Curvature Mode Shape-based Damage Assessment of Carbon/Epoxy Composite Beams

http://jim.sagepub.comSystems and Structures

Journal of Intelligent Material

DOI: 10.1177/1045389X06064355 2007; 18; 189 originally published online Oct 10, 2006; Journal of Intelligent Material Systems and Structures

Wahyu Lestari, Pizhong Qiao and Sathya Hanagud Curvature Mode Shape-based Damage Assessment of Carbon/Epoxy Composite Beams

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Curvature Mode Shape-based Damage Assessmentof Carbon/Epoxy Composite Beams

WAHYU LESTARI,1 PIZHONG QIAO2,* AND SATHYA HANAGUD

3

1Department of Aerospace Engineering, Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA

2Department of Civil and Environmental Engineering, Washington State University

Pullman, WA 99164-2910, USA

3School of Aerospace Engineering, Georgia Institute of TechnologyAtlanta, GA 30332-0150, USA

ABSTRACT: In this article, a combined analytical and experimental damage assessmentmethod using curvature mode shapes is developed. The curvature mode is selected due to itssensitivity to the presence of the damage and the localized nature of the changes. An analyticalrelationship between the damaged and the healthy beams is formulated, for which the effectof damage in the form of stiffness loss is accounted. This relationship is later used to estimatethe extent of damage from the experimentally identified changes in structural dynamiccharacteristics. Surface-bonded piezoelectric sensors are used to directly acquire the curvaturemodes of composite structures, which simplify the identification procedure. The specimensare made of carbon/epoxy laminated composite beams. Several different types of damagesare introduced in the beams (i.e., delamination, impact, and saw-cut damages) to simulatepossible damage scenarios. Several limitations and remarks of the proposed experimental anddamage identification approaches are discussed. The study shows that the present techniqueusing curvature mode shapes and piezoelectric materials can be used effectively to locate thedamage in the laminated composite structures.

Key Words: damage detection, dynamic response, curvature mode shape, laminatedcomposites.

INTRODUCTION

STRUCTURAL health monitoring (SHM) is one of theimportant tools to maintain the safety and integrity

of structures, such as aerospace, automotive, machinery,and civil structures. A reliable nondestructive damageidentification and assessment is essential for the devel-opment of such monitoring systems, since undetectedor untreated damage may grow and lead to structuralfailure. The challenge is to interpret the changes of theresponse parameters due to damage and correlate themwith the corresponding measured parameters. Specifyingthe relationship between the damage and characteristicparameters provides the foundation of identificationand assessment algorithm required for the SHM system.Furthermore, the anisotropy of material and the factthat much of the damage in composites occurs beneaththe surface of laminates increase the complexity ofdamage assessment in composite structures. The presentresearch focuses on developing the relationship between

the dynamic response and the damage as a basis of thedamage identification method for composite structures.

Structural dynamic response-based damage detectiontechnique offers an identification method with basicassumptions that the dynamic parameters such asnatural frequencies, mode shapes, transfer functions,or frequency response functions (FRFs) are functions ofthe physical properties of the structures. Therefore, thechanges in these dynamic characteristics can be used tolocate and assess damages. The experimentally measureddata from the surface-bonded sensors provide usefulinformation about the structural health without costlydismantling procedures of the structures. By comparingthe identified structural dynamic characteristics of thestructure at a later date in service with the intact orhealthy structure, damage locations and correspondingmagnitudes can be identified. Zhou et al. (2000)reviewed some of the vibration-based detection techni-ques for identification of delamination in compositestructures. The modeling technique for delaminatedbeam, including effects of delamination on dynamicscharacteristic parameters, was presented, and variousvibration-based identification methods were compared.

*Author to whom correspondence should be addressed.E-mail: [email protected] 2, 7 and 8 appear in color online: http://jim.sagepub.com

JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES, Vol. 18—March 2007 189

1045-389X/07/03 0189–20 $10.00/0 DOI: 10.1177/1045389X06064355� 2007 SAGE Publications

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Several of the earliest studies on dynamic response-based damage detection used the natural frequency as aparameter (Adam et al., 1978; Cawley and Adams,1979a, b; Gomez and Silva, 1991; Salawu, 1997; Messinaet al., 1998). Using a small number of sensors, thenatural frequencies of large structures can be measuredeffortlessly. Although there are many advantages tousing the frequency response as detection techniques,the effect of damage on frequency response primarilyprovides global information about the condition ofstructures. In addition, the natural frequency measure-ments are very sensitive to interference, especially atthe low order modes. Examples of interferences includefiber misalignment during manufacturing, introductionof non-negligible mass by sensors, and simulatedapproximate boundary conditions that prompt thelargest error in the frequency measurement (Kessleret al., 2002). Nevertheless, the natural frequency canbe used as an early warning system of global structuralcondition.The curvature mode shapes are utilized as a base

parameter for damage identification and assessmenttechnique in the present study. The changes of thecurvature mode shapes are localized in the region ofthe damage and consequently may be used effectivelyto identify damage location in structures. Pandey et al.(1991) was among the first who demonstrated thepossibility of curvature mode shape application inhealth monitoring. The curvature mode shape informa-tion in combination with data of frequency changes wasused to identify crack by Pabst and Hagedorn (1993).Salawu and Williams (1994) compared the performanceof both curvature and displacement mode shapes forlocating damage, which confirmed the advantage ofcurvature mode in locating damage as compared to thedisplacement mode.Several papers have documented research on damage

detection utilizing curvature modal changes in variousforms and techniques. Stubb and Kim (1996) introduceda concept of damage location indicator withoutbaseline parameter by using the modal parameters offinite element model. Luo and Hanagud (1997) intro-duced a method of flaw detection by using an integralequation that related the modes in damaged conditionsand experimental data of intact and damaged structures.The measured data were used to identify the locationof damage and corresponding damage magnitudeof a cantilever beam. Curvature information in thefrequency domain data in the form of FRF or transferfunction was also employed in several damage identifi-cation techniques by Keilers and Chang (1995), Sampaioet al. (1999), Schultz et al. (1999) among others.Recently, Lestari and Qiao (2005) employed thecurvature-based method to detect the damage inhoneycomb composite sandwich beams. The FRFcurvature methods performed well in detecting and

locating the damage, especially for large magnitude ofdamage.

Lestari and Hanagud (2001) used only a few lowerorder curvature modes to identify damage locationbased on the difference between the measured data ofdamaged and healthy structures, and the mathematicalrelationship of the measured data and dynamic param-eters was used to estimate the severity of the damage.This detection technique is extended in the presentstudy, and the amplitude difference of curvaturemode shapes is employed to estimate the local stiffnessloss due to damage. The first three curvature modesare used in the damage assessment, since the curvaturenodal points of damaged structures at high modesmay shift significantly from the original undamagedcase thus generating misleading results. Moreover, it isrelatively difficult to experimentally obtain the modeshapes at the higher modes using surface-bondedsensors; while at the lower modes, the mode shapesmay not be sensitive to small damage. In this study, thefirst three low curvature mode shapes of the structuresbetween an undamaged state and a damaged stateare extracted from the experimental data. Then, thedifferences of these curvature modes are used todetermine damage locations and the correspondingmagnitudes. The procedure illustrates the damage statefrom the original undamaged state; however, it can alsobe modified to consider the changes from one damagedstate to another damaged state. The study is conductedby using carbon/epoxy laminated composite beams,and the curvature mode shapes are measured by usingsurface-bonded piezoelectric sensors. Several damageforms are introduced in the specimens during orafter manufacturing process, i.e., delamination, impact,and saw-cut damages, to simulate different possibledamage scenarios. The results of damage identificationfor the carbon/epoxy laminated beams, including stiff-ness loss estimation, are presented, and the remarkson the experimental and identification approaches areprovided.

