Journal of Composite
Materials
http://jcm.sagepub.com/
Dynamics-based Damage Detection of Composite Laminated Beams using Contact
and Noncontact Measurement Systems
Pizhong Qiao, Wahyu Lestari, Mitali G. Shah and Jialai Wang
Journal of Composite Materials 2007 41: 1217
DOI: 10.1177/0021998306067306
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Dynamics-based Damage Detection
of Composite Laminated Beams
using Contact and Noncontact
Measurement Systems
PIZHONG QIAO*
Department of Civil and Environmental Engineering, Washington State University
Pullman, WA 99164-2910, USA
WAHYU LESTARI
Department of Aerospace Engineering, Embry-Riddle Aeronautical University
Prescott, AZ 86301, USA
MITALI G. SHAH
Department of Civil Engineering, The University of Akron
Akron, OH 44325-3905, USA
JIALAI WANG
Department of Civil, Construction, and Environmental Engineering
The University of Alabama, Tuscaloosa, Alabama 35487-0205, USA
ABSTRACT: A reliable and effective damage detection technique is one of the
significant tools to maintain the safety and integrity of structures. A dynamic
response offers viable information for the identification of damage in the structures.
However, the performance of such dynamics-based damage detection depends on the
quality of measured data and the effectiveness of data processing algorithms. In this
article, the experimentally measured data of two sensor systems, i.e., a surfacebonded piezoelectric sensor system and a noncontact scanning laser vibrometer
(SLV) system, are studied, and their effectiveness in damage identification of
composite laminated beams is compared. Three dynamics-based damage detection
algorithms are evaluated using the data acquired from these two measurement
systems. The curvature mode shape is selected as a parameter to locate damage due
to its sensitivity. The piezoelectric sensors directly acquire the curvature mode shapes
of the structures, while the SLV measures the displacement mode shapes. The
difference in the measurement characteristics of these systems and their influence
in the damage identification performance are addressed. The beam specimens
*Author to whom correspondence should be addressed. E-mail: qiao@wsu.edu
Figures 1–4, 7–9, 12 and 13 appear in color online: http://jcm.sagepub.com
Journal of COMPOSITE MATERIALS, Vol. 41, No. 10/2007
0021-9983/07/10 1217–36 $10.00/0
DOI: 10.1177/0021998306067306
ß 2007 SAGE Publications
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ET AL.
are made of E-glass/epoxy composites, and several different types of damages
are introduced in the beams (i.e., delaminations, and impact and saw-cut damages).
This study provides a thorough assessment of the two sensor systems in damage
detection of composite laminated beams and verifies the validity of dynamics-based
damage detection methodology in locating the local defects in composite structures.
KEY WORDS: damage detection, dynamic response, curvature mode shapes,
scanning laser vibrometer, piezoelectric sensors, delamination, laminated beams.
INTRODUCTION
DAMAGE DETECTION has gained increasing attention from the
scientific community because unpredicted failure causes major economic loss and
casualties. Higher operational loads, greater complexity of design (e.g., structures made
of composite and hybrid materials), and longer lifetime periods imposed on civil,
mechanical, and aerospace structures make it increasingly important to monitor the
health of these structures. The availability of practical and robust non-destructive
evaluation techniques for damage detection is critical to ensure acceptable performance
of structures in terms of serviceability, reliability, durability, and prevention of
catastrophic failure.
Dynamic responses, which in many cases can be obtained easily, offer damage
information such as the location and severity of the damage. The performance of the
dynamics-based damage identification strongly depends on the quality of the measured
dynamic responses. In general, the damage in the structure is identified by comparing
the dynamic responses of original (pristine) structures with those of damaged
structures or those after a certain period of time in service. When the original dynamic
response is not available, the comparison can be performed by using the numerical
simulation or mathematical approximation based on the current condition of the
structures.
A review on vibration-based delamination detection methods for composite structures
by Zou et al. [1] discussed several approaches using different dynamic parameters, such as
frequency, damping, and mode shape. The comparative study of various damage detection
methods showed that the modal analysis method in general is global in nature, and it
requires the data of original (or undamaged) structures as the benchmark. Although the
frequency domain method seems cost-effective, it alone is not sufficient for locating
structural damage. However, it can still be used as an indication of the presence of
damage. The time domain method, which is usually in combination with frequency
information, is capable of detecting damage events, both locally and globally, by changing
the input frequencies. The impedance domain method offers a reliable approach, and it is
particularly suitable for detecting planar defects such as delamination. Application of
frequency in damage identification in the form of the response spectrum [2] showed that
the use of vibration at higher frequencies allows the identification of delamination
occurrence in the cantilever composite beams. Although the method can differentiate the
size of delamination, it is unable to determine their quantity. The response spectrum of the
sample was analyzed to infer the presence of delamination by comparing it with the
baseline spectrum of the undamaged structure.
S
TRUCTURAL
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Dynamics-based Damage Detection of Composite Laminated Beams
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Owing to the localized effect of stiffness change at the damage location, curvature mode
shapes have been employed and studied for structural damage identification by many
researchers since it was introduced by Pandey and Biswas [3]. A comparison of the
effectiveness of the curvature mode shape method and frequency response function (FRF)
curvature method as damage detection techniques was investigated by Sampaio et al. [4].
The damage indication parameters are determined by two methods called the ‘mode shape
curvature method’ and the ‘damage index method’. The stiffness change of the damaged
element was modeled as a percentage reduction of the undamaged one. Their results
showed that the FRF curvature method performed well in detecting, locating, and
quantifying damage, especially for a range of frequency before the occurrence of the first
resonance or anti-resonance.
Wahab and Roeck [5] investigated the application of modal curvature (MC) change to
identify various levels of damage in a prestressed concrete bridge, while considering
a currently intact bridge before it was artificially damaged as the reference measurement.
The results confirmed the application of MC in detecting damage in civil engineering
structures. However, MC was found to be more accurate for lower modes, and it was
recommended that the fine measurement grid be used when the higher modes were desired
for damage detection. The experimental study on carbon/epoxy composite laminated
beams carried out by Hamey et al. [6] by using the piezoelectric sensor system provided
information on the efficiency and drawback of several existing damage detection
algorithms (e.g., absolute difference, damage factor, damage index, and FRF curvature
methods). The effects of damage type (i.e., delamination, saw-cut, and impact damages)
and size (i.e., delamination length) were studied as well.
A comparative numerical study of damage identification algorithms applied to a bridge
was performed by Farrar and Jauregui [7]. After benchmarking a finite element (FE)
model against previously measured modal data from a bridge in its undamaged and
damaged conditions, extensive numerical studies were performed to further evaluate
various damage detection techniques, i.e., change in stiffness, damage index, change in
mode curvature, change in uniform load surface (ULS) curvature, and change in
flexibility. In general, all the methods identified the various damage locations correctly
in the case of detecting severe damage like a cut completely through the bottom flange.
But the methods were found to be inconsistent and failed to clearly identify the damage
location when they were applied to less-severe damage cases. Results showed that the
damage index method performed the best and was found to be the most convincing of all
methods. An improved damage index formulation was presented by Kim et al. [8]. Both,
the natural frequency- and mode-shape-based damage detection were developed and
evaluated to locate and estimate the size of damage in structures. A damage index
algorithm to localize and estimate the severity of damage was developed from monitoring
the changes in the modal strain energy, and the required natural frequencies and mode
shapes were generated from the FE models. The frequency-based method was observed to
locate damage with some localization error, whereas the mode-shape-based method was
able to detect damage accurately.
A procedure for locating variability in structural stiffness using only the data
obtained from the damaged structure was introduced by Yoon et al. [9]. Assuming the
original healthy mode shapes are smooth without irregularity and using a curvefitting technique, the original mode shapes were approximated. A structural irregularity
index was generated for each measurement data, and was later averaged over the
obtained modes to increase the sensitivity of the indices. Numerical analysis and
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ET AL.
experimental vibration tests were performed to demonstrate the proposed method, which
produced successful results in detecting the size and location of small, localized stiffness
reduction.
