finite element analyses, a mathematical
formulation of a non-linear shell finite element for piezoelectric active composite was proposed. The
formulation contemplates both the problem of the electrical-mechanical coupling problem, by introducing
first order electrical field polarization theory and electrical field-strains coupling. Due to the objective of
SHM simulations, a linear, first order shear theory element was preferred over more complex models due
to the efficiency of such elements and the fact that modal and frequency analysis require only
displacement solutions. The final formulation was implemented using an eight nodes serendipity quadratic
finite element. The element was implemented in a Fortran subroutine and compiled through the finite
element commercial package AbaqusTM using its User Element (UEL) subroutine. Finally, FRFs were
analysed by using some metrics, which were compared in terms of their capability for damage
identification.
2 Experimental Analyses
The experimental analyses were carried out via vibration tests on composite plates. The plates are made of
8 plies stacked in [0]8 lay-up configuration. The specimens are manufactured by filament winding. The
composite plates are made of carbon fibre with epoxy resin (Carbon Fibre Reinforced Polymer – CFRP).
The plate geometries consist of 305 mm length, 245 mm width and 2.16 mm total thickness (Fig. 1). Three
versions of nominally similar plates were investigated in this study, one intact, another one damaged by
drilling a centre hole (controlled damage), which has diameter equal 5mm, and the other one is damaged
by low-velocity impact loading (uncontrolled damage). Due to fibre orientation, this damage has length
equal 130mm in the fibre direction. Firstly, the Frequencies Response Functions (FRFs) were obtained
using accelerometers (Fig. 1(a)). The accelerometers were model 352C22 lightweight. Accelerometer 1
(sensitivity 9.00 mV/g) was set on the position 1, accelerometer 2 (sensitivity 9.31 mV/g) was set on the
position 2, accelerometer 3 (sensitivity 9.57 mV/g) was set on position 3 and accelerometer 4 (sensitivity
9.94 mV/g) was set on position 4, which can be seen in Fig. 2. Then, secondly, piezoelectric transducers
were used (Fig. 1(b)) M2814-P1 type MFC (Macro Fibre Composite) manufactured by Smart Material
Inc., which use the 33 mode of piezoelectricity. The piezoelectric geometries consist of 38 and 28 mm
overall and active length, respectively, 20 and 14 mm overall and active widths, respectively, and 0.305
mm total thickness (Fig. 3). The excitation for both sets of vibration tests was applied by using an impulse
signal through an impact hammer PCB Model 0860C3 (Piezotronics).The input was set on the position 1
in the back side of the plate.
(a) (b)
Figure 1: Schematic experimental set (a) with accelerometers and (b) with MFCs
STRUCTURAL HEALTH MONITORING 3753
Six experimental and three computational models were studied in this work. The first, second and third
models (P1A, P2A and P3A) represent the intact plate (P1), centre hole plate (P2) and impacted plate (P3)
which are experimentally measured using accelerometers. The fourth, fifth and sixth models (P1P, P2P
and P3P) represent the intact plate (P1), centre hole plate (P2) and impacted plate (P3) which are
experimentally measured using piezoelectric transducers. The dataset contains FRFs, including
information on natural frequencies and damping factor, which can be used to identify the presence of
damage at the structure. However, sometimes, it is necessary to use appropriate metrics in order to identify
the damage.
Fig. 2 to Fig. 4 show all data acquisition set-ups used in the experimentation. The specimen is suspended
on elastomeric wires to simulate “free-free” boundary condition, the accelerometers (Fig. 4(a)) and MFCs
transducer (Fig. 5(a)) and the hammer linked to a LMS SCADAS equipment, which was controlled by the
Test.Lab software (LMS Test.Lab). The LMS SCADAS is a plug and play equipment and it has
multifunction analog, digital and timing I/O board for USB bus computers.
(a) (b) (c)
Figure 2: Experimental Setup with accelerometers: (a) intact; (b) damaged by central hole and (b)
damaged by impact
(a) (b) (c)
Figure 3: Experimental Setup with MFCs: (a) intact; (b) damaged by central hole and (c) damaged by
impact
3754 PROCEEDINGS OF ISMA2014 INCLUDING USD2014
(a) (b)
Figure 4: Experimental layout by using (a) accelerometers and (b) piezoelectric sensors
The input signals are generated by an impact force hammer in the position 1 (Fig. 1(a) and Fig. 1(b)). This
type of input provides an excitation over a wide range of the required frequencies. This is important
because different types of damage can affect different frequency ranges, and the resonant and anti-
resonant characteristics of a structure may be good indicators of damage. This approach, which uses
impulse vibration, is a more global damage indicator compared to other methods, which uses single
frequency tone bursts and wave reflection. The FRF can indicate damage, which is inside the structure.