THEORETICAL BACKGROUND

Equation of Motion

The analytical relationship is developed based onEuler–Bernoulli beam theory, and the governing equa-tion for beam in vibration can be expressed as

@2

@x2EIðxÞ

@2

@x2Wðx,tÞ½ �

� �þmðxÞ

@2

@t2Wðx,tÞ½ � ¼ 0 ð1Þ

where EI(x) is the bending stiffness distribution of thebeam, m(x) is the mass distribution of the beam per unitlength along the x-axis, and W(x, t) is the displacementof the beam as a function of the location (x) and time (t).

190 W. LESTARI ET AL.

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By assuming the displacement function as

W x,tð Þ ¼ �ðxÞe jffiffi�

pt ð2Þ

Equation (1) can be rewritten as

d2

dx2EIðxÞ

d2

dx2�iðxÞ½ �

� ��mðxÞ�i �iðxÞ½ � ¼ 0 ð3Þ

where �i and �i are the ith eigenvalue and itheigenfunction, respectively, with i¼ 1, 2, . . . .In this study, only the stiffness loss due to damage is

considered. The stiffness loss varies with damage sizeand location in the structure as shown in Figure 1. Theeffect of the neutral axis changes due to the damageis assumed to be negligible. The distribution of thebending stiffness along the beam is a function oflocation of damage, and the loss of stiffness due to thedamage is expressed as a non-dimensional parameter.The stiffness loss factor is introduced in the model asa measure of the extent of the damage presence in thestructures. This factor represents equivalent bendingstiffness loss in the damaged area, which can be causedby a combination of several factors. Examples mayinclude changes in the second moment of inertia,material loss due to damage, friction or contact effectsbetween delaminated part and primary part for delami-nation case. In this model, the authors do not attemptto capture the physical behavior inside the damage.The derivation of mathematical relationship of highlylocalized or notched type of damage could be found inthe previous work by one of the authors (Lestari, 2001).By assuming " is the stiffness loss parameter at the

location of damage, the effect of damage on the stiffnessdistribution of the beam can be expressed as

EIdðxÞ ¼ EI0 1� " H x� x1ð Þ �H x� x2ð Þ½ �� �

ð4Þ

where H is a Heaviside step function; EI0 is the bendingstiffness of the undamaged structures; x1 and x2 are thebeginning and the end of damage area, respectively.The governing equation for the defective beam can

be written as follows

d2

dx2EIdðxÞ

d2

dx2~�iðxÞ

� �� �� ~�im ~�iðxÞ

� �¼ 0 ð5Þ

where EId(x) is defined in Equation (4); ~�iðxÞ and ~�i arethe eigenfunctions and eigenvalues of the damaged

structure, respectively. With the assumption that thedamage magnitude parameter, ", is small, the perturba-tion method to the intact state of the beam can be usedto solve the governing equation for the damaged beam.Hence, the eigensolutions of the damaged structure canbe expressed in the following forms

~�i ¼ �0i � "�1i � "2�2i~�i ¼ �0

i � "�1i � "2�2

i

ð6Þ

Substituting Equations (4) and (6) into Equation (5)yields

d2

dx2EI0 1� " H x� x1ð Þ �H x� x2ð Þ½ �ð Þ

�

�d2

dx2�0i xð Þ � "�1

i xð Þ � "2�2i xð Þ

� �� �0i � "�1i �

m �0i xð Þ�

"�1

i xð Þ � "2�2i xð Þ

�¼ 0

ð7aÞ

or

d2

dx2EI0

d2

dx2�0i xð Þ

� ��

� "d2

dx2EI0

d2

dx2�1i xð Þ

� ��

þ EI0 H x� x1ð Þ �H x� x2ð Þ½ �d2

dx2�0i xð Þ

� �

� "2d2

dx2EI0

d2

dx2�2i xð Þ

� ��

� EI0 H x� x1ð Þ �H x� x2ð Þ½ �d2

dx2�1i xð Þ

� �þ "m �0i �

1i xð Þ þ �1i �

0i xð Þ

� �þ "2m �0i �

2i xð Þ � �1i �

1i xð Þ þ �2i �

0i xð Þ

� �þO "3

�¼ 0

ð7bÞ

By retaining only the terms up to "2-order andcollecting the coefficients "0, "1, and "2-order, respec-tively, the governing equation of the damaged structurecan be written as

"0 : EI0d4

dx4�0i ðxÞ

� �� �0i m�0

i ðxÞ ¼ 0 ð8aÞ

"1 : EI0d4

dx4�11ðxÞ

� �� �0i m�1

i ðxÞ

þ EI0d2

dx2H x� x1ð Þ �H x� x2ð Þ½ �

d2

dx2�0i xð Þ

� �� � �1i m�0

i xð Þ ¼ 0 ð8bÞ

"2 : EI0d4

dx4�2i ðxÞ

� �� �0i m�2

i ðxÞ

� EI0d2

dx2H x� x1ð Þ �H x� x2ð Þ½ �

d2

dx2�11ðxÞ

� �� þ �1i m�1

i ðxÞ � �2i m�0i ðxÞ ¼ 0 ð8cÞ

∆x

x1

x2

hx

z

Damage

Figure 1. Details of the damage region.

Damage Assessment of Composite Beams 191

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The zeroth order equation of ", Equation (8a),represents the equation of motion of the beam inhealthy condition, and the eigensolutions of �0

i ðxÞ and �0iare readily available for cantilevered boundary condi-tion. The solutions of damaged condition, �1

i ðxÞ and �1i ,are solved by assuming the effect of the damage inthe form of step function. In this study, for theperturbation method with small disturbance to theoriginal structure, only the first-order perturbation isevaluated. Hence, only the terms up to "1-order isretained. The first-order perturbation governing differ-ential equation for �1

i ðxÞ is

EI0d4

dx4�11ðxÞ

� �� �0i m�1

i ðxÞ

¼ �EI0d2

dx2H x� x1ð Þ �H x� x2ð Þ½ �

d2

dx2�0i xð Þ

� �� þ �1i m�0

i xð Þ

ð9Þ

By assuming the solution of homogeneous equation inthe form of linear combination of the healthy solutions,�1i ¼

Pnk¼1 �ik�

0i , and the particular solution provided

in the Appendix, the eigensolutions for the damagedbeam can be written as

~�i ¼ �0i 1� " G1i �G2i þG3i �G4i �G5i½ �� �

ð10Þ

~�i ¼ �0i � "

Xnj¼1

�0i�0i � �0j

G1j �G2j þG3j �G4j �G5j

� ��0j xð Þ

"

þ < x� x1 >d

dx�0i x1ð Þ

� ��< x� x2 >

d

dx�0i x2ð Þ

� �þH x� x1ð Þ�0

i x1ð Þ �H x� x2ð Þ�0i x2ð Þ

� H x� x1ð Þ �H x� x2ð Þ½ ��0i xð Þ

#ð11Þ

Now, the curvature mode shapes for the damagedstructure can be obtained by taking the secondderivative of ~�i as

~�i,xx ¼d2

dx2�0i � "

Xnj¼1

�0i�0i ��0j

G1j�G2jþG3j�G4j�G5j

� �"

�d2

dx2�0j xð Þ� H x�x1ð Þ�H x�x2ð Þ½ �

d2

dx2�0i xð Þ

ð12Þ

and the frequency of damaged beam, ~!, can be obtainusing the expression

~! ¼

ffiffiffiffi~�i

p2�

¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�0i 1� " G1i � G2i þ G3i � G4i � G5i½ �� �q

2�ð13Þ

the parameters and variables of which are described inthe Appendix.

Health Monitoring

When damage is introduced in a structure, the bendingstiffness at the location of the damage is reduced whileat the same time the magnitude of the curvature modesincreases. The absolute differences between the curvaturemodes of the intact and damaged structures are thehighest in the region of the damage and negligibly smalloutside this region. Hence, the absolute curvaturedifference between the healthy and damaged structuresfor each mode can be represented as:

��00i, j ¼ �00

h

� �i, j� �00

d

� �i, j

��� ��� ð14aÞ

Dj ¼Xi

��00i, j ð14bÞ

where �00i or �i,xx is the ith curvature mode shapes; h and

d denote healthy and damaged, respectively; and i and jdenote the mode number and the measurement location,respectively. The curvature damage factor (CDF), Dj, isthe summation of damage differences from each modebeing evaluated. Let the differences of curvature modesbe ��i,xxðxÞ. At a certain damage location, for exampleat station k¼ kd where x¼ xd, the value of ��i,xxðxdÞis significantly higher than the ones at other stations.Based on the curvature difference values and CDFs, thelocation of damage in the structure can be identified.The diagram in Figure 2 describes the procedure of theproposed damage assessment technique.