A damage identification approach using the changes in the strain energy based on
measured modal parameters was discussed by Cornwell et al. [10]. This method
requires that the mode shapes before and after damage be known, but the modes need
not be mass-normalized and only a few modes are required. The 1-D strain energy method
could be applied to only beam-type structures; however, a modification in the method
can extend the application to the plate-type structures. This algorithm was found to be
effective in locating areas with a stiffness reduction as low as 10% using relatively few
modes. The strain energy-based damage identification using axial or torsional response
was studied by Duffey et al. [11]. The changes of strain energy in discrete elements of
the structure from the undamaged to damaged states were used as the damage parameter
that was illustrated by numerical simulation and experimental spring–mass systems.
The overall identification results depend strongly upon damage location, damage level,
and the number of modes included.
To minimize the sensitivity of the mode shapes to experimental error, truncation
effects, and selection of mode shapes in damage identification, Zhang and Akhtan [12]
proposed a new deformation parameter – ULS, which is based on the assumption that
a structure is subjected to a uniform loading. Calculation of the ULS that uses the modal
flexibility and measured mode shapes has an averaging effect. This process reduces the
sensitivity of the damage identification method to the truncation effects, experimental
error, and selection of mode shapes. Application of the ULS curvature to 2-D structures
was demonstrated by Wu and Law [13]. The ULS curvature was calculated based on the
Chebyshev polynomial, instead of the central difference method, to reduce the edge
effects. The numerical examples considering different support conditions, measurement
noises, mode truncation, and sensor sparsity were studied to evaluate the effectiveness
of the proposed method. When the modal parameter of healthy structures was
approximated by using the gapped-smoothing method, the results of the numerical
examples revealed that the change in ULS curvature was found to be very sensitive
to local damages and robust to truncation effects. Thus, the combination of the gapped
smoothing with ULS was highly successful in detecting and locating damage in
the structure.
Direct use of the modal flexibility for identification of damage was proposed by
Gao et al. [14], and it was called the damage localization vector (DLV) method.
The technique was based on the determination of a special set of DLVs that have the
property that, when they are applied to the structure as static forces at the sensor locations,
no stress is induced in the damaged elements. The experimental demonstration using the
truss structure indicated that the flexibility-based DLV method could be utilized to detect
and locate damage using a limited number of sensors and truncated modes of the
structure. Lu et al. [15] demonstrated numerically that the changes in flexibility and
flexibility curvature have high sensitivity to closely distributed damages and can be
effectively used for detecting multiple damage locations.
Essentially, the success of damage identifications depends strongly on the quality
and selection of the parameters involved, such as the number of mode shapes, mode
selection, and frequency bandwidth. This article reports a comparative study of the
performance of two measurement systems in providing the dynamic parameters for
structural damage identification of composite laminated beams. One is a non-contact
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Dynamics-based Damage Detection of Composite Laminated Beams
1221
scanning laser vibrometer (SLV) system, and the other utilizes a surface-bonded
piezoelectric (polyvinylidenefluoride, PVDF) sensor array system. While the SLV is very
convenient and efficient in acquiring dynamic responses, it does not have the feasibility
that the piezoelectric sensors can offer to be developed for an onboard sensor system.
On the other hand, the piezoelectric sensor is sensitive to interference and requires
considerable time for employment. The results measured from both sensor systems are
evaluated to identify damage in composite laminated beams with various damage
configurations (i.e., delaminations, saw-cut damage, and impact damage). Three damage
detection algorithms (i.e., gapped-smoothing method (GSM), generalized fractal
dimension (GFD), and strain energy method (SEM)) are used in analyzing the measured
data. The theoretical background of the damage detection algorithms is described briefly,
and the numerical FE analysis is performed to verify the validity of the algorithms
and guide the experimental procedure. The efficiency and effectiveness of the two sensor
systems are examined, and the shortcomings are discussed.
DAMAGE DETECTION ALGORITHMS
The quality of the measurement systems in providing data for damage identification is
evaluated by three newly modified damage detection algorithms. All three approaches use
the curvature mode shapes of the structure as the main parameter to extract the damage
information. The first approach is known as the GSM, which considers damage as a
disturbance in the mode shape that is otherwise a smooth one. The second one is a GFM
[16], developed based on the fractal theory with modifications in the variable. The last one,
SEM, is based on the concept of strain energy, in which the beam bending stiffness and
curvature are interrelated, and the change in mode shapes is associated with the change
of beam bending stiffness due to damage.
The modal parameters obtained from the PVDF sensor system are directly in the form
of curvature mode shapes, and the mode shapes can thus be utilized as the input data to
the damage detection algorithms, whereas the measured results from SLV system are in the
form of displacement mode shapes. Therefore, the required curvature mode shapes are
calculated by the second-order derivatives based on the fourth-order central difference
approximation as
0 ¼
wiþ2 þ 16wiþ1 30wi þ 16wi1 wi2
12h2
ð1Þ
where 0 is the curvature mode shape calculated at the ith grid point; wi is the displacement
measured at node i for a mode j; and h is the distance between the measurement nodes
i and i þ 1, where i denotes the node under observation along the length of the beam.
The curvature mode shapes are then normalized before being further utilized as input for
damage detection algorithms.
Instead of employing the curvature mode shapes individually, a new surface
deformation parameter is constructed based on the measured frequencies and curvature
mode shapes as well as the assumption that the structure is subjected to uniform loading.
Since this parameter is calculated from the collective mode shapes, it has an averaging
effect that makes it less sensitive to mode shape selection and measurement errors.
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ET AL.
The obtained parameter, which was introduced by Zhang and Akhtan [12], is known as
uniform surface loading (ULS). This approach is especially useful to improve the
performance of measured experimental data.
Uniform Load Surface (ULS) Method
Assuming that all degrees of freedom are subjected to a unit load together, the resulting
displacement vector can be obtained by multiplying the flexibility matrix with the loading
vector of the uniform load along the structure. Although it is difficult to achieve this
condition in the actual structure, a linear system approximation of the mode shape under
uniform loading based on the flexibility matrix is valid. For a structural system with
m mode shapes data and n degrees of freedom, the deflection vector U of the structure
under ULS can be defined as
2
f1, 1
6
6 f2, 1
U ¼ fi, j lj ¼ 6 .
4 ..
fn, 1
f1, 2
f2, 2
..
.
..
.
fn, 2
3
9
f1, n 8
1>
>
>
=
< >
f2, n 7
7 1
.. 7 ..
>
>.>
. 5>
: ;
1
fn, n
ð2Þ
with
uðiÞ ¼
n
X
fi, j ¼
m
n
X
r ðiÞ X
r¼1
j¼1
!2r
r ð jÞ
ð3Þ
j¼1
or
U¼FL
ð4Þ
where F is the modal flexibility matrix and L ¼ f1, . . . ,1gT1n is the unit vector representing
the uniform load acting on the structure. Each term in the summation for the deflection
vector u(i) has the corresponding frequency in the denominator, and this results in a rapid
decrease of the higher-mode term-contribution. Hence, the ULS can be well-approximated
by only a few lower-mode terms. Because the technique considering the ULS reduces the
sensitivity of the damage identification to the mode shape choices, such a technique is
adapted in this study to evaluate the location and relative magnitude of damage. In this
study, the mode shapes are in the form of a curvature, and correspondingly the ULS
approximation results are denoted as .
The modal flexibility matrix for a structural system with n degrees of freedom can be
determined by the following expression [12]:
F¼
n
X
r T
r
r¼1
!2r
ð5Þ
where r is the rth normalized mode shape and !r is the corresponding rth natural
frequency. In practice, the modal testing can only yield several low modes. With m modes
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Dynamics-based Damage Detection of Composite Laminated Beams
1223
available from experimental data, the modal flexibility matrix of the structure can be
approximated as
m
X
r Tr ð jÞ
F ¼ fi, j ¼
!2r
r¼1
ð6Þ
in which fi,j describes the modal flexibility at the ith point under the unit load at the point j
and is the summation of the product of the related term from available modes. Hence,
the displacement vector can be obtained by multiplying the flexibility matrix with the
loading vector.
Gapped-Smoothing Method (GSM)
In some cases such as for structures that are already in service for a long period of time,
data of healthy or undamaged structures are rarely available. These data can be
approximated by using a gapped-smoothing technique, where the basic assumption is
that the mode shape of a healthy structure has a smooth surface [17]. Using the mode
shape data of a damaged structure and an interpolation technique with polynomial
approximation, the smooth mode shape surfaces of healthy structures are estimated. In
this study, the ULS of a healthy beam is approximated as a fourth-order polynomial as
ðxÞ ¼ c0 þ c1 x þ c2 x2 þ c3 x3 þ c4 x4
ð7Þ
where the coefficients of the polynomial c0, c1, c2, c3, and c4 can be determined using
the regression analysis technique based on either the numerical or experimental data.