However it is important to highlight that they may not be as sensitive to small damage on the surface as
compared to wave propagation methods. Each signal consists of 2048 points and sampling occurred at
1024 Hz. The number of averaging individual time records was selected to be five.
3 Numerical Analyses
Modal and frequency simulations of Plate 1 (intact) and Plate 2 (with centre hole) were developed using a
finite element proposal, which was implemented in AbaqusTM via UEL (User Element Subroutine).
Figure 5: Numerical finite element model for Plate 2.
STRUCTURAL HEALTH MONITORING 3755
The material elastic properties of the plates were obtained from previous research work by the authors [22-
23]. The elastic, piezoelectric coupling and dielectric properties of the transducers were obtained based on
data from the sensors manufacturer and the methodology proposed by the authors [24]. Figure 5 shows the
finite element model used for the analysis of Plate 2, highlighting the mesh density, boundary conditions,
loads, and positions of the transducers. The mesh for Plate 1 and 2 contains respectively 5448 and 5712
quadratic elements. More details about the finite element proposal are addressed in the next section.
Using the aforementioned material properties and models, undamped direct solutions for a frequency
domain from 0 Hz to 1024 Hz were performed using 2048 equidistant steps (0.5Hz frequency step). The
same impact points, load type and FRF measurements (H11, H12, H13 and H14) used for the experimental
tests were used in the numerical simulations. The undamped approach was used for the numerical studies
to make sure experimental and numerical data were independent from each other.
3.1 Finite Element Proposal
This section gives a summary of the mathematical formulation of the finite element, including the
mechanical and electrical assumptions and the constitutive equations. This formulation is an improved
version of previous work by the authors [12], and it includes the electrical-mechanical coupling innate to
the first order electrical field theories [20-21].
3.2 Mechanical Hypothesis
The kinematics for degenerated shells and the First Order Shear Theory (FOST) were used to describe the
displacements of a given shell, based on the displacement of its reference section (ui) and its rotations (θθθθo),
as shown in Eq. (1). The matrix Tij is the transformation matrix from the global coordinate system (x1, x2,
x3) to the local coordinate system in the shell (s1, s2, s3), in which the composite principal directions are
defined. The FOST was used to increase the computational efficiency of the model. Also, as most
applications of smart composites only require displacement calculations (modal analysis, explicit dynamic
analysis), higher order theories are not necessary.
( )kjk3jijjiji HsuTuTu θ+==
,
−=
00
01
10
H
, 2..1k;3..1j,i ==
(1)
The iso-parametric coordinate system (ξ1, ξ2, ξ3) is related to the local coordinate system through Eq. (2),
where -0.5 ≤ η ≤ 0.5 is the ratio of the distance of the reference section relative to the mid-section to the
whole thickness. The engineering strains are calculated through Eq. (2).
( )η−ξ= 2
2
hs 33
,
θδ+
∂
θ∂+
∂
∂=
∂
∂+
∂
∂=ε oklj3
j
okl3
j
kik
i
j
j
iij H
2
h
sHs
s
uT
s
u
s
u
2
1
, 2..1o;3..1k,j,i ==
(2)
3.3 Electrical Hypothesis
The electrical assumptions used are: the piezoelectric layers are transversal isotropic; the transversal
normal stress is not significant (i.e. σ3≈0); and the electrodes are either continuous or inter-digitals with
symmetric polarization, i.e. E1=E2≈0, such as the M2814-P1 PZT used in the experiments. The electrical
field is assumed to evolve linearly through the thickness of a given piezoelectric layer. By using Eq. (3),
the introduced electrical-mechanical coupling naturally fulfils the Gauss law.
3756 PROCEEDINGS OF ISMA2014 INCLUDING USD2014
hss
d
ed
C
eCe
sE3
2
3
1
11
2
33
33
E
33
33
E
13
31
33
ϕ∆−
∂
ε∂+
∂
ε∂
−
−
−=
ε
ε
(3)
3.4 Constitutive Equations
A piezoelectric active lamina constitutive equation is written as Eq. (4) or in reduced form Eq. (5) using
the e-form constitutive equations for a piezoelectric material with kinematic and electrical assumptions.