For comparison and validation, the damage index(D-index) method (Stubb and Kim, 1996) is evaluatedas well, which are determined from the expressions:

�i, j ¼�00d

� �2i, jþPimax

i¼1 �00d

� �2i, j

� �Pimaxi¼1 �00

d

� �2i, j

�00h

� �2i, jþPimax

i¼1 �00d

� �2i, j

� �Pimaxi¼1 �00

d

� �2i, j

ð15aÞ

~Dj ¼Xi

�i, j ð15bÞ

Healthy mode shape

φ,xx

φ,xx

φ,xx

x x

x

Damaged mode shape

Mode shape difference

Estimation of damage location(Equation 15)

Estimation of stiffness loss(Equation 16)

Figure 2. Diagram of the proposed damage assessment procedure.

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where ~Dj is the summation of the damage indices.Once the damage is identified at station xd, the

magnitude of the damage at this location can bedefined by using the damage magnitude difference ofthe modes, ��i,xxðxdÞ, between the intact structureand the structure with damage. This damage magnitudeor stiffness loss " can be calculated using therelationship of the frequencies in Equation (10) or therelationship of the curvature modes in Equation (12).Since the frequency measurements at low frequency aresensitive to interferences, the damage magnitudeprediction is calculated based on the curvature modeshape relationship. Provided the damage location xdis known, the damage magnitude in the form ofstiffness loss can be defined from Equation (12) as

"¼�i,xx��di,xxXn

j¼1

�0i�0i ��0j

fG1j�G2jþG3j�G4j�G5jgd2

dx2�0j

�½Hðx�x1Þ�Hðx�x2Þ�d2

dx2�0i ðxÞ

ð16Þ

where �i,xx and �di,xx are the measured curvaturemodes of the healthy and damaged beams at the ithmode, respectively, and all other parameters in thedenominator are as defined in the Appendix.

NUMERICAL SIMULATIONS

Based on the aforementioned analytical approach,numerical simulations are obtained for carbon/epoxycomposite cantilever beams with through-width delami-nations, impact damage, and notch (saw-cut) damage.The laminated beams have the elastic modulus of49.6GPa and the mass density of 3.175� 10�6 kg/m3

and dimensions of 228.6� 25.4� 1.76mm3. Fivedamage configurations, i.e., different sizes and/orlocations, are considered, which reflect the damageconfigurations of the actual beam specimens. Thecomposite laminated beams with three differentdelamination configurations are considered: (1)Delamination A is located at 31.75mm with lengthof 25.4mm; (2) Delamination B is located at 31.75mmwith length of 50.8mm; and (3) Delamination C islocated at 69.85mm with length of 25.4mm. The fourthbeam contains an impact-damaged defect which islocated between 57.15 and 82.55mm from visualmeasurement. The last one is a beam with a saw-cutnotch of 1.6mm located at 80.55mm. All the locationsof damages are measured from the fixed end of acantilever beam. Detail configurations and geometriesare presented in Figure 3. The natural frequenciesand curvature mode shapes of the beams are calculatedusing the proposed analytical model for various valuesof stiffness loss, ".

Results of the frequency changes due to damage forseveral damage loss scenarios are presented in Table 1.The illustration of curvature modes of delaminationbeams is given in Figure 4, for the first four modes ofbeam delamination B with a stiffness loss of 20%, andthe curvature mode difference is presented in Figure 5.It is clearly shown that the effect of the damage onthe curvature modes is localized in the region of thedamage. However, it is also observed that when thenodal point of curvature mode is close to the location ofthe damage, the effect of the damage on the curvaturemode is less pronounced. In this damage configuration,one of the nodal point of the fourth mode, which islocated about a quarter of the beam length fromthe root, is near the location of the damage,xnode ffi xd, see Figure 4(d). However, in the differenceof curvature modes between the intact and the damagedbeams, the damage effect is still significant. It canbe seen in the curvature mode shape differences inFigure 5(d).

EXPERIMENTAL VALIDATION

Specimens

Experiments were conducted to validate the methoddiscussed in the previous section. In this study, sixcarbon/epoxy laminated composite beam specimenswere tested. The specimens were made of carbon fiberand epoxy resins and had a [0/90]4T lay-up of a totalof eight layers, with each layer thickness of 0.22mmand a total thickness of 1.76mm. Each beam specimenhas a width of 25.4mm and a length of 241.3mm.After clamping in the cantilever configuration, thebeam specimen has a free span length of 228.6mm.Piezoelectric materials were used in this study eitheras actuators or sensors, where these surface-bondedpiezoelectric sensors were capable of measuring the localcurvature of the beams under its area directly.The polyvinylidenefluoride (PVDF) films were used assensors, and to best accommodate the films, the beamspecimens were divided into 16 measurement points(Figure 6). Each point was aligned with the center of thePVDF film during the testing. Two-excitation sourceswere evaluated in this study, i.e., excitation usingimpulse hammer and continuous excitation using lead–zirconate–titanate (PZT) ceramic wafer as an actuator.An 8� 12mm2 piece of PZT ceramic was attached toeach carbon/epoxy composite sample at a location closeto the clamped end, see Figure 7.

The experiment began with two undamaged beamsof the six samples. Both of these samples were firsttested, and their undamaged mode shapes wereobtained. The undamaged mode shape used forcomparison was derived from an average of the two.

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Then, one of the undamaged beams was artificiallydamaged by cutting a through-the-width notch with ahandsaw, at a location of measurement point 6 (seeFigure 7). The other three samples contained adelamination at various locations, delaminations A, B,and C. The delamination A is located betweenmeasurement points 2 and 4; the delamination B islocated between measurement points 2 and 6; and thedelamination C is located between measurement points 5and 7. The delaminations were introduced during thefabrication by inserting a piece of Teflon tape betweenthe second and third layers of the material at the desiredlocations. The fourth beam had an impact damage,at the location between measurement points 4 and 6.The impact damage was created by dropping an 8.0 kgmass from a height of about 305mm onto an

undamaged carbon composite beam. Hence, the avail-able specimens allowed for testing and comparing fivedifferent damage conditions: one saw-cut notch, threedelaminations, and one impact damage. The summaryof damage locations for the beam specimens from thefixed end and with respect to the sensor locations isgiven in Table 2.

Data Acquisition and Modal Analysis

A data acquisition system – digital analog converterdSPACE system was used to acquire data from boththe actuator and the sensors. For continuous excitation,a Hewlett Packard 33120A waveform generator wasused to induce the sweep sine. The experimental setupconfiguration is presented in Figure 8. The sweeps took

(c)

(d)

31.75 mm25.4 mm

228.6 mm

(a)

31.75 mm 50 mm

228.6 mm

(b)

(e)

69.85 mm25.4 mm

228.6 mm

57.15 mm25.4 mm

228.6 mm

80.55 mm

228.6 mm

Figure 3. Damaged beam specimen configurations and geometry: (a) beam A: 25.4mm long delamination; (b) beam B: 50.8mm longdelamination; (c) beam C: 25.4mm long delamination; (d) beam D: impact damage; and (e) beam E: saw-cut notch.

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place over a frequency range from 1 to 2000Hz overa time of 120 s, with a magnitude of 140V. For theexcitation using an impulse hammer, the impulselocation remained stationary and was located at thefree-end of the beams. In the impulse hammer testing,20 data sets were acquired and recorded on a range

from 1 to 2000Hz for each measurement point. Then,the FRFs of each data set at each point were averagedover 20 measurements to minimize noise interferencerecorded by the sensors. The procedure for the datareduction and shape generation was conducted byusing commercial codes. The time domain data were

Table 1. Prediction of the first four natural frequencies and percentage of changes for:.