The damage parameter (GSM) based on this approach is calculated as the square of the
difference between the measured data of the damaged structure (measured) and the fitted
value represented the healthy data (GSM) from Equation (7):
GSM ¼ ½measured GSM ðxÞ2
ð8Þ
Generalized Fractal Dimension (GFD) Method
The concept of a fractal curve is based on the principle that, if the ruler length is
reduced by 1/r, then the length of the curve would correspondingly increase to L ¼ rD
multiplied by the original value of length. The power D in the expression is known as
the fractal dimension (FD) of the curve. A regular smooth curve has an FD of one,
while a curve with irregularity will have a FD greater than one. Thus, as the value of D
increases, irregularity in the curve increases, which enables the prediction of the location
of damage. The FD expression given by Katz [18] is stipulated as
FDM ðxÞ ¼
logðnÞ
logðnÞ þ logðdðxi , MÞ=lðxi , MÞÞ
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ð9Þ
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P. QIAO
lðxi , MÞ ¼
M qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
ððxiþj Þ ðxiþj1 ÞÞ2 þ ðxiþj xiþj1 Þ2
ET AL.
ð10Þ
j¼1
M qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
ððxiþj Þ ðxi ÞÞ2 þ ðxiþj xi Þ2
dðxi , MÞ ¼
ð11Þ
1jM
is the average distance between successive
where x ¼ 1/2 (x1 þ xiþM), n ¼ 1/ , and
points. The term M represents the sliding-window dimension length. However, the fractal
dimension technique has the drawback of representing an abnormality in the mode shape
as being more severe near the maximum curvature point as compared to other points
on the mode shape [16]. As a result, a modification to the above-mentioned algorithm
is carried out to produce more accurate results. The modified algorithm defined as GFD
was recently presented by Wang and Qiao [16] as
logðnÞ
logðnÞ þ logðds ðxi , MÞ=ls ðxi , MÞÞ
M qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
ls ðxi , MÞ ¼
ððxiþj Þ ðxiþj1 ÞÞ2 þ S2 ðxiþj xiþj1 Þ2
GFDM ðxÞ ¼
ð12Þ
ð13Þ
j¼1
ds ðxi , MÞ ¼
M qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
ððxiþj Þ ðxi ÞÞ2 þ S2 ðxiþj xi Þ2 :
ð14Þ
1jM
The new S parameter is a scale parameter that enables the GFD to have a multi-scale
feature. As the abnormality in the deformation mode shape is more localized in nature,
the extra peaks aroused at the other parts of the structure are eliminated by choosing
a proper scale S for the deformation abnormality peak. The GFD method receives
prime importance in online data processing because it requires only a small segment of
measured signal to detect the damage and gives a sharp peak at the location of damage.
Strain Energy Method (SEM)
The strain-energy-based damage detection algorithm aims to use the strain energy
changes as a damage indicator for structural health monitoring. As the first step, the strain
energy pertaining to each mode shape for the entire beam is calculated using the following
equation:
1
U¼
2
Z
l
o
2 2
@ w
EI
dx:
@x2
ð15Þ
As @2w/@x2 refers to the curvature of the beam, the above equation can be rewritten as
U¼
1
2
Z
l
EIðÞ2 dx ) U / 2 :
o
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ð16Þ
1225
Dynamics-based Damage Detection of Composite Laminated Beams
Based on the above analogy, we can observe that the strain energy is proportional to the
square of the curvature; thus, the square of the curvature can be used in damage detection,
and it can reflect the change of beam bending stiffness due to damage under the condition
of strain energy continuity along the beam length. Considering the measured curvature
and the resulting GSM approximation, the damage parameter based on the strain energy
approach is defined as
SEM ¼ 2measured ðxÞ2
ð17Þ
where measured is the curvature measured experimentally or obtained numerically; (x) is
the smooth-curve fit of measured using a fourth-order polynomial (Equation (7)). Thus,
SEM enables the use of beam strain energy as an alternative to the curvature for damage
detection.
NUMERICAL ANALYSIS
The numerical FE analysis is conducted to provide insight and understanding of the
structural dynamic behavior of damaged structures and to verify the validity of the abovementioned damage detection algorithms. Dynamic characteristics resulting from
numerical analysis can also be used to guide the experimental study. The modeling of
composite laminated beams and the analysis of dynamic characteristics are performed
using commercial software ANSYS.
The structure was a rectangular beam section of length 0.5588 m (22.0 in.), width
50.8 mm (2 in.), and a thickness of 4.8 mm (0.189 in.). The lamination of the composite
had a [CSM/90(0/90)3]S lay-up configuration with a total of 16 layers (where, CSM refers
to continuous-strand mat). The thickness of the outer layer is about 0.5 mm, while the
thickness of the remaining individual layer is about 0.268 mm (0.0117 in.). The beam was
discretized into 350 elements along the length, 32 elements along the width, and two
elements along the thickness. The beam specimen is modeled using the SOLID46 layered
element, and the material properties of the orthotropic composite are listed in Table 1.
The FE model for a healthy cantilevered beam is shown in Figure 1.
Table 1. Material properties for the E-glass–epoxy composite beam model.
Elastic modulus (E1)
Elastic modulus (E2)
Shear modulus (G12)
Poisson’s ratio (12)
Mass density ()
24.0 GPa
14.2 GPa
2.17 GPa
0.4
2500 kg/m3
Solid 46
0.0508m
0.5588 m
Figure 1. Finite element model of a healthy composite beam.
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ET AL.
0.5588m
(a)
0.3302m
0.0508m
44
56
0.5588m
(b)
0.2540m
0.1016m
38
58
0.5588 m
(c)
0.0508 m
0.3810 m
62
(d)
72
150
0.001 m
0.2794m
0.5588m
(e)
0.0508m
0.1778m
65
75
Figure 2. FE model of damage beams: (a) Delamination A model; (b) Delamination B model; (c) Delamination
C model; (d) Saw-cut damage model; and (e) Impact damage model.
Case Study
A numerical study of dynamic response in composite laminated beams with five
different damage cases is performed based on the numerical modal analysis. The five
damage cases are three delaminations with different sizes or locations, saw-cut, and impact
damages, which correspond to the physical specimens introduced in the experimental
program. The FE models of the beams for all the damage configurations are shown
in Figure 2.
The delamination conditions prevalent in the beam specimens are simulated in the
FE model by using the bilinear LINK10 elements. LINK10 is a 3-D spar element having
the unique feature of a bilinear stiffness matrix resulting in a uniaxial tension-only
(or compression-only) element. The tension-only option is utilized in the FE model, where
the stiffness goes to zero if the element goes into tension, whereas the stiffness is set to
2 GPa when it goes into compression. The opening of the delamination for all the cases
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Dynamics-based Damage Detection of Composite Laminated Beams
SOLID46
Bilinear LINK10
Figure 3. Detail view of the delaminated beam model.
0.5588m
0.1778m
20 40 60
1
2
3
4
65
60 40 20
5
6
Stiffness reduction
7
8
75
Figure 4. Detailed view of stiffness reduction on an impact-damaged beam.
Table 2. Details of the stiffness reduction in an
impact-damaged beam.
Beam section (percentage reduction)
1
2
3
4
5
6
7
8
(0)
(20)
(40)
(60)
(60)
(40)
(20)
(0)
Stiffness, E1 (GPa)
24.00
19.20
14.40
9.60
9.60
14.40
19.20
24.00
was taken as 0.1 mm. An enlarged view of the delaminated area and the arrangement
of the LINK10 element are detailed in Figure 3.
The saw-cut damage is induced in the beam specimen by creating a transverse
notch in the beam. It runs along the beam length from 0.2794 to 0.2804 m. The notch
has a width of around 1.0 mm (0.0394 in.) and is cut to about 50% of the beam
thickness through the width of the beam. The formulation of the saw-cut beam model
remains the same as the delaminated beams with respect to the dimensions, elements
used, and the meshing size adopted. However, the total number of FE elements along the
beam length is 285. The schematic representation of the saw-cut-damaged beam is shown
in Figure 2(d).
