Composite Structures 67 (2005) 365–373

www.elsevier.com/locate/compstruct

Damage detection of fiber-reinforced polymer honeycombsandwich beams

Wahyu Lestari, Pizhong Qiao *

Department of Civil Engineering, Auburn Science and Engineering Center, The University of Akron, 244 Sumner Street, Akron, OH 44325-3905, USA

Available online 26 February 2004

Abstract

In a framework of developing a structural health monitoring for civil infrastructure, the damage identification procedure based

on dynamic response for fiber reinforced polymer (FRP) sandwich composites is evaluated. In this paper, an experimental damage

identification procedure based on structural dynamic responses and using smart sensors is conducted. Damage identification is

estimated from comparison of dynamic responses of healthy and damaged FRP sandwich beams. Correspondingly, based on the

relationship between the changes of mechanical properties and the related changes of dynamic responses (i.e., the curvature mode

shapes in this study), damage magnitude is quantified. The composite sandwich beams are made of E-glass fiber and polyester resin,

and the core consists of the corrugated cells in a sinusoidal configuration. Artificial damage is created between the interface of core

and faceplate and also in the core of sandwich beam to simulate core–faceplate debonding and core crushing, respectively. Using

piezoelectric smart sensors, dynamic responses data is collected and dynamic characteristics of the sandwich structure are extracted,

from which the location and magnitude of the damage are evaluated. As demonstrated in this study, the present dynamic response-

based procedure using smart sensors can be effectively used to assess damage and monitor structural health of FRP honeycomb

sandwich structures.

� 2004 Elsevier Ltd. All rights reserved.

Keywords: FRP honeycomb sandwich; Sinusoidal core; Damage identification; Structural health monitoring; Piezoelectric sensors; Dynamic

response; Curvature mode shape

1. Introduction

Sandwich structures are commonly used in the aero-

space and automobile structures, since they offer greatenergy absorption and increase the inertia without sig-

nificant weight penalties. Recent growing interest in fiber

reinforced polymer (FRP) composite materials for civil

infrastructure provides a unique opportunity for deve-

lopment and implementation of sandwich structures, as

both rehabilitation and new constructions. FRP com-

posite honeycomb sandwich structures have shown effi-

cient and economic applications in highway bridges, andthey provide high mechanical performance [1]. Al-

though, the primary layout of the sandwich structure is

the same, which consists of faceplates and core, the sizes

of honeycomb sandwich in civil infrastructure are much

thicker and larger than the one regularly used in the

*Corresponding author. Tel.: +1-330-972-5226; fax: +1-330-972-

6020.

E-mail address: qiao@uakron.edu (P. Qiao).

0263-8223/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compstruct.2004.01.023

aerospace and automobile structures. As with most

sandwich structures, the FRP sandwich for civil infra-

structure has a relatively lightweight core in the form of

corrugated or closed-cell geometry encased between twofaceplates. The concept of lightweight and heavy duty

applications of FRP honeycomb sandwich panels in

highway bridge decks with sinusoidal core configuration

was introduced by Plunkett [1]. Some feasibility studies

on FRP sandwich panels show that the panels efficiently

provided high mechanical performance for minimum

weight. A study on testing and field installation was

successfully accomplished [2]. Study on design modelingand optimization of FRP sandwich panels with sinu-

soidal honeycomb core were conducted by Davalos et al.

[3]. Analytical estimation of core transverse shear stiff-

ness with general configuration was studied by Xu et al.

[4]. Due to the skin effect on core properties, modeling

and analysis of sandwich structures are usually compli-

cated. The skin effect on effective properties of sandwich

plates using homogenization technique was studied byXu and Qiao [5].