Mode number

e¼ 0.1 e¼ 0.2 e¼0.3

Frequency (Hz) Change (%) Frequency (Hz) Change (%) Frequency (Hz) Change (%)

(a) Delamination A with "¼ 0.1, 0.2, and 0.3.1 30.6336 �0.8 30.8761 �1.6 31.1167 �2.42 189.054 0.7 187.651 1.5 186.239 2.23 531.926 0.3 530.595 0.5 529.26 0.84 1049.31 �0.4 1053.72 �0.8 1058.07 �1.3(b) Delamination B with "¼ 0.1, 0.2, and 0.3.1 30.6986 1. 31.0048 �2.0 31.3081 �3.02 187.304 1.7 186.301 2.2 184.194 3.33 536.18 0.6 537.1 �0.7 539.013 �1.14 1046.28 0.1 1047.58 �0.3 1048.88 �0.4(c) Delamination C with "¼ 0.1, 0.2, and 0.3.1 30.3847 0.02 30.3803 0.03 30.3758 0.042 190.66 �0.1 190.874 �0.2 191.088 �0.33 535.726 �0.5 538.186 �0.9 540.635 �1.44 1038.0 0.7 1030.97 1.3 1023.9 2.0(d) Impact damage with "¼ 0.1, 0.2, and 0.3.1 30.4547 �0.2 30.5201 �0.4 30.5853 �0.62 189.782 0.4 189.115 0.7 188.447 1.13 537.011 �0.7 540.742 �1.4 544.447 �2.14 1041.88 0.3 1038.78 0.6 1035.66 0.9(e) Saw-cut damage with "¼ 0.1, 0.2, and 0.3.1 30.3892 0.0001 30.3891 0.0003 30.3891 0.00042 190.454 �0.004 190.462 �0.008 190.47 �0.0133 533.439 �0.03 533.642 �0.07 533.809 �0.14 1044.41 0.05 1043.85 0.11 1043.28 0.2

0 0.2 0.4 0.6 0.8 1−1

−0.8

−0.6

−0.4

−0.2

0

−1−0.75

−0.5

−0.250

0.25

0.5

0.75(a) (b)

0 0.2 0.4 0.6 0.8 1−1

−0.75−0.5

−0.250

0.250.5

0.75

0 0.2 0.4 0.6 0.8 1−1

−0.75

−0.5

−0.25

0

0.25

0.5(c)

(d)

φ,xx

φ,xx

φ,xx

φ,xx

x/L

x/L

0 0.2 0.4 0.6 0.8 1x/L

x/L

0.75

Figure 4. Curvature mode shapes, �,xx, for beam with delamination B and "¼ 0.2: (a) 1st mode; (b) 2nd mode; (c) 3rd mode; and (d) 4th mode.

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transferred into the frequency domain data or FRFs inMATLAB, and the modal analysis of the experimentalresults to generate the curvature mode shapes wasperformed by using I-DEAS Test module. For detailedprocedures of data processing and experimental results,see Hamey (2003) and Hamey et al. (2004).A PVDF film sensor was used to capture the response.

The PVDF film was surface-bonded to the structure byusing a double-sided tape, and it was removable andreusable. The PVDF film has a dimension of 30� 12mmwith a thickness of 28 mm. With the assumption thatall the in-plane strains of the specimen are negligible,the PVDF film sensor output is proportional to the localcurvature. The curvature data response for each nodallocation was acquired and stored, for both the intact andthe damaged beams, which was then used as the base ofdamage detection.

0 0.2 0.4 0.6 0.8 10

0.025

0.05

0.075

0.1

0.125

0.15

0.175

0 0.2 0.4 0.6 0.8 10

0.0250.05

0.0750.1

0.1250.15

0.175(a) (b)

(d)

0 0.2 0.4 0.6 0.8 1x/L x/L

0

0.05

0.1

0.15

0.2

∆φ, x

x∆φ

, xx

∆φ, x

x∆φ

, xx

0 0.2 0.4 0.6 0.8 1

−0.1

−0.05

0

0.05

0.1(c)

x/L x/L

Figure 5. Curvature mode shape difference, ��,xx, for beam with delamination B and "¼ 0.2: (a) 1st mode; (b) 2nd mode; (c) 3rd mode; and(d) 4th mode.

Dataacquisition

system

WavegeneratorPiezo

driver

Oscilloscope

Beamsample

Figure 8. Experimental setup for carbon/epoxy beam testing withcontinuous excitation.

Table 2. Damage locations.

Damage type

Damage location,from the fixed

end (mm)Damagearea (mm)

Damage locationaccording to

sensor location

Delaminated A 31.75– 57.15 25.4 2–4Delaminated B 31.75–82.55 50.8 2–6Delaminated C 69.85–95.25 25.4 5–7Impact 57.15–82.55 25.4 4–6Saw-cut 80.55–82.15 1.6 6

Figure 7. Carbon/epoxy composite beams with PZT wafer attachedas an actuator.

Figure 6. Dimensions of the composite beam specimen andschematic of the sensor layout.

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Experimental Results

Once the measurement data were collected andrecorded, the transfer function and modal analysiscalculation of the data were performed. The first threecurvature mode shapes were extracted very well with16 measurement points. The curvature mode shapesfrom experimental results of the healthy beamspecimens are compared to the theory and presented in

Figures 9 and 13 for the impulse hammer and sweep sineexcitation, respectively. The mode shapes of the healthybeam are weighted with respect to the theoretical one,for comparison purposes. Then, the weights areapplied to the damaged beam mode shapes to allowfor greater ease in comparison. In some cases, when ameasurement at a certain point was farther away fromthe general shape trend and such an abnormality (maybe due to material imperfection) repeated at each beam

(a) (b)

(c) (d)

(e)

Sensor location Sensor location

Sensor locationSensor location

Sensor location

HealthydelA

HealthydelC

HealthydelB

HealthyImpact

HealthySawcut

Figure 10. Comparison of the first curvature mode shapes of damage and healthy beams from experiment with impulse hammer excitation:(a) delamination A; (b) delamination B; (c) delamination C; (d) impact damage; and (e) saw-cut notch.

(a) (b)

(c)

Sensor location Sensor location

Sensor location

TheoryExperiment

TheoryExperiment

TheoryExperiment

Figure 9. Comparison of the first three curvature mode shapes of a healthy beam from theory and experiment with impulse hammer excitation:(a) the first mode; (b) the second mode; and (c) the third mode.

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measurement, one or two measurement points werereplaced by the average of the neighboring points. Thefirst three measured natural frequencies are presented inTables 3 and 4 for the sweep sine and impulse hammerexperiments, respectively. Slight discrepancies in themeasured natural frequency between both the excitationmethods might be caused by the additional stiffnessfrom actuator bonding, the discrepancies in the repeat-ability of the boundary condition, and the repeatabilityof the impulse force excitation. The first three curvature

mode shapes of the five damaged beams from theexperiment with impulse hammer excitation arepresented in Figures 10–12 and the results from theexperiment with continuous sweep sine excitation arepresented in Figures 14–16.

DAMAGE IDENTIFICATIONComparison of results for curvature damage factor

(CDF) (Equation (14b)) and damage index (D-index)(Equation (15b)) are presented in Figures 17 and 18for the impulse hammer and sweep sine excitation,respectively. In general, the trends of damage identifica-tion from both the damage factor and the damage indexmethods are similar. However, when the location of thedamage is close to the nodal point of the mode shapes,the curvature damage factor sometimes gave inconclu-sive results. As mentioned in the numerical simulation,the changes of mode shapes are not well pronouncedwhen the damage location is close to the nodal point.The differences in the mode shape become the same levelas the imperfection or deviation in the experimentalresults. Hence, the results of curvature damage factor,which is a summation of several modes considered,become unclear. However, when those modes, whichhave a nodal point close to the damage location, areexcluded from the summation, the damage factor resultsare improved.