The impact damage is modeled by reducing the stiffness of the beam elements gradually
along the beam length in the damaged area. The beam is divided into eight sub-elements
in the area of damage, as highlighted in Figure 4. The longitudinal stiffness (E1) in the
element is reduced in steps of 20% and the stiffness properties for the impact-damaged
beam elements are organized in Table 2. The impact damage ranged from 0.1778
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ET AL.
Table 3. Natural frequencies obtained from the numerical modal analysis.
Specimen
Second mode (Hz)
Third mode (Hz)
Fourth mode (Hz)
62.55
60.63
57.45
59.20
58.15
55.75
160.50
156.22
152.30
155.00
154.10
153.30
315.25
311.10
304.80
310.00
309.90
308.10
Healthy
Delamination A
Delamination B
Delamination C
Saw-cut
Impact
Mode 2
Mode 3
Mode 4
4
(b)
Curvature
Displacement
(a)
2
0
0.2
Mode 2
Mode 3
Mode 4
0.1
0.0
−0.1
−2
0
20
40
60
−0.2
80
0
20
Mode 2
Mode 3
Mode 4
4
2
(d)
60
80
0
0.3
Mode 2
Mode 3
Mode 4
0.2
Curvature
Displacement
(c)
40
Sensor location
Sensor location
0.1
0.0
−0.1
−2
0
20
40
60
−0.2
80
0
20
Sensor location
Mode 2
Mode 3
Mode 4
4
2
(f)
60
0
0.3
80
Mode 2
Mode 3
Mode 4
0.2
Curvature
Displacement
(e)
40
Sensor location
0.1
0.0
−0.1
−2
−0.2
0
20
40
60
Sensor location
80
0
20
40
60
80
Sensor location
Figure 5. Displacement and curvature mode shapes obtained from the numerical analysis: (a) Healthy –
displacement – FE; (b) Healthy – curvature – FE; (c) Delamination A – displacement – FE (44–56);
(d) Delamination A – curvature – FE (44–56); (e) Delamination B – displacement – FE (38–58);
(f) Delamination B – curvature – FE (38–58); (g) Delamination C – displacement – FE (62–72);
(h) Delamination C – curvature – FE (62–72); (i) Saw-cut damage – displacement – FE (150); (j) Saw-cut
damage – curvature – FE (150); (k) Impact damage – displacement – FE (65–75); and (l) Impact damage –
curvature – FE (65–75).
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Dynamics-based Damage Detection of Composite Laminated Beams
(g)
Mode 2
Mode 3
Mode 4
(h)
2
0
Mode 2
Mode 3
Mode 4
0.1
0.0
−0.1
−0.2
−2
0
20
40
60
Sensor location
(i)
−0.3
80
Mode 2
Mode 3
Mode 4
(j)
Curvature
4
Displacement
0.3
0.2
Curvature
Displacement
4
2
0
0
20
40
60
Sensor location
0.4
Mode 2
Mode 3
Mode 4
0.2
0.0
−0.2
−2
0
50
100
150
200
250
0
50
100
Sensor location
(k)
150
200
250
Sensor location
Mode 2
Mode 3
Mode 4
4
2
(l)
0
−2
0.3
Mode 2
Mode 3
Mode 4
0.2
Curvature
Displacement
80
0.1
0.0
−0.1
0
50
100
150
0
Sensor location
50
100
150
Sensor location
Figure 5. Continued.
to 0.2286 m (elements 65–75). The FE mesh used comprises a total of 185 elements along
the beam length as shown in Figure 2(e).
Numerical Results
The natural frequencies obtained from the numerical modal analysis are presented in
Table 3. The curvature mode shapes are obtained by using the central difference derivation
of displacement mode shapes from the numerical modal analysis (Equation (1)). Figure 5
shows the displacement and curvature mode shapes obtained from the numerical analysis,
side by side for each case. The actual locations of damage in terms of node points are given
in parentheses. The damages are hardly visible in the displacement mode shapes, and
only the difference or shift of nodal points are noticeable. While in the curvature mode
shapes, the damage effects on the mode shapes are very discernable by the discontinuity of
the curvature at the boundaries of the damages.
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P. QIAO
ET AL.
UM 1208 (CSM+unidirectional)
C1800 [0/90] cross-ply
Figure 6. Lay-up of composite samples.
4.8mm
0.6096 m
50.8 mm
Figure 7. Dimension of beam specimens.
EXPERIMENTAL PROGRAM
Beam Specimens
The experiment is conducted on six composite laminated beam samples, i.e., one healthy
and five damaged beams. Each test sample was made of E-glass fiber and epoxy resins and
has a [CSM/0(90/0)3]S lay-up for a total of 16 layers as shown in Figure 6. UM 1208
(CSM þ unidirectional) stitched combo layer has a thickness of 0.49 mm (0.0189 in.) for
unidirectional ply and 0.23 mm (0.0087 in.) for CSM ply. The thickness of C1800 is
0.28 mm/ply (0.0117 in.) and 0.56 mm/mat (0.0220 in.). The 16 layers lead to a total
composite thickness of 4.8 mm (0.189 in.). A composite plate is fabricated using a vacuum
bagging process, and it is then cut in the beam samples with dimensions of 0.0508 m (2 in.)
wide and 0.6096 m (24 in.) long as shown in Figure 7. The length of the beam for a
cantilevered condition is 0.5588 m (22 in.). Figure 8 shows the picture of the beam
specimens with different damage types.
As aforementioned, six E-glass–epoxy composite laminated beam specimens are tested
in this study. Experimental modal analysis is first conducted on an intact (healthy) beam
specimen. The intact curvature modes were recorded for reference. To study the effect
of the location and size of different types of damage on the modal parameters, three
delamination damage cases of different length and location (i.e., delamination A,
delamination B and delamination C) as well as saw-cut and impact damages are studied.
The delamination is introduced in the beam by inserting a Teflon film between the second
and third layer of the composite laminate during the manufacturing process of the
composite plate. After curing, the plate is cut into beam samples, and the Teflon film is
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Dynamics-based Damage Detection of Composite Laminated Beams
(a) Delamination C
(b) Delamination B
(c) Delamination A
(d) Impact damage
(e) Saw-cut damage
Figure 8. Specimens with various types of damage.
Table 4. Damage location and size of the specimens.
No.
1
2
3
4
5
Damage position according to
sensor location
Damage type
Damage location from
the fixed end (m)
PVDF
SLV
FE
Delamination A
Delamination B
Delamination C
Saw-cut
Impact
0.3302–0.3810
0.2540–0.3556
0.3810–0.4318
0.2794–0.2804
0.1778–0.2286
11–13
8–12
13–15
9
5–7
37–43
27–39
53–59
48
22–28
44–56
38–58
62–72
150
65–75
pulled out, leaving a debonded area (delamination) in the beam sample between the second
and third layers. For example, the beam with delamination A has a 50.8 mm (2 in.)
delamination beginning at 0.3302 m from the cantilevered end. The saw-cut damage
is introduced at 0.2794 m from the cantilevered end. The depth of the through width
saw-cut is about half the specimen thickness. To simulate impact damage, the beam sample
is impacted in the region of 0.1778–0.2286 m from the supporting end, using the material
testing systems (MTS) machine. Details of all the beam specimens and damage
configurations are summarized in Table 4, and the corresponding specimen geometry
and PVDF sensor locations are also shown in Figure 9.
Sensor Systems
The complexity and sensitivity of damage detection methods depend on the quality of
the measurement of the parameter and also on the sensitivity of that parameter to possible
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P. QIAO
1
(a)
2
3
4
5
6
7
8
9
ET AL.
10 11 12 13 14 15 16 17 18 19
0.3302 m
0.0508 m
0.5588 m
1
(b)
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19
0.1016 m
0.2540 m
0.5588 m
1
(c)
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19
0.3810 m
0.0508 m
0.5588 m
(d)
1
2
3
4
5
6
7
8
9
10 11 12 13 14
15 16 17 18 19
0.001 m
0.2794 m
0.5588 m
(e)
1
2
0.1778 m
3
4
5
6
7
8
9
10 11 12 13 14
15 16 17 18 19
0.0508 m
0.5588 m
Figure 9. Damage configuration and PVDF sensor location in the specimens: (a) Delamination A;
(b) Delamination B; (c) Delamination C; (d) Saw-cut damage; and (e) impact damage.
structural damage. When damage occurs, a structure suffers a change (a decrease in most
cases) in stiffness, and as a consequence, a change is reflected in the dynamic parameters,
such as the frequencies, mode shapes, FRF, etc.