366 W. Lestari, P. Qiao / Composite Structures 67 (2005) 365–373

The enclosure of core design in sandwich structures

also raises some other concerns as it restricts the access

to the core for measuring or inspection purposes, and

thus increases the difficulty to measure and monitor thestructural conditions during a period in service. Dam-

ages in sandwich structures, such as delamination within

faceplates, core–faceplate debonding, and/or core

crushing failure, can initiate tremendous property and

function degradation, which may lead to some cata-

strophic failure. The inspection method based on dy-

namic response with capability of monitoring large area

offers more effective procedure than the traditionalexisting inspection methods [6], which in many cases are

based on visual inspection techniques, especially when

the damages are not surface type. Damage in a structure

can cause changes in its dynamic response. Hence, once

the relationships between the damage and the response

changes are established, the information on the condi-

tion of structure can be extracted and estimated.

Application of piezoelectric smart sensors with flexibilityto be easily bonded to the structures makes the imple-

mentation of the damage assessments less troublesome

and more efficient.

The simplicity of structural health monitoring tech-

niques based on dynamic response has created many

interests for several years. Changes in natural frequency

and mode shapes are the most common parameters used

in identification of damage. Various methods of damagedetection that used natural frequency information were

reported by Salawu [7]. Although, the natural frequency

changes can be used to indicate the presence of damage,

in most cases the frequency alone is insufficient to un-

iquely identify the damage. Some applications on

vibration-based health monitoring of delaminated

composite structures using various parameters were re-

viewed by Zou et al. [8]. Although a damping changecan be a better indicator, the structural damping is a

complex phenomenon that is difficult to model and

quantitatively identify through experimental measure-

ments.

Interesting phenomenon on the changes in the cur-

vature mode shapes was demonstrated by Pandey, et al.

[9]. The curvature mode shapes are very sensitive to

damage, and the effect is highly localized in the region ofthe damage. Hence, the changes in the curvature mode

shapes can be applied effectively to detect damage

location in structures. Salawu and Williams [10] com-

pared the performance of both curvature and displace-

ment mode shapes for locating damage, which

confirmed this phenomenon as well. The curvature

mode shape information was used by Pabst and

Hagedorn [11] in combination with data of frequencychanges. Comparison of the measurement of cracked

beam data with mathematical model for undamaged

beam illustrated the effectiveness of the method. Simi-

larly, Luo and Hanagud [12] used the information in the

form of an integral equation relationship to identify the

location and severity of damage. Stubb and Kim [13]

used the damage index of curvature modes as an indi-

cation of damage. The curvature mode shape in theform of frequency domain information was used by

Keilers and Chang [14]; while Sampaio et al. [15] and

Schultz et al. [16] used the transfer function information.

These frequency response function (FRF) curvature

methods performed well in detecting and locating the

damage, especially for large magnitude of damage.

Lestari and Hanagud [17] introduced a method of

damage detection that used only a few low-order modesand with consideration of using mathematical relation-

ship to simultaneously detect the damage magnitude.

However, the applications of the dynamic response-

based monitoring technique to civil infrastructure are

still few, especially to civil engineering structures made

of FRP composites. Several studies on health monitor-

ing of civil infrastructure using vibration response for

bridges were reported. Detection of real damage sce-nario on a bridge was studied by Wahab and Roeck [18]

utilizing modal curvature. The modal curvature was

calculated by using the central difference approximation

of the modal displacement. The average modal curva-

ture difference was used to identify the location of

damage. The results showed that in general the lower

mode estimations were more accurate than the higher

mode ones. Using the direct stiffness calculation fromthe measured displacement mode shapes, Maeck et al.

[19] demonstrated that the cracks on a concrete bridge

could be detected as long as they remained open.

However, when the settlement that opened the cracks

was removed, the cracks were hardly identified. Com-

parative study of dynamic response-based damage

detection on a bridge was reported by Farrar and

Jauregui [20], and the sensitivity and accuracy of eachmethod were discussed. They suggested that more tests

on actual structures were needed, before the damage

detection algorithm could be applied with sufficient

confidence to warrant the field deployment of remote

monitoring systems.