(e)

(a)

(c)

(b)

(d)

Sensor location Sensor location

Sensor locationSensor location

Sensor location

HealthydelA

Healthy

HealthySawcut

delC

Healthy

HealthyImpact

delB

Figure 11. Comparison of the second curvature mode shapes of damage and healthy beams from experiment with impulse hammer excitation:(a) delamination A; (b) delamination B; (c) delamination C; (d) impact damage; and (e) saw-cut notch.

Table 4. The measured natural frequencies from sweepsine experiment.

Mode Healthy Delam. A Delam. B Delam. C Impact Saw-cut

1st 32.8 29.12 39.61 29.23 33.82 27.992nd 180.8 175.45 171.54 179.06 181.78 169.233rd 500.5 481.89 492.84 489.01 505.06 481.99

Table 3. The measured natural frequencies from impulsehammer experiment.

Mode Healthy Delam. A Delam. B Delam. C Impact Saw-cut

1st 29.67 30.43 32.29 32.08 29.26 29.602nd 177.82 177.73 176.43 184.81 177.04 170.623rd 478.47 493.11 517.35 501.33 495.59 478.90

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Identification results of delamination A (seeFigures 17(a) and 18(a)) are inconclusive. The size ofdelamination is small, which makes relatively smallchanges in the mode shapes. Additionally, the fact thatlocation of the delamination is very close to the fixedend reduces the stiffness loss effect due to limitation ofdelamination opening. The same size delaminationat different location, delamination type C, gave better

results (Figures 17(c) and 18(c)). The identificationprocess shows that the delamination is located in thearea between points 5 and 8, which is close to theactual location of delamination between points 5 and7. The damage indicators at these locations are veryclear and higher than at other locations, with anexception at point 10. After careful examination of thespecimens, it has been found that all the delaminated

(a)

Cur

vatu

reC

urva

ture

0.5

HealthydelA

HealthydelB

HealthyImpact

HealthydelC

HealthySawcut

0.4

0.2

0

0 2 4 6 8Sensor location

10 12 14 16

0 2 4 6 8Sensor location

10 12 14 16

−0.2

−0.4

−0.6

Cur

vatu

re

0.4

0.2

0

0 2 4 6 8Sensor location

10 12 14 16

−0.2

−0.4

−0.6

Cur

vatu

re

0.4

0.2

0

0 2 4 6 8Sensor location

10 12 14 16

−0.2

−0.4

−0.6

0

−0.5

Cur

vatu

re

0.5

0 2 4 6 8Sensor location

10 12 14 16

0

−0.5

(b)

(c) (d)

(e)

Figure 12. Comparison of the third curvature mode shapes of damage and healthy beams from experiment with impulse hammer excitation:(a) delamination A; (b) delamination B; (c) delamination C; (d) impact damage; and (e) saw-cut notch.

(a) 0

0 2 4 6 8Sensor location

TheoryExperiment

TheoryExperiment

TheoryExperiment

10 12 14 16

0 2 4 6 8

Sensor location10 12 14 16

0

0.6

0.4

0.2

0

−0.2

−0.4

2 4 6 8Sensor location

10 12 14 16

Cur

vatu

re

Cur

vatu

re

0.4

0.2

0

−0.2

−0.4

−0.6

Cur

vatu

re

−0.1

−0.2

−0.3

−0.4

−0.5

(b)

(c)

Figure 13. Comparison of the first three curvature mode shapes of healthy beam from analytical theory and experiment with sweep sineexcitation: (a) the first mode; (b) the second mode; and (c) the third mode.

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(a) 0

0 2 4 6 8

Sensor location

10 12

HealthydelA

14 16

Cur

vatu

re

−0.1

−0.2

−0.3

−0.4

−0.5

0

0 2 4 6 8

Sensor location

10 12

HealthydelB

14 16

Cur

vatu

re

−0.1

−0.2

−0.3

−0.4

−0.5

0

0 2 4 6 8

Sensor location

10 12

HealthyImpact

14 16

Cur

vatu

re

−0.1

−0.2

−0.3

−0.4

−0.5

0

0 2 4 6 8

Sensor location

10 12

HealthydelC

14 16

Cur

vatu

re

−0.1

−0.2

−0.3

−0.4

−0.5

0

0 2 4 6 8Sensor location

10 12

HealthySawcut

14 16

Cur

vatu

re

−0.1

−0.2

−0.3

−0.4

−0.5

(b)

(c) (d)

(e)

Figure 14. Comparison of the first curvature mode shapes of damage and healthy beams from experiment with sweep sine excitation:(a) delamination A; (b) delamination B; (c) delamination C; (d) impact damage; and (e) saw-cut notch.

(a) 0.6

0.4

0.2

Cur

vatu

re

0

0 2 4 6 8

Sensor location

Healthy HealthydelBdelA

Healthy

HealthySawcut

delC

10 12 14 16

−0.2

−0.4

0.6

0.4

0.2

Cur

vatu

re

0

0 2 4 6 8

Sensor location

10 12 14 16

−0.2

−0.4

HealthyImpact

0.6

0.4

0.2

Cur

vatu

re

0

0 2 4 6 8

Sensor location

10 12 14 16

−0.2

−0.4

0.6

0.4

0.2

Cur

vatu

re

0

0 2 4 6 8

Sensor location

10 12 14 16

−0.2

−0.4

0.6

0.4

0.2

Cur

vatu

re

0

0 2 4 6 8

Sensor location

10 12 14 16

−0.2

−0.4

(b)

(c) (d)

(e)

Figure 15. Comparison of the second curvature mode shapes of damage and healthy beams from experiment with sweep sine excitation:(a) delamination A; (b) delamination B; (c) delamination C; (d) impact damage; and (e) saw-cut notch.

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specimens have a small bump (imperfection) betweenpoints 10 and 11, which may develop during manufac-turing of the composite specimens. The effect of thisimperfection was also picked up by the sensor atlocation 12, since the size (length) of the sensors islarger than the distance between the measurementlocations.Furthermore, in most cases, the measured data from

the points close to both the ends, the first and the lastone, are unreliable, and they are mainly caused by theboundary effect, which is picked up when the sensor isclose to the boundary. Interference of the actuator andsensor being close to each other at the fixed end in thesweep sine test also worsen the condition. For delamina-tion type B, the results from impulse hammer excitation(Figure 17(b)) indicate that the damages are presentaround points 2 and 7 for D-index indicator and aroundpoints 4 and 7 for CDF indicator, with both showingthem as two separate damages. This means that thesensors picked the curvature changes at the boundariesof the delamination; while at the delaminated areathe sensors picked the curvature of the delaminatedsegment. The results from the sweep sine excitation(Figure 18(b)) indicated that delamination is locatedbetween points 2 and 7 from the CDF method andbetween points 6 and 8 from the D-index method.In general, the predictions for delamination B locationare quite close to the actual location, which is between

points 2 and 6, especially for the end of delaminationboundary that is far from the fixed end. However, theCDF at location 13 from the impulse hammer testshowed possible location of damage as well.

Prediction with the data from the impulse hammerexcitation suggested that the location of the impactdamage (Figure 17(d)) is around point 6, which is theborder of impact damage area. The real impact damagearea is between points 4 and 6. The prediction from thesweep sine excitation (Figure 18(d)) suggested a broaderarea, although slightly shifted to the right, betweenpoints 5 and 8. Although there are some undulations ofdamage indicator, the prediction for impact-damagedbeam is quite apparent, as the peak at the suggestedlocations is superior to the other locations (Figures 17(d)and 18 (d)). For the saw cut damaged beam, theresults from impulse hammer (Figure 17(e)) gavea quite good prediction at location 6, which is thereal location of the damage, although there aresome significant peaks around point 10, which arepossibly due to imperfection caused by deficiencyin averaging of the measurement data. Predictionfrom the data generated by sweep sine excitation(Figure 18(e)) suggested that the location of damage isat point 9. This is far away from the real damagelocation.