+−−
+
+
−−−−
−−−−
=
3
13
23
12
22
11
11
2
33
33
33
3313
31
33
3313
31
11
2
15
44
11
2
15
44
66
33
3313
31
33
2
13
22
33
2
13
12
33
3313
31
33
2
13
12
33
2
13
11
3
13
23
12
22
11
000
00000
00000
00000
000
000
E
d
ed
C
eCe
C
eCe
d
eC
d
eC
C
C
eCe
C
CC
C
CC
C
eCe
C
CC
C
CC
D
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
γ
γ
γ
ε
ε
τ
τ
τ
σ
σ
ε
ε
(4)
γ
ε
−
=
τ
σ
3
offplane
plane
s
t
b
3
offplane
plane
Ed0e
0C0
e0C
D (5)
3.5 Finite Element Equations
Using the Hermite serendipity shape functions ϕn [17], the displacements, rotations and electrical voltages
are calculated based on nodal values using the expressions in Eq. (6).
nnonnoinni uu ϕφϕθφθφ ˆ,ˆ,ˆ === (6)
Using these expressions and the strains and electrical fields, Eqs. (7) are derived.
uBsB
BsB
1s30s
1b30b
+
+=ε
, uBsˆBE 130 ϕϕ +ϕ=
(7)
The variational equilibrium equation of a single element is found in Eq. (8), where U is the volume
integration over the element of the specific electric-mechanical enthalpy, also called Gibbs’ piezoelectric
energy, given by Eq. (9) and P is the work from the external loads.
(8)
(9)
Using the simplification matrices B from Eq. (7), and the constitutive equation; the final finite elemental
equilibrium equations main be written as Eq. (10).
0PU =δ+δ=Πδ
∫Ω ⋅δ−σ⋅δε=δ DEU
STRUCTURAL HEALTH MONITORING 3757
QKuK
FKuK
u
uuu
=ϕ⋅+⋅
=ϕ⋅+⋅
ϕϕϕ
ϕ
(10)
Where the Kuu, Kϕu, Kuϕ and Kϕϕ matrixes were obtained using the hypothesis of a parabolic distribution
of off-plane distortions and the common development for finite elements.
As the final finite element was implemented within AbaqusTM UEL, and modal and frequency analysis
solvers were used in the solution phase, with the external forces F and Q taken to be concentrated nodal
forces.
Γ= ]F[F , Γ= ]Q[Q (11)
4 Vibration-Based Metrics
Different modal parameters can be used in order to identify the damage in the structure, such as resonance
frequencies, amplitudes, phases and vibration modes. These parameters must be chosen taking into
account several factors, such as the type of analysis used, previously known experimental data of the
structure, the type of sensors attached to the structure, as well as their location and the type and extent of
damage, which is required to be detected. Hence, in the present work, different metrics were compared
based on FRFs magnitude and frequency.
Maia et al. [25] presented a metric that use the FRF curves differences between two FRFs, which are
measured at specific positions. This metric will be used in order to determine the influence of the MFCs in
the free-free vibration analysis. This method can be defined as:
( ) ( ) ( )ωαωαωα D
ki
H
kiik −=∆ (12)
If more than one frequency and force are considered, the index is the sum of the damage indices from each
frequency and force. The researchers divided by the sum of the FRF of the healthy structure in order to
obtain a ratio rather than an absolute value. This method can be defined as:
( )
( )∑∑
∑∑∆
=
ω
ω
ωα
ωα
k
H
ki
k
ki
iMSFRF _ (13)
where the superscripts H and D represent the healthy and damaged structures, respectively, the subscripts i
and k denote the location of measure and force, respectively. α(ω) denotes the frequency response
function, and ω denotes the frequency range. The D expression returns value “zero”, if there is no
variation in the structural dynamic behaviour.
Silva et al. [26] showed a damage metric chart obtained by frequency response from input-output data.
The damage metric is an index based on the root-mean-square deviation (RMSD). This feature is
computed with data in the frequency domain. This damage index is used for electrical impedance signal,
but in this present work, it is adapted in order to use in vibration analysis and investigated range of
frequency. So, this metric can be defined as:
( ) ( )[ ]
∑−
=ω
ωαωα
nMFRF
D
ki
H
ki
i
2
_ (14)
Where n is the number of frequency lines. These values once collected for different sensor/actuator pairs
can roughly quantify the amount of damage in a structure. The D expression returns values greater than
zero if any variation in the structural response occurs, and D will return “zero”, if there is no damage in
the structure.