In this paper, the damage assessment procedure for

full-size FRP honeycomb sandwich structures in high-

way bridge applications based on dynamic responsesand using piezoelectric smart sensors is presented. The

technique is developed based on the relationship of

curvature mode shapes of both healthy and damaged

structures. This study is a further development of pre-

vious works [21], which primarily dealt with damage

detection of small coupon scale composite laminated

beams. A brief description of the damage identification

method using the curvature mode shapes is first pre-sented, followed by the experimental testing of healthy

and damaged composite sandwich beams. Damage

assessment is applied to FRP sandwich beams with two

different artificial damages, i.e., debonding of a faceplate

W. Lestari, P. Qiao / Composite Structures 67 (2005) 365–373 367

from core and crushing failure of the core. Dynamic

responses of the damaged beams are provided, as well as

the prediction of damage information.

2. Damage detection based on curvature mode shapes

2.1. Governing equations

Relationship of the curvature mode shapes to the

bending stiffness of the beam at any point of a beam

structure can be expressed as

w00 ¼ M=EI ð1Þ

where w is the transverse displacement of the beam; w00 is

the curvature at a section;M is the bending moment; E is

the modulus of elasticity; I is the second moment of the

cross-sectional area; and EI is the beam bending stiff-ness. When the damage is introduced in a structure, the

stiffness at the location of the damage will be reduced

while at the same time the magnitude of the curvature

modes increases. Motivated by this relationship, the

damage detection that utilized changes in curvature

modes was developed [21]. In this paper, the mathe-

matical relationships, which relate the damage infor-

mation, natural frequency changes, and the modes ofthe healthy and damaged structures, are briefly re-

viewed. Only the stiffness loss due to the damage is

considered, which varies with the damage size in the

structure.

Assuming e is the stiffness loss ratio at the location of

damage (Fig. 1), the effect of damage on the stiffness

distribution of the beam can be expressed in the fol-

lowing equation

EIdðxÞ ¼ EI0f1� e½Hðx� x1Þ �Hðx� x2Þ�g ð2Þ

where H is a Heaviside step function; x1 and x2 are the

beginning and end of damage area, respectively; and EI0and EId are the bending stiffness of healthy (undamaged)and damaged beams, respectively.

The governing equation for the defective beam based

on Euler–Bernoulli beam theory and using the trans-

verse displacement function of wðx; tÞ ¼ ~/ðxÞejffiffik

pt can be

written as

x damagez

x1

x2 h

x

Fig. 1. Detailed damage region.

d2

dx2EIdðxÞ

d2

dx2~/iðxÞ

h i� �� ~kim ~/iðxÞ

h i¼ 0 ð3Þ

where m is the mass of structure, ~/i is the eigen func-

tions, and ~ki is the eigenvalues of the damaged structure.

Considering the stiffness loss parameter (e) is small, and

by using perturbations from the intact state of the beam,

the eigensolutions of the structure with the defect can be

expressed in the following form

~ki ¼ k0i � ek1i � e2k2i~/i ¼ /0

i � e/1i � e2/2

i

ð4Þ

Substituting Eqs. (2) and (4) into Eq. (3), retaining

only the terms up to e1-order and collecting the coeffi-cients for e0 and e1, the governing equations of the

damaged structure can be written as follows

e0 : EI0d4

dx4/0

i ðxÞ� �

� k0i m/0i ðxÞ ¼ 0 ð5aÞ

e1 : EI0d4

dx4/1

1ðxÞ� �

� k0i m/1i ðxÞ

¼ EI0d2

dx2e½Hðx

�� x1Þ �Hðx� x2Þ�

d2

dx2/0

i ðxÞ� ��

� k1i m/0i ðxÞ ð5bÞ

The governing equation of the zeroth order repre-

sents the ordinary differential equation for the undam-

aged structure. In this case, the stiffness and mass

distribution are constants, namely EI0 and m, with the

eigensolutions k0i and /0i . The first order perturbation

represents the governing equation of the damaged

structure. After applying the proper boundary condi-tions and assuming the homogeneous solution for the