In summary, the results from experimental datagenerated by the impulse hammer excitation

(a) 0.4

0.2

0

0 2 4 6 8

Sensor location

10 12

HealthydelA

HealthydelC

14 16

Cur

vatu

re

−0.2

−0.4

−0.6

0.4

0.2

0

0 2 4 6 8

Sensor location

10 12

HealthydelB

14 16

Cur

vatu

re

−0.2

−0.4

−0.6

0.4

0.2

0

0 2 4 6 8

Sensor location

10 12

HealthySawcut

14 16

Cur

vatu

re

−0.2

−0.4

−0.6

0.4

0.2

0

0 2 4 6 8

Sensor location

10 12 14 16

Cur

vatu

re

−0.2

−0.4

HealthyImpact

0.4

0.2

0

0 2 4 6 8

Sensor location

10 12 14 16

Cur

vatu

re

−0.2

−0.4

(b)

(c) (d)

(e)

Figure 16. Comparison of the third curvature mode shapes of damage and healthy beams from experiment with sweep sine excitation:(a) delamination A; (b) delamination B; (c) delamination C; (d) impact damage; and (e) saw-cut notch.

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(Figure 17) yield better identification of damagecompared to the ones by the sweep sine excitation(Figure 18). The sweep sine testing produces smoothercurvature mode shapes compared to the impulsehammer testing. However, the averaging process in thesweep sine testing also reduced the local effect due to

damage, which affected the damage assessment estima-tion. In the case of large delamination, the methodpredicts changes at the boundary of delamination,instead of the whole area of delamination segment.This can be mistaken as multiple delaminations ordefects in the beam. Comparison of the peak damage

(a)

3.3

3.25

3.2

3.15

3.10

3.05

3

2.95

2.9

2.85

0.450.4

0.3

0.2

0.1

0.36

0.27

CD

F

0.45

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

CD

F

CD

F

0.4

0.5

0.3

0.2

0.1

0

CD

F

0.4

0.5

0.3

0.2

0.1

0

CD

F

0.18

0.09

3.2

D-in

dex

D-in

dex

Damage identification for delA beam

Damage identification for delC beam

Damage identification for delB beam

Damage identification for impact beam

Damage identification for sawcut beam

D-indexCDF

D-indexCDF

D-indexCDF

D-indexCDF

D-indexCDF

3.1

3

2.9

3.3

3.2

D-in

dex 3.1

3

2.9

3.3

3.4

3.2

D-in

dex

3.1

3

2.9

3.3

3.4

3.2

D-in

dex

3.1

3

2.9

0 2 4 6 8

Sensor location

10 12 14 16

0 2 4 6 8

Sensor location

10 12 14 16

0 2 4 6 8

Sensor location

10 12 14 16

0 2 4 6 8

Sensor location

10 12 14 16

0 2 4 6 8

Sensor location

10 12 14 16

(b)

(c) (d)

(e)

Figure 17. Comparison of curvature damage factor (CDF) and damage index (D-index) from impulse hammer excitation: (a) delA beam; (b) delBbeam; (c) delC beam; (d) impact beam; and (e) saw-cut beam.

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indicated in Figures 17 and 18, both from the curvaturedamage factor or damage index, shows that the impactand saw-cut damaged beams have the same degree ofstiffness loss. The beam with delamination type Bhas a lower stiffness loss compared to both theimpact and the saw-cut damaged beams, but higher

than the delamination type C which has a smaller sizeof delamination.

Table 5 presents the summary of the locationestimation results from both experiments, i.e., impulsehammer excitation and continuous excitation by piezo-wafer, where the damage locations are presented with

(a)D-index

Damage identification for delA beam

3.1 0.280.3

0.4

0.32

0.24

0.16

0.08

0.24

0.18

0.12

0.06

0.21

0.14

0.07

3.05

D-in

dex

3

0 2 4 6 8

Sensor location

10 12 14 16

2.95

Damage identification for delB beam

3.1

3.05

D-in

dex

3

0 2 4 6 8

Sensor location

10 12 14 16

2.95

2.9

CDFD-indexCDF

Damage identification for impact beam

0 2 4 6 8

Sensor location

10 12 14 16

D-indexCDF

Damage identification for delC beam

3.1

3.05

D-in

dex

3

0 2 4 6 8

Sensor location

10 12 14 16

0 2 4 6 8

Sensor location

10 12 14 16

2.95

3.1

3.15

3.05

D-in

dex

3

2.95

3.1

3.15

3.05

D-in

dex

3

2.95

2.9

D-indexCDF

CD

F

CD

FC

DF

0.25

0.2

0.15

0.1

0.05

Damage identification for sawcut beam

D-indexCDF

CD

F

0.3

0.24

0.18

0.12

0.06

CD

F

(b)

(c) (d)

(e)

Figure 18. Comparison of curvature damage factor (CDF) and damage index (D-index) from sweep sine excitation: (a) delA beam; (b) delBbeam; (c) delC beam; (d) impact beam; and (e) saw-cut beam.

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respect to the measurement points. In general, boththe CDF and D-index methods produce almost thesame results. When the results are different from theCDF method, the D-index results are presented inthe brackets.

STIFFNESS LOSS ESTIMATIONDamage magnitude of each beam was predicted

based on Equation (16) and evaluated based on eachcurvature mode shape difference independently.Then, the predicted value of stiffness loss for eachbeam was averaged from the modes considered.When the curvature mode difference was not apparentat a certain mode, the result from this particular modewas excluded. Since the location of delamination Acould not be predicted properly, only the stiffness lossesdue to the other four damage configurations arecalculated.

Figures 19 and 20 present comparisons of the firstthree curvature mode shapes of the healthy and thedamaged beams from both the experiments, andthe mode shapes from the analytical model for thebeams with delamination B and C, and impact damage

0.0 0.2 0.4 0.6 0.8 1.0

Am

plitu

de

Am

plitu

de

0.0

0.2

0.4

0.6Exp-delB-ham

0.0

0.1

0.2

0.3

0.4

0.5

0.6

−0.4

−0.2

0.0

0.2

0.4

0.6

Analytic Exp-healthy Exp-delC-ham Exp-delC-exp

(a)

Am

plitu

deA

mpl

itude

Am

plitu

deA

mpl

itude

(b)

(d)

−0.4

−0.2

0.0

0.2

0.4

−0.4

−0.2

0.0

0.2

0.4

−0.4

−0.2

0.0

0.2

0.4

Analytic Exp-healthyExp-delB-hamExp-delB-swp

Analytic Exp-healthy Exp-delC-ham Exp-delC-swp

(e)

Analytic Exp-healthyExp-delB-ham Exp-delB-swp

Analytic Exp-healthy Exp-delC-ham Exp-delC-swp

(c)(f)

x/L

0.0 0.2 0.4 0.6 0.8 1.0

x/L

0.0 0.2 0.4 0.6 0.8 1.0

x/L

0.0 0.2 0.4 0.6 0.8 1.0

x/L

0.0 0.2 0.4 0.6 0.8 1.0

x/L

0.0 0.2 0.4 0.6 0.8 1.0

x/L

Analytic Exp-healthy

Exp-delB-swp

Figure 19. Curvature mode shapes comparison for beams with delamination B and C: (a) the first mode shape of delamination B; (b) thesecond mode shape of delamination B; (c) the third mode shape of delamination B; (d) the first mode shape of delamination C; (e) the secondmode shape of delamination C; and (f) the third mode shape of delamination C.

Table 5. Damage location estimation.

Damage type

Damage location estimationActualdamagelocation

Impulsehammer

Sweep sineexcitation

Delamination A 6 7, 13 2–4Delamination B 4–7 (2–7) 2–7 (6–8) 2–6Delamination C 5–8 5–8 5–7Impact 6 5–8 4–6Saw-cut 6 9 6

204 W. LESTARI ET AL.

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and saw-cut notch, respectively. In Figures 19 and 20,the thick solid line is the result of the analytical modelof damaged condition, the solid line with small dots isthe measured healthy curvature, the dotted line withcircle markers is the measured damaged curvature fromsweep sine test, and the dashed dotted line with squaremarkers is the measured damaged curvature fromimpulse hammer test.The results of stiffness loss prediction from the

curvature measurement with the hammer and sweepsine excitations are presented in Table 6. In general,both the measurement data obtained similar trends.Delamination with larger size (delamination B)caused more stiffness loss than the smaller one(delamination C). The saw-cut damage caused thelargest stiffness loss (22.5%), though it was lower thanas expected. The impact damage on the beam producedlower stiffness loss than the damage by saw-cut.