Structural vibration measurements can be conveniently divided into two major types:
(1) discrete point measurements, using an accelerometer or equivalent transducer; and
(2) spatial field measurements, of which speckle pattern interferometry is a modern
example. In this study, two discrete-point measurement-based sensor systems (i.e., PVDF
sensor and SLV) are employed to acquire the dynamic response of the composite beam
samples. The dynamic response obtained from the SLV system is in the form of
displacement mode shapes; whereas the PVDF sensor system directly yields the desired
curvature mode shapes. Piezoelectricity is a phenomenon observed in certain crystal
(e.g., quartz) PZT (lead–zirconate–titanate) ceramic materials, and PVDF (polyvinylidenefluoride) polymer. In both cases, the vibration excitation is generated through
a piezoelectric actuator. The PZT ceramic actuators have the dimensions
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Dynamics-based Damage Detection of Composite Laminated Beams
Sensor
dSPACE
connector
Actuator
Data acquisition
system
Beam
specimen
Power amplifier
Figure 10. Experimental setup for the PVDF sensor system.
of 15 10 0.25 mm, and are attached near the cantilever-supporting location of the
beam.
PVDF SENSOR ARRAY SYSTEM
The PVDF sensor films, from MSI (Measurement Specialties Inc.), are 30 mm
(1.19 in.) in length, 12 mm (0.484 in.) in width, and have a thickness of 28 mm. The beam
sample is divided into 19 sensor locations (Figure 9) to best accommodate the films. Each
point is aligned with the center of the PVDF film during testing. The PVDF sensor
locations are illustrated in Figure 9.
The experiment is first conducted for the intact (undamaged) specimen with the
cantilevered boundary conditions, followed by performing similar tests on damaged beam
specimens. Continuous-sweep sine excitation generated by a waveform generator with a
magnitude of 140 V is run through the PZT actuators to excite the beams, and the
responses are recorded by a dSPACE data acquisition system as time domain responses.
The experimental setup of the dynamic testing is presented in Figure 10. The dynamic
responses are measured by roving the position of the sensor at 19 locations along the beam
length as shown in Figure 9.
The measured time domain data is then post-processed to construct the input data
for modal analysis calculation, which is performed in commercial software ME-Scope.
The curvature mode shapes and the corresponding natural frequencies are acquired
after processing the data in the ME-Scope. This data is then further post-processed
using MATLAB and Microsoft Excel to evaluate the modal parameters and the
aforementioned damage detection algorithms are employed to locate the damage.
The above-mentioned experimental procedure is summarized in the form of a flowchart,
as presented in Figure 11.
SCANNING LASER VIBROMETER (SLV) SYSTEM
On the other hand, SLV is a noncontact measurement technique that has the capability
of handling a large number of measurement points and at the same time eliminates the
problem with wiring management of conventional or surface-bonded sensor systems.
The measurement capabilities of SLV, such as sensitivity, accuracy, and reduced
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1234
P. QIAO
ET AL.
Experimental setup
dSPACE data
acquisition system
Experimentation
Processing data
using MATLAB
Data collection
ME-Scope
Calculation of modal parameters
(natural frequencies and mode shapes)
Employment of damage detection
algorithms
Damage evaluation
Figure 11. Schematic of experimental procedure.
intrusivity, allow such systems to establish themselves as an important diagnostic
instrument in structural health monitoring and damage detection.
A PSV 400 SLV from Polytec is used to obtain the dynamic response, which is later used
for damage detection in the composite laminated beams. The same excitation source and
signal as the vibration testing with the PVDF sensor system are applied in this testing.
Each testing specimen is scanned using almost 530 scanning points. The experimental
setup for laser vibrometry testing is shown in Figure 12.
The PSV 400 measures the 2-D distribution of vibration velocities on the basis of laser
interferometry. The main system components of PSV 400 are controller, junction box,
scanning head, and the data management system. The junction box is the central
connection between the system components and provides the interfaces for peripheral
devices. The scanning head consists of the interferometer, the scanner mirrors to deflect
the laser beam, and a video camera to visualize the measurement object. The measurement
data is digitally recorded in the data management system. The PSV software controls
the data acquisition and offers user-friendly functions to evaluate the measurement data.
The obtained responses are the natural frequencies and the displacement mode shapes.
The curvature mode shapes are calculated by using the central difference method of
Equation (1), similar to the approach applied for the numerical FE analysis.
The SLV sensor system provides the output in the form of displacement mode shapes,
which is sorted to acquire the displacement mode shape pertaining to the centerline of
the beam (Figure 13) and is used in further evaluation. The displacement mode shapes
are further processed using the central difference method (Equation (1)) to arrive at
the curvature mode shapes. The curvature mode shapes derived from the measured
displacement mode shapes are very sensitive to slight measurement discrepancies and
noise. The data shows lots of undulations owing to the local and global errors accumulated
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Dynamics-based Damage Detection of Composite Laminated Beams
(a)
Laser beam
Reference
sensor
Actuator
Beam specimen
PSV400
scanning head
Controller/computer system
(b)
Figure 12. Experimental setup for the SLV sensor system: (a) experimental measurement using the SLV
system and (b) laboratory testing using the SLV system.
in the calculation of the second derivative of displacements. To minimize these calculation
errors, the filtering process of the calculated curvature mode shapes is performed [19].
The Savitzky–Golay smoothing filters, also called digital smoothing polynomial filters or
least-squares smoothing filters, are used to ‘smooth out’ a noisy signal whose frequency
span (without noise) is large. The Savitzky–Golay filters are optimal, i.e., they minimize
the least-squares error in fitting a polynomial to frames of noisy data.
Experimental Results
The extracted modal frequencies of the healthy and damaged composite beams for the
first three bending modes are listed in Table 5. However, as the quality of the first mode
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1236
P. QIAO
(a)
37
0.3302 m
ET AL.
43
0.0508 m
0.5588 m
(b)
27
39
0.2540 m
0.1016 m
0.5588 m
(c)
53
0.3810 m
59
0.0508 m
(d)
48
0.001 m
0.2794 m
0.5588 m
(e)
22
0.1778 m
28
0.0508 m
0.5588 m
Figure 13. Scanning array and damage configurations for the SLV system: (a) Delamination A;
(b) Delamination B; (c) Delamination C; (d) Saw-cut damage; and (e) Impact damage.
Table 5. Natural frequencies obtained from experimental analysis.
PVDF – f (Hz)
SLV – f (Hz)
Specimen type Second mode Third mode Fourth mode Second mode Third mode Fourth mode
Healthy
Delamination A
Delamination B
Delamination C
Saw-cut
Impact
61.75
58.13
55.00
59.10
57.75
59.30
158.20
150.60
148.95
151.63
155.00
152.50
316.90
309.35
302.10
305.15
311.60
308.80
59.00
56.17
53.20
55.75
54.00
56.50
155.20
149.15
146.90
150.30
151.00
149.55
318.25
302.25
297.10
308.60
311.60
305.20
shape obtained from experimental analysis results is not good, the three consecutive mode
shapes starting from the second mode are presented and considered for further analysis
of the results.
The presence of damage or deterioration in the structure causes changes in the natural
frequencies of the structure. The existence of damage in a section of the beam is equivalent
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1237
Dynamics-based Damage Detection of Composite Laminated Beams
(a)
(b)
Mode 2
Mode 3
Mode 4
0.6
0.4
Curvature
Curvature
0.4
Mode 2
Mode 3
Mode 4
0.6
0.2
0.0
−0.2
0.2
0.0
−0.2
0
5
10
15
20
0
5
Sensor location
(c)
20
15
20
15
20
Mode 2
Mode 3
Mode 4
0.6
0.4
0.4
Curvature
Curvature
15
(d)
Mode 2
Mode 3
Mode 4
0.6
10
Sensor location
0.2
0.0
0.2
0.0
−0.2
−0.2
−0.4
0
5
10
15
20
0
5
Sensor location
(e)
(f)
Mode 2
Mode 3
Mode 4
0.6
Mode 2
Mode 3
Mode 4
0.6
0.4
0.4
Curvature
Curvature
10
Sensor location
0.2
0.0
0.2
0.0
−0.2
−0.2
−0.4
0
5
10
Sensor location
15
20
0
5
10
Sensor location
Figure 14. Curvature mode shapes of the specimens obtained from the PVDF sensor system: (a) Healthy –
curvature–PVDF; (b) Delamination A – curvature – PVDF (11–13); (c) Delamination B – curvature – PVDF
(8–12); (d) Delamination C – curvature – PVDF (13–15); (e) Saw-cut – curvature – PVDF (9); and (f) Impact
damage – curvature – PVDF (5–7).
to a reduction in the second moment of area of the beam. This leads to a reduction in the
local bending stiffness at that cross section. The consequence of reduced local bending
stiffness in lowering the values of the natural frequencies in bending is justified by
the results in Table 5. The observation of the results shown in Table 5 indicates that
the natural frequency of the beam decreases with the increase in the damage
(e.g., delamination).