damaged structure as the combination of the solution of

the undamaged problem, with some mathematical

manipulation, the eigensolution for the damage problem

can be obtained as

~ki ¼ k0i � ek0i /0i;xðx1Þ

Z L

0

hx�

� x1i/0j dx

� /0i;xðx2Þ

Z L

0

hx� x2i/0j dxþ /0

i ðx1ÞZ L

0

Hðx

� x1Þ/0j dx� /0

i ðx2ÞZ L

0

Hðx� x2Þ/0j dx

�Z L

0

½Hðx� x1Þ �Hðx� x2Þ�/0i/

0j dx

þ #ðe2Þ ð6Þ

where cL

�4 ¼ k0i m0

EI0,

~/i ¼ /0i � e

Xn

j¼1

bij/0j

(þ /0

i;xðx1Þhx� x1i/0i;xðx2Þhx

� x2i þ /0i ðx1ÞHðx� x1Þ � /0

i ðx2ÞHðx� x2Þ

� ½Hðx� x1Þ �Hðx� x2Þ�/0i

)þ #ðe2Þ ð7Þ

368 W. Lestari, P. Qiao / Composite Structures 67 (2005) 365–373

with

bij ¼1

k0j � k0i

� /0i;xðx1Þ

Z L

0

hx�

� x1i/0j dx

� /0i;xðx2Þ

Z L

0

hx� x2i/0j dxþ /0

i ðx1ÞZ L

0

Hðx

� x1Þ/0j dx� /0

i ðx2ÞZ L

0

Hðx� x2Þ/0j dx

�Z L

0

½Hðx� x1Þ �Hðx� x2Þ�/0i/

0j dx

ð8Þ

Taking the second derivative of the expression in Eq.

(6), one can clearly observe that the changes or discon-tinuity of the curvature modes due to damage are rep-

resented by Heaviside step function, at the location of

the damage, between x1 and x2.

2.2. Damage identification

Using Eq. (1), one can deduce that the absolute dif-

ferences between the curvature modes of the intact and

damaged structures are the highest in the region of the

damage and negligibly small outside this region. Based

on such differences, the characteristic damage in the

structure can be located. For any arbitrary location x,the absolute curvature difference between the healthy

and damaged structures for each mode can be repre-

sented as follows:

D/00i;j ¼ /00

h

n oi;j

���� � /00d

n oi;j

���� ð9aÞ

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

d denote healthy and damaged, respectively; and i and jdenote the measurement location and the mode number,

respectively. At a certain location where the damage

presents, for example at x ¼ xd, the value of D/i;xxðxdÞ issignificantly higher than the values at other locations. In

some cases, single mode identification is insufficient to

locate the damage, such as for multiple damage case or

location of damage in the proximity of a nodal point.The average of several curvature differences offers

excellent alternative and is defined as follows

Di ¼1

N

XNj

D/00i;j ð9bÞ

which Di, is the summation of damage differences fromeach mode being evaluated, noted as the curvature

damage factor (CDF) [18]; D/00i;j is the curvature differ-

ence defined in Eq. (9a) and N is the number of curva-

ture modes considered in the evaluation.

As a comparison and validation, the damage index

method is evaluated as well, where the indices and the

summation are defined as follows

bi;j ¼/00

d

n o2

i;jþPimax

i¼1 /00d

n o2

i;j

� �Pimax

i¼1 /00d

n o2

i;j

/00h

� �2

i;jþPimax

i¼1 /00d

� �2

i;j

� Pimax

i¼1 /00d

� �2

i;j

ð10aÞ

eD i ¼Xj

bi;j ð10bÞ

where eDi is herein noted as the damage index.

Once the damage is identified at station xd, the

magnitude of the damage at this location can be defined

by using the damage magnitude difference of the modes,

D/i;xxðxdÞ, between the intact structure and the one with

damage. This damage magnitude or stiffness loss (e) canbe calculated using the relationship of the frequencies inEq. (6) or the relationship of the curvature modes in Eq.