CONCLUSIONS

In this article, a damage assessment technique ofcarbon/epoxy laminated composite beams based oncurvature mode shapes is presented. The mathematicalrelationship between the damaged and healthy struc-tures is derived by assuming damage effect in the formof stiffness loss, which is represented as discontinuity

0.0 0.2 0.4 0.6 0.8 1.00.0

0.1

0.2

0.3

0.4

0.5

0.6Analytic Exp-healthy Exp-imp-ham Exp-imp-swp

Analytic Exp-healthy Exp-sawcut-ham Exp-sawcut-swp

(a) (d)

−0.4

−0.2

0.0

0.2

0.4

−0.4

−0.2

0.0

0.2

0.4

−0.4

−0.2

0.0

0.2

0.4

Analytic Exp-healthy Exp-imp-ham Exp-imp-swp −0.4

−0.2

0.0

0.2

0.4

0.6

Analytic Exp-healthyExp-sawcut-hamExp-sawcut-swp

(e)

Analytic Exp-healthy Exp-imp-ham Exp-imp-swp

Analytic Exp-healthyExp-sawcut-hamExp-sawcut-swp

(c) (f)

Am

plitu

de

(b)

Am

plitu

deA

mpl

itude

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Am

plitu

deA

mpl

itude

Am

plitu

de

x/L

0.0 0.2 0.4 0.6 0.8 1.0

x/L

0.0 0.2 0.4 0.6 0.8 1.0

x/L

0.0 0.2 0.4 0.6 0.8 1.0

x/L

0.0 0.2 0.4 0.6 0.8 1.0

x/L

0.0 0.2 0.4 0.6 0.8 1.0

x/L

Figure 20. Curvature mode shapes comparison for beams with impact and saw-cut damages: (a) the first mode shape of impact damage;(b) the second mode shape of impact damage; (c) the third mode shape of impact damage; (d) the first mode shape of saw-cut damage;(e) the second mode shape of saw-cut damage; and (f) the third mode shape of saw-cut damage.

Table 6. Stiffness loss predictions.

Beam type

Stiffness loss in %

Hammer excitation Sweep sine excitation

Delamination B 15.2 12.5Delamination C 7.2 7.6Impact damage 15.5 8.7Saw-cut damage 22.5 n/a

Damage Assessment of Composite Beams 205

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in the solution. Numerical simulation method showsdiscontinuities of the curvature modes due to thepresence of damage. The damage location and thecorresponding stiffness loss in the structure wereidentified simultaneously, by using information fromeach mode. Although the information can be obtainedjust by using a single mode, using data from othermodes will enhance and validate the results. By usingthe surface-bonded PVDF film as sensors, thecurvature modes were measured directly, compared tothe measurement from displacement modes. Hence, thederivation process and accuracy loss can be avoided.Estimation results of damage location from the

proposed method are in reasonably good agreementwith the actual damage location for some damagescenarios. Comparison with the damage index methodshows that the proposed method yields equally welllocation predictions, even better prediction for somedamage configurations. The prediction shows a goodtrend to indicate stiffness loss, although in some casesa bit lower than expected. This can be improved byconducting a parametric study of different types orsizes of damaged beams with known stiffness loss.Delamination A does not contain a damage configura-tion that is conducive to detection through the curvaturemode shape methods. In the case of large area ofdamage, such as in condition of delamination B,where it might be detected by peaks at the edges ofthe delamination, the damage may also be viewed asa multiple instance of some highly localized damages.Both the impulse hammer excitation and sweep sineexcitation work well in generating mode shapes. Theresults from measurement with the impulse hammerexcitation provide better prediction with higheramplitude of damage indicator. Considering properaveraging process for the sweep sine testing to minimizesmoothing of damage local effect will improve theestimation results using measured data from the sweepsine testing.The present study indicates that the various damages

in laminated composite beams can be identified by thecurvature mode shape methods, and the combinedanalytical and experimental approach can be used toquantify and locate the damage through measuredcurvature mode shapes. The quality of measuredcurvature mode shapes can be improved by using asmaller sized film sensor with a larger number ofmeasurement stations. Hence, information adjacent tothe measurement station is measured in detail andlocal effects will be more apparent. Using a non-contactscanning laser vibrometer system that can obtain a largenumber of measurement points in a short period of timewill also increase the quality of measured displacementmode shapes, hence the accuracy of the identificationmethod.

ACKNOWLEDGMENTS

The carbon/epoxy composite test samples wereprovided by Honeywell, Inc. This study was partiallysupported by the College of Engineering at theUniversity of Akron and Ohio Aerospace Institute –Collaborative Core Research Program (OAI-CCRP).Mr Cole Hamey’s contribution in compiling the experi-mental measurements is greatly appreciated.

APPENDIX

In this method, a solution that separates the effect ofthe damage, in the form of step function, is presented.The curvature mode shapes are obtained explicitlyin the form of step functions and only the terms upto "1-order is retained. The governing equation(Equation (8a)) to the zeroth order of " represents theordinary differential equation for the undamagedstructure with eigensolutions of �0

i ðxÞ and �0i . Hence,we need to solve for the eigensolutions of Equation (8b),the governing equation to the first order, i.e., �1

i ðxÞand �1i .

The first-order perturbation governing differentialequation for �1

i ðxÞ is

EI0d4

dx4�11ðxÞ

� �� �0i m�1

i ðxÞ

¼ �EI0d2

dx2H x� x1ð Þ �H x� x2ð Þ½ �

d2

dx2�0i xð Þ

� �� þ �1i m�0

i xð Þ

ðA1Þ

The solution of homogeneous equation can beassumed in the form of linear combination of zerothorder eigenfunction as

�1i ¼

Xnk¼1

�ik�0i ðA2Þ

For the particular solution, it is noted that thesingularity, introduced by the step-function in the firstterms on the right hand-side of Equation (9), should beaccounted by the highest order derivative term on theleft hand-side. Thus, for the first terms in Equation (9),the solution is described as:

EI0d4

dx4�11ðxÞ

� �¼ �EI0

d2

dx2H x� x1ð Þ �H x� x2ð Þ½ �

d2

dx2�0i xð Þ

� �� ðA3Þ

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or

d4

dx4�11ðxÞ

� �¼ �

d2

dx2H x� x1ð Þ �H x� x2ð Þ½ �

d2

dx2�0i xð Þ

� �� ðA4Þ

then,

d3

dx3�11ðxÞ

� �¼ �

d

dxH x� x1ð Þ �H x� x2ð Þ½ �

d2

dx2�0i xð Þ

� �� þ C1 ðA5aÞ

d2

dx2�11ðxÞ

� �¼ � H x� x1ð Þ �H x� x2ð Þ½ �

d2

dx2�0i xð Þ

� �� þ C1xþ C2 ðA5bÞ

d

dx�11ðxÞ

� �¼ H x� x1ð Þ

d

dx�0i x1ð Þ

� ��

d

dx�0i xð Þ

� ��

�H x� x2ð Þd

dx�0i x2ð Þ

� ��

d

dx�0i xð Þ

� ��

þ1

2C1x

2 þ C2xþ C3 ðA5cÞ

�11ðxÞ ¼< x� x1 >

d

dx�0i x1ð Þ

� �� < x� x2 >

d

dx�0i x2ð Þ

� �þH x� x1ð Þ�0

i x1ð Þ

�H x� x2ð Þ�0i x2ð Þ

� H x� x1ð Þ �H x� x2ð Þ½ ��0i xð Þ

þ1

6C1x

3 þ1

2C2x

2 þ C3xþ C4 ðA5dÞ

In the above equations, H(x�xd) is the Heaviside stepfunction and hx� xdi is a ramp function. Then, byapplying the boundary conditions at x¼ 0 and x¼L,the constants C1–C4 can be determined as equal to zero.Thus, a combination of the homogeneous and particularsolution results gives an expression for the solution ofthe first-order perturbation equation