Zang et al. [27] presented the global shape correlation function (GAC) and global amplitude correlation
function (GSC) for structural health monitoring. Similar to the definitions in [27], it can be defined as:
3758 PROCEEDINGS OF ISMA2014 INCLUDING USD2014
( )[ ] ( )[ ]
( )[ ] ( )[ ]( ) ( )[ ] ( )[ ]( )ωαωαωαωα
ωαωα
D
ki
TD
ki
H
ki
TH
ki
D
ki
TH
ki
iGAC⋅⋅⋅
⋅=
2
(15)
∑=ω
ii GACFRFGACFRF __ (16)
( )[ ] ( )[ ]
( )[ ] ( )[ ]( ) ( )[ ] ( )[ ]( )ωαωαωαωα
ωαωα
D
ki
TD
ki
H
ki
TH
ki
D
ki
TH
ki
iGSC⋅+⋅
⋅⋅=
2 (17)
∑=ω
ii GSCFRFGSCFRF __ (18)
Where the superscript T is a transpose column vector, Δω is the frequency increment between
measurement points. ω1 is the lower frequency and ω2 is the upper frequency of the range of interest.
Based on Eq. (15) and Eq. (17), it can be seen that GACi and GSCi are a real-valued function of frequency
between zero and unity. Also, the shape correlation coefficient is sensitive to mode shape differences but
not to relative scales. On the other hand, the amplitude correlation coefficient uses damaged response
amplitudes. Moreover, The FRF_GACi and FRF_GSCi will be a real constant between zero and unity to
indicate total/zero change of structural responses [27].
Prada et al. [28] presented metrics in order to compare the normalized FRFs magnitudes in specific
frequencies: the change in measured ratio metric (CMRM) and the transmissibility ratio metric (TRM).
These metrics can be defined as:
2
1_
sensor
D
i
H
sensor
D
i
H
iCMRMFRF
=
α
ϕα
ϕ
α
ϕα
ϕ
(19)
2
1_
sensor
D
i
sensor
D
i
iTRMFRF
=
α
ϕ
α
ϕ
(20)
Where φ is the natural frequency of the structure. The Eq. (19) compares the ratio between two different
sensors. Eq. (20) uses the transmissibility ratio between the normalized magnitudes of the FRF of a given
frequency obtained from two different sensors for a given parameter. This approach does not require
previously known data, but requires more sensors to work. These sets of expressions returns values “1”, if
there is no variation in the structural behaviour, but they will return other value, if any variation occurs.
5 Results and Discussion
The feasibility of using vibration-based NDT for damage identification in laminated composites is
assessed by comparing the experimental results for both healthy and damaged structure. Also, different
STRUCTURAL HEALTH MONITORING 3759
types of damage were considered. Moreover, special attention is paid to the relation between the damage
metrics. Figures 6 and 7 show the experimental and numerical FRFs using accelerometers and
piezoelectric sensors for all measured points. Indeed, it is difficult to identify the damage by visual
inspection of the FRFs only; so it is necessary to introduce metrics in order to identify the presence or not
of the damage.
(a) (b)
Figure 6: FRFs obtained for (a) Plate 1 and (b) Plate 2 by using accelerometers experimental data and
MFCs experimental and computational data
(a) (b)
Figure 7: FRFs obtained for (a) Plate 1 and (b) Plate 3 by using accelerometers experimental data and
MFCs experimental and computational data
3760 PROCEEDINGS OF ISMA2014 INCLUDING USD2014
Table 1 shows the different resonance frequencies measured by accelerometers and piezoelectric
transducers experimentally and just piezoelectric transducers computationally for health and damaged
composite plates. First, it can be observed that the values obtained for the different types of damage do not
exhibit large changes. This fact is associated to the small magnitude of the exciting pulse loading, which
was selected to avoid that the structures would go in a non-linear regime, making the resonance
frequencies remain practically unaltered. Therefore, an SHM metric, which takes into account only the
variation in the frequencies, might not be the best strategy for this type of damage. However, when it was
compared the intact structure (Plate 1) to the damaged by impact loading (Plate 3), it was possible to
observe significant differences between the second and third modes. This is because the presence of
damage changes the stiffness of the structure.