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P. QIAO
(a)
(b)
Mode 2
Mode 3
Mode 4
0.3
Mode 2
Mode 3
Mode 4
0.3
0.2
Curvature
Displacement
0.2
0.1
0.0
ET AL.
0.1
0.0
−0.1
−0.1
−0.2
−0.2
0
(c)
10
20
30
40
50
Sensor location
60
70
(d)
0.2
40
60
0.3
Mode 2
Mode 3
Mode 4
0.2
Curvature
Displacement
20
Sensor location
Mode 2
Mode 3
Mode 4
0.3
0
0.1
0.0
0.1
0.0
−0.1
−0.1
−0.2
−0.2
0
(e)
10
20
30
40
50
Sensor location
60
70
40
60
(f)
Mode 2
Mode 3
Mode 4
0.3
0.2
0.2
Curvature
Displacement
20
Sensor location
Mode 2
Mode 3
Mode 4
0.3
0
0.1
0.0
0.1
0.0
−0.1
−0.1
−0.2
0
10
20
30
40
50
Sensor location
60
70
−0.2
0
20
40
60
Sensor location
Figure 15. Displacement and curvature mode shapes of the specimens obtained from the SLV
measurements and numerical derivation, respectively: (a) Healthy – displacement – SLV; (b) Healthy –
curvature – SLV; (c) Delamination A – displacement – SLV (37–43); (d) Delamination A – curvature – SLV
(37–43); (e) Delamination B – displacement – SLV (27–39); (f) Delamination B – curvature – SLV (27–39);
(g) Delamination C – displacement – SLV (53–59); (h) Delamination C – curvature – SLV (53–59); (i) Saw-cut
damage – displacement – SLV (48); (j) Saw-cut damage – curvature – SLV (48); (k) Impact damage –
displacement – SLV (22–28); and (l) Impact damage – curvature – SLV (22–28).
RESULTS FROM THE PVDF SENSOR SYSTEM
The PVDF sensor system, which has the potential to be implemented as an
efficient, automatic, real-time, and onboard measurement technique, acquires the
curvature mode shapes directly. For comparison, the mode shapes are first normalized
by evaluating their root mean square. Figure 14 shows the curvature mode shapes for
all the testing specimens, i.e., the healthy and the damaged ones. The actual locations of
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Dynamics-based Damage Detection of Composite Laminated Beams
(g)
(h)
Mode 2
Mode 3
Mode 4
0.3
0.2
Curvature
Displacement
0.2
Mode 2
Mode 3
Mode 4
0.3
0.1
0.0
0.1
0.0
−0.1
−0.1
−0.2
−0.2
0
10
20
30
40
50
60
70
0
20
Sensor location
(i)
Mode 2
Mode 3
Mode 4
0.3
0.2
Curvature
Displacement
0.2
60
(j)
Mode 2
Mode 3
Mode 4
0.3
40
Sensor location
0.1
0.0
0.1
0.0
−0.1
−0.1
−0.2
0
10
20
30
40
50
60
−0.2
70
0
20
Sensor location
(k)
Mode 2
Mode 3
Mode 4
0.3
0.2
0.2
Curvature
Displacement
60
(l)
Mode 2
Mode 3
Mode 4
0.3
40
Sensor location
0.1
0.0
0.1
0.0
−0.1
−0.1
−0.2
0
10
20
30
40
50
60
70
−0.2
0
Sensor location
20
40
60
Sensor location
Figure 15. Continued.
the damage, represented by the number of sensor locations, are given in parentheses.
As the curvature mode shapes are the second derivative of the displacement, it is
observed that the curvature mode shapes provide a relatively clear indication of the
presence of damage.
RESULTS FROM THE SCANNING LASER VIBROMETER (SLV) SYSTEM
Both the measured displacement mode shapes and the derived curvature mode
shapes are presented in Figure 15. Again, the actual locations of the damage, represented
by the number of sensor locations (scanning points), are given in parentheses. As shown
in Figure 15, the locations of various damages cannot be proved by simply examining
the displacement mode shapes; whereas they are discernable in the derived curvature
mode shapes. These derived curvature mode shapes from the displacement mode shapes
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1240
(a)
P. QIAO
(b)
1.0
ULS
GSM
1.0
ULS
GSM
0.8
0.6
ULS/GSM
ULS/GSM
0.8
0.4
0.2
0.0
0.6
0.4
0.2
0.0
−0.2
0
20
40
60
−0.2
80
0
20
Sensor location
(c)
ET AL.
0.8
40
60
80
Sensor location
(d)
ULS
GSM
0.6
ULS
GSM
0.5
0.6
ULS/GSM
ULS/GSM
0.4
0.4
0.2
0.3
0.2
0.1
0.0
0.0
−0.2
0
20
40
60
0
80
50
(e)
150
200
250
1.0
ULS
GSM
0.8
ULS/GSM
100
Sensor location
Sensor location
0.6
0.4
0.2
0.0
0
50
100
150
Sensor location
Figure 16. Results of ULS and GSM calculation based on numerical FE analysis: (a) Delamination A – FE
(44–56); (b) Delamination B – FE (38–58); (c) Delamination C – FE (62–72); (d) Saw-cut damage – FE (150);
and (e) Impact damage – FE (65–75).
are later used as inputs in all the aforementioned damage detection algorithms for further
damage evaluation.
APPLICATION OF DAMAGE DETECTION ALGORITHMS
Based on the curvature mode shapes obtained from either the PVDF or SLV sensor
systems, ULS is calculated. In this study, the first three mode shapes beginning from the
second mode (i.e., the second, third, and fourth modes) are considered. Even the damage
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1241
Dynamics-based Damage Detection of Composite Laminated Beams
(a)
(b)
1.0
ULS
GSM
ULS
GSM
0.8
0.6
ULS/GSM
ULS/GSM
0.8
1.0
0.4
0.6
0.4
0.2
0.2
0.0
0.0
0
5
10
15
20
5
Sensor location
(c)
(d)
1.2
1.0
ULS
GSM
10
Sensor location
15
10
15
1.0
ULS
GSM
0.8
ULS/GSM
ULS/GSM
0.8
0.6
0.4
0.2
0.6
0.4
0.2
0.0
0.0
5
10
Sensor location
(e)
5
20
Sensor location
1.0
ULS
GSM
0.8
ULS/GSM
0
15
0.6
0.4
0.2
0.0
0
5
10
15
20
Sensor location
Figure 17. Results of ULS and GSM calculation based on piezoelectric (PVDF) sensor data: (a) Delamination
A – PVDF (11–13); (b) Delamination B – PVDF (8–12); (c) Delamination C – PVDF (13–15); (d) Saw-cut
damage – PVDF (9); and (e) Impact damage – PVDF (5–7).
location can be detected in the experimentally based curvature mode shapes directly
(Figures 14 and 15 for the PVDF and SLV systems, respectively), the damage indications
are not very obvious on the curves and sometimes the exact locations are difficult to
discern. To further facilitate the damage detection effort, damage location is determined
based on the aforementioned ULS technique and the three damage detection algorithms
(i.e., GSM, GFD, and SEM). The detection results based on the numerical data are first
presented, followed by the results using the experimental data. To indicate the validity
of the detection results, the actual locations of damage in terms of sensor points (PVDF),
scanning points (SLV), or node points (FE) are given in parentheses.
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1242
(a)
P. QIAO
(b)
1.0
ULS
GSM
0.6
0.4
0.2
0.0
10
20
30
40
50
Sensor location
60
0.4
0.2
70
0
(d)
1.0
ULS
GSM
0.8
0.6
0.4
10
20
30
40
50
Sensor location
60
70
20
30
40
50
Sensor location
60
70
1.0
ULS
GSM
0.8
ULS/GSM
ULS/GSM
0.6
−0.2
0
0.6
0.4
0.2
0.2
0.0
0.0
−0.2
ULS
GSM
0.0
−0.2
(c)
1.0
0.8
ULS/GSM
ULS/GSM
0.8
ET AL.