�1i xð Þ ¼

Xnk¼1

�ik�0i xð Þþ < x�x1 >

d

dx�0i x1ð Þ

� �

�< x�x2 >d

dx�0i x2ð Þ

� �þH x�x1ð Þ�0

i x1ð Þ

�H x�x2ð Þ�0i x2ð Þ� H x�x1ð Þ�H x�x2ð Þ½ ��0

i xð Þ

ðA6Þ

Thus, after considering Equation (A6), Equation (A1)becomes

EI0d4

dx4

Xnk¼1

�ik�0i xð Þ

�m�0iXnk¼1

�ik�0i xð Þ þ < x� x1 >

d

dx�0i x1ð Þ

� �(

� < x� x2 >d

dx�0i x2ð Þ

� �þH x� x1ð Þ�0

i x1ð Þ

�H x� x2ð Þ�0i x2ð Þ

� H x� x1ð Þ �H x� x2ð Þ½ ��0i xð Þ

)¼ m�1i �

0i xð Þ ðA7Þ

Multiplying Equation (A7) by �0j ðxÞ and integrating

over the domain, x¼ 0 to x¼L, and using theorthogonality conditions, give

�0j �ij � �0i �ij þ G1j � G2j þ G3j � G4j � G5j

� �¼ �1i �ij

ðA8Þ

where

G1j ¼d

dx�0i x1ð Þ

� � Z L

0

< x� x1 > �0j xð Þ

Z L

0

dx,

G2j ¼d

dx�0i x2ð Þ

� � Z L

0

< x� x2 > �0j xð Þdx

G3j ¼ �0i x1ð Þ

Z 1

0

H x� x1ð Þ�0j xð Þdx,

G4j ¼ �0i x2ð Þ

Z 1

0

H x� x2ð Þ�0j xð Þdx

G5j ¼

Z 1

0

H x� x1ð Þ �H x� x2ð Þ½ ��0i xð Þ�0

j xð Þdx

The unknowns in Equation (A8) are �ij and �1i .Hence, by using two equations, namely for i¼ j and i 6¼ j,we can solve for these unknowns. �ii is the arbitrarymagnitude of �0

i ðxÞ, which is the ith mode of the intactbeam.

For i¼ j:

�1i ¼ �0i G1i � G2i þ G3i � G4i � G5if g ðA9Þ

For i 6¼ j:

�ij ¼�0i

�0i � �0jG1j � G2j þ G3j � G4j � G5j

� �ðA10Þ

Using Equations (A9), (A10), and (6), and keepingonly the first-order perturbation terms, the eigen-solutions for the damaged beam can be written as

~�i ¼ �0i 1� " G1i � G2i þ G3i � G4i � G5i½ �� �

ðA11Þ

~�i ¼ �0i � "

Xnk¼1

�0i�0i � �0j

G1j �G2j þG3j �G4j �G5j

� ��0j xð Þ

"

þ< x� x1 >d

dx�0i x1ð Þ

� ��< x� x2 >

d

dx�0i x2ð Þ

� �þH x� x1ð Þ�0

i x1ð Þ �H x� x2ð Þ�0i x2ð Þ

� H x� x1ð Þ �H x� x2ð Þ½ ��0i xð Þ

#:

ðA12Þ

Damage Assessment of Composite Beams 207

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REFERENCES

Adams, R.D., Cawley, P., Pye, C.J. and Stone, B.J. 1978. ‘‘AVibration Technique for Non-destructively Assessing theIntegrity of Structures,’’ Journal of Mechanical EngineeringScience, 20(2):93–100.

Cawley, P. and Adams, R.D. 1979a. ‘‘The Localization of Defects inStructure from Measurements of Natural Frequencies,’’ Journal ofStrain Analysis, 2:49–57.

Cawley, P. and Adams, R.D. 1979b. ‘‘A Vibration Technique for Non-destructive Testing of Fiber Composite Structures,’’ Journal ofComposite Materials, 13(3):161–175.

Gomez, A.J.M.M. and Silva, J.M.M. 1991. ‘‘On the use of ModalAnalysis for Crack Identification,’’ In: Proceeding of the 8thInternational Modal Analysis, FL, pp. 1108–1115.

Hamey, C.S. 2003. ‘‘Dynamic Response-based Damage Detection ofComposite Structures using Smart Materials,’’ MS Thesis,Department of Civil Engineering, The University of Akron,Akron, OH.

Hamey, C.S., Lestari, W., Qiao, P. and Song, G. 2004. ‘‘ExperimentalDamage Identification of Carbon/Epoxy Composite Beams usingCurvature Mode Shapes,’’ International Journal of StructuralHealth Monitoring, 3(4):333–353.

Keilers, Jr., C.H. and Chang, F.K. 1995. ‘‘Identifying Delaminationin Composite Beams using Built-in Piezoelectrics: Part I:Experiments and Analysis,’’ Journal of Intelligent MaterialSystems and Structures, 6:649–663.

Kessler, S.S., Spearing, S.M., Atalla, M.J., Cesnik, C.E.S. and Soutis,C. 2002. ‘‘Damage Detection in Composite Materials usingFrequency Response Methods,’’ Composites Part B: Engineering,33(1):87–95.

Lestari, W. 2001. ‘‘Damage in Composite Structures: DetectionTechnique, Dynamic Response and Residual Strength,’’ PhDThesis, Georgia Institute of Technology, Atlanta, GA.

Lestari, W. and Hanagud, S. 2001. ‘‘Detection of an EdgeNotch Defect by using a Single Mode Based Methods,’’

In: Proceedings of 3rd International Workshop on SHM,pp. 1343–1355.

Lestari, W. and Qiao, P. 2005. ‘‘Damage Detection of Fiber-reinforcedPolymer Honeycomb Sandwich Beams,’’ J. Composite Structures,67(3):365–373.

Luo, H. and Hanagud, S. 1997. ‘‘An Integral Equation for Changesin the Structural Dynamics Characteristics of DamageStructures,’’ International Journal of Solids and Structures,34(35–36):4557–4579.

Messina, A., Williams, E.J. and Contursi, T. 1998. ‘‘StructuralDamage Detection by a Sensitivity and Statistical-basedMethod,’’ Journal of Sound and Vibration, 216(5):791–808.

Pabst, U. and Hegedorn, P. 1993. ‘‘On the Identification of LocalizedLosses of Stiffness in Structures,’’ ASME, DE59:99–104.

Pandey, A.K., Biswas, M. and Samman, M.M. 1991. ‘‘DamageDetection from Changes in Curvature Mode Shapes,’’ Journal ofSound and Vibration, 145(2):321–332.

Salawu, O.S. 1997. ‘‘Detection of Structural Damage through Changesin Frequency: A Review,’’ Engineering Structures, 19:718–723.

Salawu, O.S. and Williams, C. 1994. ‘‘Damage Location usingVibration Mode Shapes,’’ In: Proceeding of the 12th InternationalModal Analysis Conference, pp. 933–939.

Sampaio, R.P.C., Maia, N.M.M. and Silva, J.M.M. 1999.‘‘Damage Detection using The Frequency-response-functionCurvature Method,’’ Journal of Sound and Vibration,226(5):1029–1042.

Schultz, M.J., Pai, P.F. and Inman, D.J. 1999. ‘‘Health Monitoringand Active Control of Composite Structures using PiezoceramicPatches,’’ Composites: Part B Engineering, 30:713–725.

Stubb, N. and Kim, J.T. 1996. ‘‘Damage Localization inStructures without Baseline Modal Parameter,’’ AIAA Journal,34:1644–1649.

Zhou, Y., Tong, L. and Steven, G.P. 2000. ‘‘Vibration-based Model-dependent Damage (Delamination) Identification and HealthMonitoring for Composites Structures – A Review,’’ Journal ofSound and Vibration, 230(2):357–378.

208 W. LESTARI ET AL.

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