ω1 [Hz] ω2 [Hz] ω3 [Hz] ω4 [Hz] ω5 [Hz] ω6 [Hz]
Position Mode type /
Measure
1st
torsion
1st
flexural
2nd
torsion
2nd
flexural
3rd
torsion
3rd
flexural
Plate 1
H11
AExp 61.5 153.8 163.8 226.0 254.8 333.0
PExp 61.7 154.8 165.3 226.0 255.0 336.0
PComp 56.5 158.4 169.9 244.4 268.4 332.8
H12
AExp 61.2 153.8 163.3 226.0 255.5 333.0
PExp 62.0 154.8 163.5 226.3 255.8 334.8
PComp 56.5 158.4 169.9 244.4 268.4 332.8
H13
AExp 61.2 153.8 163.8 226.3 254.3 333.0
PExp 61.7 154.8 165.0 226.3 255.3 335.3
PComp 56.5 158.4 169.9 244.9 268.4 332.8
H14
AExp 61.5 153.8 163.3 226.3 254.5 333.0
PExp 62.0 154.8 163.8 226.3 255.0 335.3
PComp 56.5 158.4 169.9 244.9 268.4 332.8
Plate 2
H11
AExp 60.5 149.5 161.0 224.5 253.3 334.8
PExp 61.2 150.8 162.8 224.8 253.8 330.8
PComp 56.5 158.4 169.4 241.4 268.4 331.8
H12
AExp 60.2 149.8 160.8 224.5 253.8 328.5
PExp 61.0 150.5 161.3 225.0 254.3 328.5
PComp 56.5 158.4 169.4 240.9 268.4 331.8
H13
AExp 60.2 149.5 161.0 224.8 252.5 334.8
PExp 60.7 150.5 162.3 225.0 253.8 337.5
PComp 56.5 158.4 169.4 241.4 268.4 332.3
H14
AExp 60.5 149.8 160.8 224.8 252.8 333.5
PExp 60.7 150.5 160.8 225.0 253.8 330.0
PComp 56.5 158.4 169.4 241.4 268.4 331.8
Plate 3
H11 AExp 60.5 150.0 130.5 225.5 251.8 327.5
PExp 60.5 151.8 132.3 225.5 252.0 331.3
H12 AExp 60.2 149.8 130.5 225.8 252.5 327.8
PExp 61.0 150.5 132.0 225.8 252.5 330.3
H13 AExp 60.2 150.3 130.5 226.0 251.3 327.5
PExp 60.7 151.5 132.0 225.8 252.0 330.5
H14 AExp 60.5 149.8 130.5 225.8 251.5 327.8
PExp 61.0 150.5 132.0 225.8 252.0 330.8
* Subscripts Exp. and Comp. are experimental and numerical data, respectively.
Table 1: Experimental and numerical resonances frequencies
Furthermore, one of the first conclusions, which can be obtained from this data, is that the simulation of
damage in the structure by drilling a hole cannot be representative for the case of stiffness degradation of
the material. In fact, this damage does not change the total mass such as debonding of layers in composite
materials or degradation of the structural resistance due to aging. However, the impact damage brings
about changes in the dynamic behaviour. As observed from the FRFs (Fig.6 and 7 and Table 1), it is very
STRUCTURAL HEALTH MONITORING 3761
complicated to identify the damage in the composite plates, because it depends on the size and location of
the damage, as well as the interest frequency range and the mode shape. On the other side, the FRF is
desirable from the viewpoint of applications for SHM systems, because structural FRFs are sensitive to
small changes and damage in a structure. To quantify this sensitivity, a damage indicator was used in
order to calculate the difference in the FRF responses between health (intact) and damaged structures.
Using the data from the FRFs, both numerical and experimental, tables 2 to 4 were obtained using the
calculated damage metrics shown previously. Different metrics based on the magnitude of the amplitude
of the FRFs in specific frequencies were calculated using relations between the response from either
sensors or both. As the numerical analysis was done with zero damping, the magnitudes at the resonance
frequencies may go up to infinite. As such, for the numerical case, the chosen frequencies are close to, but
not coinciding with the resonance peaks. Only the real part of the signal is analysed, because it is more
sensitive to structural modifications than the imaginary part. This last term is dominated by capacitive
response of the sensor and, therefore, it is less sensitive to structural damage effect [24].
Damage Position Measure FRF_MS FRF_M FRF_GAC FRF_GSC
Centre
Hole
H11
AExp. 0.5428 11.2756 0.3303 0.5747
PExp. 0.3759 1.3747 0.5630 0.7483
PComp. 0.7953 4.1464 0.0459 0.1983
H12
AExp. 0.5411 11.0456 0.3353 0.5789
PExp. 0.4687 1.4727 0.4708 0.6822
PComp. 0.7868 4.1474 0.0452 0.1969
H13
AExp. 0.4466 11.0403 0.4120 0.6413
PExp. 0.4514 1.4345 0.4806 0.6877
PComp. 0.7871 4.7066 0.0472 0.2011
H14
AExp. 0.5353 10.5568 0.3613 0.6004
PExp. 0.4994 1.4916 0.4753 0.6763
PComp. 0.7776 4.7079 0.0462 0.1992
Impact
H11 AExp. 0.9545 15.2700 0.0664 0.2573
PExp. 0.5833 1.5647 0.4327 0.6576
H12 AExp. 0.9260 14.0921 0.0932 0.3053
PExp. 0.6985 1.5303 0.3416 0.5823
H13 AExp. 0.7142 14.9227 0.1365 0.3684
PExp. 0.6641 1.6666 0.2670 0.5167
H14 AExp. 0.8743 13.7689 0.0983 0.3134
PExp. 0.6928 1.6112 0.2828 0.5318
Table 2: Damage indicators for different types of damaged and sensors position
Table 2 shows that the metrics are sensitive to different types of damage. As expected, the impact damage
is more severe than the centre hole. This is probably due to the fact that the damage by low-velocity
impact causes a higher changes in the stiffness of the composite plates. In fact, values of FRF_MS and
FRF_M are “zero” for healthy state while those for damaged states are greater than “zero”. However,
values of FRF_GAC and FRF_GSC are near unity for healthy state while those for damaged states are
sharply reduced. Clearly, damage indicators are sensitive to damaged states and they can be used for
damage identification purposes in structural health monitoring systems. Furthermore, all damage metrics
present in table 2 can be presented in a graph in order to show the damage variation for each frequency
value.