(7). As the frequency measurements at low frequency are

sensitive to interferences, hence the damage magnitude

estimation is calculated based on the mode shape rela-

tionship. Provided the location xd is known, the damage

magnitude in the form of stiffness loss can be defined as

follows

e ¼/i;xx � /di;xxPn

k¼1

Gj

k0i �k0j

d2

dx2 /0j � ½Hðx� x1Þ �Hðx� x2Þ� d2

dx2 /0i ðxÞ

ð11Þ

with

Gj ¼ /0i;xðx1Þ

Z L

0

hx� x1i/0j dx� /0

i;xðx2ÞZ L

0

hx� x2i/0j dx

þ /0i ðx1Þ

Z L

0

Hðx� x1Þ/0j dx� /0

i ðx2ÞZ L

0

Hðx

� x2Þ/0j dx�

Z L

0

½Hðx� x1Þ �Hðx� x2Þ�/0i/

0j dx

where /i;xx and /di;xx are the measured curvature modes

of the healthy and damaged beams at the ith mode,respectively.

3. Experimental procedure and results on a

cantilevered beam

3.1. Sandwich specimens

The sandwich panel investigated in this study was

manufactured by Kansas Structural Composites, Inc.

(KSCI, Russell, Kansas). The sandwich panel consists oftwo faces FRP laminates, which are co-cured with the

core. The configuration of the sandwich beam is shown

in Fig. 2. The core geometry composes of closed hon-

eycomb type FRP cells. The waved flutes or core ele-

ments are produced by forming the FRP sheets to a

corrugated mold. Unlike the traditional honeycomb

sandwich structures, the shape of the FRP corrugated

z

y

x

Fig. 2. Configuration of sandwich panel with transverse sinusoidal

core.

W. Lestari, P. Qiao / Composite Structures 67 (2005) 365–373 369

cell wall is defined by a sinusoidal function. Flat andwaved FRP cells are combined and bonded sequentially,

which is similar to the process of paper resin sandwich

panel. The distance between two flat is about 50.8 mm

(2.0 inches), while the half wave length of sinusoidal cell

is about 101.6 mm (4.0 inches). Then, the assembled

cellular core is co-cured with the upper and bottom face

laminates to build a sandwich panel.

Sandwich beam specimen with transverse core (seeFig. 2) was used in this experiment. The beam has a

cross-section of 127 · 203 mm (5.0 · 8.0 inches) with

length about 2.6 m (102 inches). The thickness of the

face laminate is 11.0 mm (0.428 inches); while the

thickness of the core is 105 mm (4.125 inches). Material

properties of the sandwich beam used in this calcula-

tion are obtained from macro/micro mechanics analysis

of the composite materials [3,4,22] and are listed inTable 1.

Table 1

Material properties of the sandwich beams

Face laminate Sinusoidal core

Exx (108 N/m2) 196.2248 Exx (10

8 N/m2) 5.2937

Eyy (108 N/m2) 127.5530 Eyy (10

8 N/m2) 0.4492

Gxy (108 N/m2) 37.6454 Gxz (10

8 N/m2) 3.2859

– – Gyz (108 N/m2) 1.2638

Fig. 3. Experime

3.2. Health monitoring experiments

A cantilever beam configuration was used in the dy-

namic tests. The free length of the beam after clampingwas 2.3876 m (94.0 inches) and was divided equally into

31 measurement points with distance of 76.2 mm (3 in-

ches) apart. To simulate a cantilevered condition, one

end of the beam was clamped in the Baldwin machine

with enough pressure such that the beam specimen

posed well in place. The excitation force was provided

by an impulse hammer PCB 086C03 by hitting at the tip

of the beam. Piezoelectric materials in the form ofpolymer film (polyvinylidenefluoride, PVDF) were used

as sensors, and the PVDF sensor films were bonded to

the specimen using double-sided tapes. Data from sen-

sor and actuator were connected and recorded through a

data acquisition system. In these experiments, the mul-

tiple sensors connected to multiple channels were used at

each set of test data. Consequently, very short time was

required to collect one set of data, which allowed us toacquire more data at each measurement point. The