−0.2
0
10
20
30
40
50
Sensor location
(e)
70
0
10
1.0
ULS
GSM
0.8
ULS/GSM
60
0.6
0.4
0.2
0.0
−0.2
0
10
20
30
40
50
Sensor location
60
70
Figure 18. Results of ULS and GSM calculation based on SLV system data: (a) Delamination A – SLV (37–43);
(b) Delamination B – SLV (27–39); (c) Delamination C – SLV (53–59); (d) Saw-cut damage – SLV (48); and
(e) Impact damage – SLV (22–28).
Uniform Load Surface (ULS)/Gapped Smoothing Method (GSM)
The results from the GSM based on the numerical FE analysis data, as well as the
approximated ULS, are presented in Figure 16. The results based on the experimental data
from the PVDF sensor and SLV measured data are presented in Figures 17 and 18,
respectively.
The GSM results acquired using the ULS curvatures show the location of damage in
the form of distinct peaks or discontinuities in the curve. However, the results from
experimentally measured data also show multiple peaks at locations other than the actual
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1243
Dynamics-based Damage Detection of Composite Laminated Beams
(a)
(b)
3.0
2.5
2.5
GFD
GFD
2.0
2.0
1.5
1.5
1.0
1.0
0
(c)
10
20
30 40 50 60
Sensor location
70
80
0
90
(d)
2.4
10
20
30
40
50
Sensor location
60
70
4
2.2
3
1.8
GFD
GFD
2.0
1.6
2
1.4
1
1.2
1.0
0.8
0
0
20
40
60
Sensor location
(e)
80
0
50
100
150
200
Sensor location
250
8
GFD
6
4
2
0
0
50
100
150
Sensor location
Figure 19. Results of GFD calculation based on numerical FE analysis data: (a) Delamination A – FE (44–56);
(b) Delamination B – FE (38–58); (c) Delamination C – FE (62–72); (d) Saw-cut damage – FE (150); and
(e) Impact damage – FE (65–75).
damage, which challenges the accuracy and efficiency of the method in determining the
exact location of damage. The results from the piezoelectric (PVDF) sensor have broad
peaks due to the coarse sensor grid. However, it has fewer small undulations in other
places than in the damage location. On the contrary, the results from SLV measurements
have sharp discontinuities, typically at the boundaries of the damages. The undulation at
other places rather than at the damage location is quite significant (about one third of the
peak at the damage location), and this occurs in a few places. This small discontinuity may
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1244
(b)
6
5
4
4
3
3
2
2
1
1
0
5
10
15
20
0
5
Sensor location
(d)
6
5
4
4
3
2
1
1
10
15
20
0
5
Sensor location
(e)
20
15
20
3
2
5
15
6
5
0
10
Sensor location
GFD
GFD
(c)
ET AL.
6
5
GFD
GFD
(a)
P. QIAO
10
Sensor location
6
GFD
5
4
3
2
1
0
5
10
15
20
Sensor location
Figure 20. Results of GFD calculation based on piezoelectric (PVDF) sensor data: (a) Delamination A – PVDF
(11–13); (b) Delamination B – PVDF (8–12); (c) Delamination C – PVDF (13–15); (d) Saw-cut damage – PVDF
(9); and (e) Impact damage – PVDF (5–7).
be magnified during the derivative calculation process, because the SLV-based curvature
mode shapes are obtained from the measured displacement mode shapes.
Generalized Fractal Dimension (GFD)
The results from the GFD algorithm using the ULS curves based on the numerical
analysis data are presented in Figure 19. The results based on the experimental data
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1245
Dynamics-based Damage Detection of Composite Laminated Beams
(a)
(b)
3.5
3.5
3.0
3.0
GFD
2.5
GFD
4.0
2.0
2.5
2.0
1.5
1.5
1.0
1.0
0
10
20
30
40
50
60
70
0
10
20
Sensor location
(d)
3.0
2.5
2.0
2.0
1.5
1.5
1.0
1.0
0
10
20
30
40
50
60
70
0
10
20
Sensor location
(e)
40
50
60
70
60
70
3.0
2.5
GFD
GFD
(c)
30
Sensor location
30
40
50
Sensor location
3.0
GFD
2.5
2.0
1.5
1.0
0
10
20
30
40
50
60
70
Sensor location
Figure 21. Results of GFD calculation based on SLV system data: (a) Delamination A – SLV (37–43);
(b) Delamination B – SLV (27–39); (c) Delamination C – SLV (53–59); (d) Saw-cut damage – SLV (48); and
(e) Impact damage – SLV (22–28).
from the piezoelectric (PVDF) sensor and SLV measured data are presented in Figures 20
and 21, respectively.
Although the FD curves indicate the location of damage and do not require the smooth
curve fitting as in the GSM, the method has the abnormality of highlighting the regions of
higher curvature with peaks other than those peaks at the location of damage when
experimentally measured data (either PVDF or SLV) are used. Furthermore, the extra
peaks in the results based on the measured SLV data have the same level as the peaks at
the damage location and can easily be mistaken as other damage. The effect of numerical
derivation to obtain curvature modes is amplified in the GFD algorithm. Although the
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1246
(b)
0.10
0.08
0.06
0.06
0.04
(c)
0.04
0.02
0.02
0.00
0.00
0
10
20
30 40 50 60
Sensor location
70
80
0
90
(d)
0.4
ET AL.
0.10
0.08
SEM
SEM
(a)
P. QIAO
10
20
30 40 50 60
Sensor location
70
80
90
0.10
0.08
0.3
SEM
SEM
0.06
0.2
0.04
0.1
0.02
0.0
0.00
0
10
20
30
40 50 60
Sensor location
(e)
70
80
90
0
50
100
150
200
250
Sensor location
0.010
0.008
SEM
0.006
0.004
0.002
0.000
0
50
100
Sensor location
150
Figure 22. Results of SEM calculation based on numerical FE analysis data: (a) Delamination A – FE (44–56);
(b) Delamination B (38–58); (c) Delamination C – FE (62–72); (d) Saw-cut damage – FE (150); and (e) Impact
damage – FE (65–75).
derivation procedure already includes the filtering process, calculating the curvature from
the second derivative of experimentally measured displacement data is still a challenge.
In addition, the scale parameter ‘S’ in the GFD algorithm [Equations (12)–(14)] involves
some trial and error in order to achieve the results in the desired scale ratios.
Strain Energy Method (SEM)
The results from the SEM algorithm using the ULS from the numerical analysis data are
presented in Figure 22, while the results based on experimental data, from the piezoelectric
(PVDF) sensor and SLV measured data are presented in Figures 23 and 24, respectively.
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1247
Dynamics-based Damage Detection of Composite Laminated Beams
(a)
(b)
0.020
0.16
0.14
0.12
0.015
SEM
SEM
0.10
0.010
0.08
0.06
0.005
0.04
0.02
0.000
0.00
0
5
10
15
20
0
5
Sensor location
0.025
(d)
15
20
15
20
0.05
0.020
0.04
0.015
0.03
SEM
SEM
(c)
10
Sensor location
0.010
0.02
0.01
0.005
0.00
0.000
0
5
10
15
20
0
5
(e)
10
Sensor location
Sensor location
0.030
0.025
SEM
0.020
0.015
0.010
0.005
0.000
0
5
10
15
20
Sensor location
Figure 23. Results of SEM calculation based on piezoelectric (PVDF) sensor data: (a) Delamination A – PVDF
(11–13); (b) Delamination B – PVDF (8–12); (c) Delamination C – PVDF (13–15); (d) Saw-cut damage –
PVDF (9); and (e) Impact damage – PVDF (5–7).
The identification results based on the modal strain energy shows more irregularity in
the SEM curve. Although, the SEM algorithm indicates the presence and location
of damage (with large peaks at the beginning and end of the damage), multiple small peaks
at other locations near the actual damage invokes doubt regarding the actual damage
location and small imperfections present in the corresponding locations.