Based on tables 3 and 4, it can be concluded that metrics, which use data from more than one sensor, were
more reliable. These metrics, as the other, are sensitive to different types of damage. As expected, the
impact damage is more severe than the centre hole. Table 4 shows that there is an advantage when it does
not need previously known data (healthy structure). This metric relates the transmissibility between the
sensors.
3762 PROCEEDINGS OF ISMA2014 INCLUDING USD2014
Comparing the numerical and experimental results, the differences in the damage metrics can be verified.
This difference can be explained because the numerical simulations did not use a damping model. Thus,
the FRFs present different orders of magnitude. Indeed, it presents the same behaviour for both the
experimental and numerical results.
Damage Position Measure ω1 [Hz] ω2 [Hz] ω3 [Hz] ω4 [Hz] ω5 [Hz] ω6 [Hz]
Centre
Hole
H11 – H12
AExp. 0.7767 0.6911 1.354 1.0432 1.1658 1.5444
PExp. 1.6440 0.8432 1.0732 0.9555 1.0802 2.1662
PComp. 0.9999 1.0004 0.8279 2.2417 1.0009 1.5680
H11 – H13
AExp. 0.7914 0.9850 1.0409 0.9677 1.4731 0.9550
PExp. 0.7791 0.8340 0.4602 0.9457 1.2815 1.3949
PComp. 1.0017 0.9996 1.0361 2.2700 1.0052 1.8398
H11 – H14
AExp. 0.8344 0.7648 1.3985 0.9587 1.3586 1.4195
PExp. 0.1758 1.0184 0.0940 15.9357 1.2191 4.4862
PComp. 1.0042 1.0003 0.8267 0.5661 1.0039 0.8343
Impact
Loading
H11 – H12 AExp. 0.8189 0.7877 1.0143 1.0011 1.0844 1.1634
PExp. 0.4411 2.4198 0.5796 1.0646 1.0470 1.2494
H11 – H13 AExp. 0.8162 1.1109 1.1447 0.9764 1.2133 1.0023
PExp. 6.4325 2.3616 0.5008 1.0081 1.1137 1.1152
H11 – H14 AExp. 0.8151 1.0223 1.2040 0.9601 1.0835 1.2099
PExp. 2.3104 1.8590 0.7283 0.9403 1.0758 1.0764
Table 3: FRF_CMRM damage indicator
Damage Position Measure ω1 [Hz] ω2 [Hz] ω3 [Hz] ω4 [Hz] ω5 [Hz] ω6 [Hz]
Centre
Hole
H11 – H12
AExp. 0.9935 1.2203 0.7283 0.9800 0.8562 0.2321
PExp. 0.1987 1.0841 0.4038 1.0630 1.0508 0.2850
PComp. 1.1355 1.1399 1.1907 0.9939 1.1434 0.8361
H11 – H13
AExp. 1.1503 1.1212 1.1131 0.9993 1.0769 1.0169
PExp. 0.5383 1.0591 0.7789 1.1346 0.8491 0.8817
PComp. 0.9992 0.9968 0.9905 0.8989 1.0134 0.7914
H11 – H14
AExp. 0.9588 1.3314 0.8035 0.9912 0.7494 0.2334
PExp. 0.7482 0.9975 6.2569 0.0624 0.9372 0.4941
PComp. 1.1325 1.1390 1.1915 1.1063 1.1343 1.2656
Impact
Loading
H11 – H12 AExp. 0.9422 1.0707 0.9726 1.0212 0.9204 0.3081
PExp. 0.7404 0.3777 0.7477 0.9541 1.0841 0.4941
H11 – H13 AExp. 1.1154 0.9941 1.0122 0.9904 1.3075 0.9689
PExp. 0.0652 0.3740 0.7159 1.0644 0.9770 1.1028
H11 – H14 AExp. 0.9814 0.9960 0.9333 0.9897 0.9397 0.2738
PExp. 0.0570 0.5465 0.8078 1.0571 0.9837 0.6805
Table 4: FRF_TRM damage indicator
6 Conclusions
Different metrics are used to identify damage in composite plates by monitoring the vibration response of
the structure. Accelerometers and piezoelectric transducers are used for data acquisition. The analyses
were carried out to obtain modal parameters of both an undamaged and a damaged specimen of a
nominally identical structure. Damaged metrics were compered. The metrics were calculated for data
retrieved from each sensor alone and by the ratio of the data retrieved by each sensor. Experimental and
numerical analyses were presented. For the numerical analyses, a non-linear shell finite element for
piezoelectric active composite was implemented in Abaqus via UEL subroutine. The analyses were
performed to obtain modal parameters of both healthy and damaged structures, simulated in the structure
STRUCTURAL HEALTH MONITORING 3763
by drilling a centre hole. The experimental and numerical results showed that the vibration-based damage
identification methods combined to the metrics can be used in SHM systems. This method has the
advantages that it can be to implement and has low cost. Also, it gives information on the overall
condition of the system. The experimental analyses combined to the damage metrics diagnose if the
structure is damaged or not. These metrics show that the impact damage is more severe than the centre
hole. Finally, it is possible to conclude that there is a great future perspective for the application of
vibration-based methods by using MFCs sensors on SHM systems for composite structures.