experimental set-up is shown in Fig. 3. Every set of

measurement consisted up to seven sensors. For each

set, 30 hits of the hammer were conducted, which yiel-

ded 30 measurement data for each point. Accordingly,

with more data for averaging, the noise effects were re-

duced, and better dynamic response results were ac-

quired.After acquiring data for the healthy sandwich beam,

the beam was artificially damaged into two conditions at

distance between 762 and 965 mm (30–38 inches) from

the root or around sensor locations 11–13. First, the

bonding between the core and faceplate was cut off

through width at the above certain given location, to

simulate core-faceplate debonding. Second, the core

beneath the core–faceplate debonding was crushed, tosimulate core crushing failure. At each damage condi-

tion, the same testing procedure as the healthy beam was

repeated. Once the measurement data were acquired,

ntal set-up.

Fig. 4. FRF comparison among the healthy and damaged beams from

measurement point 30 (healthy––the healthy beam; delam––the beam

with core–face sheet debonding; and crush––the beam with core

crushing).

Fig. 5. Curvature mode shapes of the first six m

370 W. Lestari, P. Qiao / Composite Structures 67 (2005) 365–373

these time domain data were transferred into the fre-

quency domain using a MatLab routine. Examples of

the frequency response function (FRF) results for the

healthy and damaged beams are presented in Fig. 4.Modal analysis for obtaining mode shapes was per-

formed by using the commercial code IDEAS Test

modules. The PDVF film sensors measured the average

curvature under its area. Hence, the results of modal

analysis are the curvature mode shapes. This is an

apparent advantage, since the procedure of taking sec-

ond derivatives from the displacement mode shapes is

avoided, which may cause loss in accuracy. From 31measurement points, up to the first six modal shapes can

be well extracted. The curvature mode shapes of the first

six modes for healthy and damaged modes are presented

in Fig. 5, and the corresponding curvature differences

for both damage configurations are presented in Fig. 6.

odes for the healthy and damaged beams.

W. Lestari, P. Qiao / Composite Structures 67 (2005) 365–373 371

From the curvature mode shapes (Fig. 5), the com-

parison shows that the damage indeed changes the

modal curvature. The core crushed damage caused more

stiffness loss than the core–faceplate debonding asindicated by the level of magnitude in the peaks. These

effects can be seen clearly in the form of curvature dif-

ferences as shown in Fig. 6. It is also noticeable that at

higher modes, the nodal points of damaged curvature

modes are shifted away from the original of the

undamaged modes. This phenomenon can be clearly

observed from the fourth mode and up, see Fig. 6(d)–(f).

The difference of modal curvature due to this shiftingcan be quite significant as demonstrated in Fig. 6(d) and

(f), which can cause misleading peaks in the curvature

difference and misinterpreted as damage. For the beam

with the crushed core, the curvature differences of modes

4 and 6 have another major peak around sensor location

Fig. 6. Curvature mode shape differences of th

20, besides the peak at damage location (location 13).

For mode 5, the peak due to shifting is much smaller.

When the damage is minor, such as in the case of core–

faceplate debonding, the curvature difference magnitudebetween the one caused by damage and the other caused

by shifting are at the same level, see Fig. 6. Conse-

quently, the curvature difference results are less apparent

and the damage location estimation becomes more

complicated.

The curvature damage factor (Di) and damage index

summation (eDi) are calculated according to Eqs. (9b)

and (10b), respectively, using the first six modes. Theresults are presented in Fig. 7. In general, the results

show good prediction for the location of damage, which

are between sensor locations 11–13, for both cases. For

the core–faceplate debonding case, the curvature dam-

age factor (CDF) method has peaks at the border of the

e first six modes for the damaged beams.

Fig. 7. Damage identification for both the damage configurations, (a) curvature damage method and (b) damage index method.

372 W. Lestari, P. Qiao / Composite Structures 67 (2005) 365–373

damage (locations 11 and 13). However, it has notice-able peaks at other location as well. The damage index

method also generated peaks at other location, yet is

much lower than the peak at the damage location.