SUMMARY AND DISCUSSION
Comparisons of the estimated damage location using the three proposed algorithms
(i.e., GSM, GFD, and SEM) from each system methods, for the numerical FE
analysis data, the piezoelectric PVDF sensor data, and the SLV system data are
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P. QIAO
(b)
0.008
0.008
0.006
0.006
SEM
SEM
(a)
ET AL.
0.004
0.004
0.002
0.002
0.000
0.000
0
10
20
30
40
50
60
0
70
10
20
30
40
50
60
70
60
70
Sensor location
Sensor location
(d)
(c)
0.008
0.006
0.006
SEM
SEM
0.004
0.004
0.002
0.002
0.000
0.000
0
10
20
30
40
50
60
0
70
10
20
(e)
30
40
50
Sensor location
Sensor location
0.008
SEM
0.006
0.004
0.002
0.000
0
10
20
30
40
50
60
70
Sensor location
Figure 24. Results of SEM calculation based on SLV system data: (a) Delamination A – SLV (37–43);
(b) Delamination B – SLV (27–39); (c) Delamination C – SLV (53–59); (d) Saw-cut damage – SLV (48); and
(e) Impact damage – SLV (22–28).
Table 6. Comparison of estimated and actual damage locations – FE.
Estimated damage locations
Damage
Delamination A
Delamination B
Delamination C
Saw-cut
Impact
Actual damage location
GSM
GFD
SEM
44–56
38–58
62–72
150
65–75
44–56
38–59
62–72
150
65–75
40–58
36–60
58–74
150
55–75
44–56
40–58
62–72
150
65–75
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1249
Dynamics-based Damage Detection of Composite Laminated Beams
Table 7. Comparison of the actual and estimated damage locations –PVDF.
Estimated damage locations
Damage
Actual damage location
Delamination A
Delamination B
Delamination C
Saw-cut
Impact
11–13
8–12
13–15
9
5–6
GSM
12
8–12
14
9
6
GFD
11
8–12
11–15
9
5
SEM
12
8–12
14
8–9
6
Table 8. Comparison of the actual and estimated damage locations – SLV.
Estimated damage locations
Damage
Delamination A
Delamination B
Delamination C
Saw-cut
Impact
Actual damage location
GSM
GFD
SEM
37–43
27–39
53–59
48
22–28
38–44
25–38
55–58
48
21–28
32–45
26–46
50–60
45
28–32
38–44
25–39
48–56
48
21–38
summarized in Tables 6–8, respectively. In all three damage detection algorithms, the ULS
data are used to obtain the respective damage parameters. The data of healthy structures
are not required when all three algorithms are implemented. The detection based on
numerical FE analysis data shows good indication of the damage location and size of the
damage for all three damage detection algorithms (Table 6), thus verifying the validity
of the algorithms in damage detection implementation. It validates the promise that all
three proposed algorithms are capable of performing the damage detection analysis if the
validated input data are provided. As shown in Table 6 and also in Figures 16 (GSM),
19 (GFD), and 22 (SEM), damage detection from the FE data based on GSM and SEM
seems more accurate and effective than the one from GFD. However, GFD does
not involve the processing of smooth curve fitting; while both GSM and SEM have
similar algorithms by comparing them with the smooth curve fits, which are assumed to be
the healthy ones.
While in the damage detection using the data measured from the piezoelectric (PVDF)
sensor system, relatively smooth curves with few peaks (Figures 17 (GSM), 20 (GFD),
and 23 (SEM)) are produced for all three algorithms, because of the limited number of
PVDF sensors used (a total of 19 PVDF sensors along the beam length are used in the
experiment, Figure 9). Since the PVDF sensor acquires the curvature over the sensor
length (about 38.1 mm (1.5 in.) in length), the measured data are averaged in nature,
thus smoothing out some local effect over the sensor length. But the PVDF sensor system
is still viable in damage detection with one or two large peaks over the damage location,
and it has the potential of performing real-time and onboard structural monitoring by
embedding or surface-bonding the piezoelectric sensors in or on the structure.
For the SLV sensor systems, denser scanning grids (sensor points) are employed
(Figure 13), compared to those in the PVDF sensor system. This grid measures the local
displacement at the particular point, thus acquiring the displacement mode shapes.
In order to implement the damage detection algorithms with the SLV measured data,
the central difference method (see Equation (1)) is used to obtain the curvature mode
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1250
P. QIAO
ET AL.
shape from the measured displacement mode shapes. As shown in Shah [19], the
implementation of the damage detection algorithms directly with the measured
displacement mode shapes from SLV does not warrant the damage detection. As shown
in Figures 18 (GSM), 21 (GFD), and 24 (SEM), more peaks and irregularities are observed
for all three damage detection methods, and they may be caused by the refined scanning
grids used in the experiment (Figure 13). Even though all three algorithms locate the
damage relatively well, additional peaks in the damage parameter curves may promote
false detection of the damage. In particular, more sharp peaks are observed in the GFD
curve (Figure 21), indicating that the GFD algorithm based on the SLV measured data
may not be capable of uniquely picking up the actual damage location. While for the GSM
and SEM, multiple peaks appear, the peaks at the actual damage location are significantly
larger than the ones from the non-damage locations, and are capable of locating
the damage.
In summary, with the validation of the proposed three damage detection algorithms
based on numerical FE analysis, it is indicated that all the algorithms using the ULS
curvature curve are capable of detecting the presence and size (e.g., the delamination
length) of the damage if the validated mode shape data is available. Two sensor systems
(PVDF vs. SLV) are both capable of acquiring such validated mode shape data useful for
damage detection analysis. The results (Tables 6–8 and Figures 16–24) indicate that the
detection based on GSM and SEM provides better outcome than the one based on GFD.
However, GFD eliminates the necessity of smooth curve fitting as is required in GSM
and SEM.
CONCLUSIONS
The present study focuses on the comparison of two sensor systems (i.e., PVDF sensors
and SLV system) in providing reliable measured dynamic response data for damage
detection purposes and verifies the validity of three damage detection algorithms. Two
sensor systems of contact (by surface-bonding of PVDF sensors) and noncontact (by laser
scanning of the specimens) are used to acquire the dynamic response (e.g., frequency and
mode shapes). The numerical FE modal analysis is conducted to show the validity of the
proposed damage detection algorithms. The experimental program comprises testing of six
E-glass–epoxy composite beams with different damage configurations (i.e., delamination,
saw-cut, and impact damage).
The ULS curvature is used in this study to minimize the effect of data truncation effects
and measurement error, as well as the selection of curvature mode shapes, because the
use of individual curvature mode shapes may yield misleading results in detecting the
location of damage. Once the ULS curvatures are obtained by the numerical FE analysis,
PVDF, or SLV systems, they are implemented in the three damage detection algorithms
(i.e., GSM, GFD, and SEM).
In general, the damage identification results using the SLV measured data have lots of
peaks or significant undulations that may cause a misunderstanding in locating damage
and can be mistaken for a multiple-damage case. The probable sources of this irregularity
may be from the numerical process in estimating the curvature mode shapes from
measured displacement mode shapes or the inherent imperfection in the composite beams.
Improvement in this process by applying suitable approximation algorithms that includes
a proper filtering process will improve the detection results. However, the noncontact SLV
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Dynamics-based Damage Detection of Composite Laminated Beams
1251
system enjoys the advantages such as simplicity in operation, ability to account for a large
number of measurement points, and absence of wiring management problems. The
damage detection using the SLV system is valid for the composite laminated beams used
in this study because the peaks of damage parameters at the actual damage location are
significantly larger than those shown at the nondamage locations.
On the other hand, the identification process based on the PVDF sensor measurement
shows less irregularity and has only one or two major peaks indicating the location of the
damage. Due to the relatively coarse sensor grid, the damage identification parameters
cover a large area (broad peak over the sensor length) that may miss the actual area of the
damage locations. However, the PVDF sensor system has a great potential of being
implemented as an automatic, real-time and onboard structural health monitoring
technique.
Successful implementation of damage detection algorithms and two sensor systems for
damage detection of composite laminated beams demonstrates that the dynamics-based
damage detection approach using the two sensor systems is a viable technology for
structural health monitoring of composite structures.
ACKNOWLEDGMENTS
This study is partially supported by the Air Force Office of Scientific Research
(AFOSR) (FA9650-04-C-0078), and their financial support is gratefully acknowledged.
The assistance provided by Kan Lu and Luyang Shan on experimental testing and
specimen fabrication is highly appreciated.
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