Acknowledgements
The authors would like to thank São Paulo Research Foundation (FAPESP process number: 2012/01047-
8), as well as Coordination for the Improvement of the Higher Level Personnel (CAPES process number:
011214/2013-09), National Council for Scientific and Technological Development (CNPq) and
FAPEMIG for partially funding the present research work through the INCT-EIE. The authors also would
like to thank Navy Technological Centre (CTM – Brazil) for manufacturing specimens and Prof.
Reginaldo Teixeira Coelho (University of Sao Paulo) for kindly providing the use of the AbaqusTM
license.
References
[1] O. Salawu, Detection of structural damage through changes in frequency: a review, Engineering
Structures, Vol. 19, No. 9, Elsevier Science (1997), pp. 718-723.
[2] S.W. Doebling, C.R. Farrar, M.B. Prime, A sumary review of vibration-based damage identification
methods, Shock and Vibration Digest, Vol. 30, No. 2, Sage Publications (1998), pp. 91-105.
[3] Y. Zou, L. Tong, G. Steven, Vibration-based model-dependent damage (delamination) identification
and health monitoring for composite structures – A review, Journal of Sound and Vibration, Vol.
230, No. 2, Academic Press (2000), pp. 357-378.
[4] E.P. Carden, P. Fanning, Vibration based condition monitoring: A review, Structural Health
Monitoring, Vol. 3, No. 4, Sage Publication (2004), pp. 355-377.
[5] D. Montalvão, N.M.M. Maia, A.M.R Ribeiro, A review of vibration-based structural health
monitoring with special emphasis on composite materials, The Shock and Vibration Digest, Vol. 38,
No. 4, Sage Publications (2006), pp. 295-324.
[6] C.C. Ciang, J-R. Lee, H-J Bang, Structural health monitoring for a wind turbine system: A review of
damage detection methods, Measurement Science and Technology, Vol. 19, No. 12, IOP Science
(2008), pp. 122001.
[7] K. Worden, C.R. Farrar, J. Haywood, M. Todd, A review of nonlinear dynamics applications to
structural health monitoring, Structural Control and Health Monitoring, Vol. 15, No. 4, John Wiley
& Sons (2008), pp. 540-567.
[8] G. Huang, F. Song, X. Wang, Quantitative modeling of coupled piezo-elastodynamic behavior of
piezoelectric actuators bonded to an elastic medium for structural health monitoring: A review,
Sensors, Vol. 10, No. 4, MDPI AG (2010), pp. 3681-3702.
[9] W. Fan, P. Qiao, Vibration-based damage identification methods: A review and comparative study,
Structural Health Monitoring, Vol. 10, No. 1, Sage Publications (2010), pp. 83-111.
[10] M.A. Pérez, L. Gil, S. Oller, Impact damage identification in composite laminates using vibration
testing, Composite Structures, Vol. 108, Elsevier Science (2014), pp. 267-276.
[11] R. Medeiros, M. Sartorato, M.L. Ribeiro, D. Vandepitte, V. Tita, Numerical and experimental
analyses about SHM metrics using piezoelectric materials, In P. Sas, D. Moens, S. Jonckheere,
3764 PROCEEDINGS OF ISMA2014 INCLUDING USD2014
editors, Proceedings of the International Conference on Noise and Vibration Engineering
ISMA2012-USD2012, Leuven, Belgium, 2012 September 17-19, pp. 3285-3300.
[12] R. Medeiros, M.L. Ribeiro, M. Sartorato, G. Marinucci, V. Tita, Computational simulation using
PZT as sensor elements for damage detection on impacted composite cylinders, In J.S.O. Fonseca,
R.J. Marczak, editors, Proceedings of the 1st International Symposium on Solid Mechanics –
MecSol2013, Porto Alegre, Rio Grande do Sul, Brazil, 2013 April 18-19, pp. 1-11.
[13] R. Medeiros, M. Sartorato, F.D. Marques, D. Vandepitte, V. Tita, Vibration-Based damage
identification applied for composite plate: Experimental analyses, In G. Ribatski, M.A. Trindade,
editors, Proceedings of the 22nd International Congress of Mechanical Engineering – COBEM2013,
Ribeirão Preto, São Paulo, Brazil, 2013 November 3-7, pp 1-12.
[14] R. Medeiros, E.N. Borges, V. Tita, Experimental analyses of metal-composite bonded joints: damage
identification, Applied Adhesion Science, Vol. 2, No. 1, Spring Open Journal (2014), pp. 1-17.
[15] M. Hajianmaleki, S. Mohamad, S. Qatu, Vibrations of straight and curved composite beams: A
review, Composite Structures, Vol. 100, Elsevier Science (2013), pp. 218-232
[16] L. Malgaca, Integration of active vibration control methods with finite element models of smart
laminated composite structures, Composite Structures, Vol. 92, No. 7, Elsevier Science (2010), pp.
1651-1663.
[17] J.N. Reddy, O.O. Ochoa, Finite Element Analysis of Composite Laminates, Kluwer Academic Print
on Demand, 3rd Edition, (1996).
[18] J.K. Nath, S. Kapuria, Coupled efficient layerwise and smeared third order theories for vibration of
smart piezolaminated cylindrical shells, Composite Structures, Vol. 94, No. 5, Elsevier Science
(2012), pp. 1886-1899.
[19] M.A. Neto, R.P. Leal, W. Yu, A triangular finite element with drilling degrees of freedom for static
and dynamics analysis of smart laminated structures, Computers and Structures, Vol. 108-109,
Elsevier Science (2012), pp. 61-74.
[20] U. Gabbert, D. Marinkovic, H. Köppe, Accurate modeling of the electric field within piezoelectric
layers for active composite structures, Journal for Intelligent Material Systems and Structures, Vol.
18, No. 5, Sage Publications (2007), pp. 503-514.
[21] H. Nasser, A. Deraemaeker, S. Belouettar, Electric field distribution in macro fiber composite using
interdigitated electrodes, Advanced Materials Research, Vol. 47-50, Scientific.Net (2008), pp. 1173-
1176.
[22] M.L. Ribeiro, V. Tita, D.Vandepitte, A new damage model for composite laminates, Composite
Structures, Vol. 94 No. 2, Elsevier Science (2012), pp. 635-642.
[23] V. Tita, J. de Carvalho, D. Vandepitte, Failure analysis of low velocity impact on thin composite
laminates: Experimental and numerical approaches, Composite Structures, Vol. 83 No. 4, Elsevier
Science (2008), pp. 413-428.
[24] R. Medeiros, Development of a computational methodology for determining effective coefficients of
the smart composites. Master’s thesis, São Carlos School of Engineering, University of São Paulo,
São Carlos, São Paulo, Brazil, (2012).
[25] N.M.M. Maia, J.M.M. Silva, E.A. M. Almas, R.P.C. Sampaio, Damage detection in structures: From
mode shape to frequency response function methods, Mechanical Systems and Signal Processing,
Vol. 17, No. 3, Elsevier Science (2003), pp. 489-498.
[26] S. Silva, M. Dias Júnior, V. Lopes Junior, Structural health monitoring in smart structures through
time series analysis, Structural Health Monitoring, Vol. 7, No. 3, Sage Publications (2008), pp. 231-
244.
[27] C. Zang, M.I. Friswell, M. Imregun, Structural health monitoring and damage assessment using
measured FRFs from multiples sensors, part I: The indicator of correlation criteria, Key
Engineering Materials, Vol. 245-246, Trans Tech Publications (2003), pp.131-140.
[28] M.A. Prada, J. Toivola, J. Kullaa, J. Hollmén, Three-way analysis of structural health monitoring
data, Neurocomputing, Vol 80, Elsevier Science (2012), pp. 119-128.
STRUCTURAL HEALTH MONITORING 3765
3766 PROCEEDINGS OF ISMA2014 INCLUDING USD2014