Shifting in the nodal point at higher mode, which dis-

cussed previously, contributes largely to these peaks.

Some of these peaks can be interpreted as other damage

with smaller stiffness loss. Considering only lower modes

of curvature will eliminate this phenomenon and im-prove the identification results.

The curvature damage factor method shows more

pronounced peak at the location of damage than the

damage index method, which has some peaks at other

locations as well. Since the curvature damage factor is

calculated directly from the results, it exhibits better

magnitude distinction between the beam with core–

faceplate debonding and with core crushing damage,which can be used as damage severity indication.

3.3. Damage identification

Once the damage location was estimated from the

measurement data, the damage effects can be quantified

Table 2

Stiffness loss estimations

Mode number Sandwich beam with debonding

Curvature

difference

Location (mm) Stiffness loss

1 0.2362 965.2 40.4

2 0.092 889 13.5

3 0.2422–0.2344a 812.8–965.2a 29.5–39.5a

4 0.2466–0.1454a 812.8–965.2a 164.6–31.9a

5 0.1439 812.8 23.1

6 0.2612 812.8 59.0

aCurvature difference at two damage boundaries, which provides a range

by using Eq. (11). The curvature differences from thefirst six modes were evaluated. The mode shapes were

normalized with respect to themselves prior to the cal-

culation procedure. In general, the curvature difference

between healthy and damaged beams yielded two peaks

at both ends of damage boundaries, though in some

cases only resulted in one clear peak. Estimation from

the curvature difference with two peaks yields a range of

stiffness loss calculations from each peak. Results ofestimation of stiffness loss from the first six modes are

presented in Table 2.

The estimation results from mode number 4 in Table

2 are unacceptable, since the damage location existed in

proximity of the nodal point of mode 4. The curvature

differences for core–faceplate debonding case of modes 2

and 5 are negligible; hence their estimation results are

incorrect as well. Omitting these results, it can be con-cluded that the debonding of a faceplate from the core

caused loss of stiffness about 30–60% in the region of

damage. On the other hand, the core crushing damage

produced larger loss of stiffness, which is between 40%

and 90%. Although the calculation only estimated fairly

wide range of stiffness reduction, it gave a good indi-

Sandwich beam with core failure

(%) Curvature

difference

Location (mm) Stiffness loss (%)

0.2946–0.2605a 812.8–965.2a 42.3–44.5a

0.5143–0.2418a 812.8–965.2a 89.6–31.4a

0.355–0.2792a 812.8–965.2a 43.2–47.1a

0.5923 965.2 130.0

0.7733 889 85.7

0.2947–0.5277a 812.8–965.2a 66.6–90.9a

of stiffness loss estimation.

W. Lestari, P. Qiao / Composite Structures 67 (2005) 365–373 373

cation of damage magnitudes due to two different

damages. Results from the high modes might not as

reliable as the lower ones, since the nodal point shifting

affected damage magnitude. The assumption in theanalytical relationship used for estimation calculation,

which did not take into account the shifting of nodal

points, added discrepancy of the results at high mode as

well. Nonetheless, this method, which provides the

quantitative estimation based on the curvature differ-

ence, indicates the local effect of damage, instead of the

global effect of damage generally offered by the fre-

quency-based method.

4. Conclusions

In this study, a damage detection and structural

health monitoring procedure based on curvature mode

shapes and using piezoelectric smart sensors is devel-oped. It indicated that the proposed technique can be

effectively and appropriately applied to full scale com-

posite structures (e.g., large FRP honeycomb sandwich

structures) suitable for civil infrastructure. The locations

of the damage for both damage configurations (i.e., the

core–faceplate debonding and core crushing, respec-

tively) were identified properly using the curvature

damage factor and damage index method, while themagnitude of the damage was evaluated through the

stiffness loss. The damage detection technique proposed

in this study can be implemented in inherent damage

identification and health monitoring of large civil com-

posite structures.

Although the implementation of the method is quite

simple, a great care needs to be taken while generating

experimental data. Number of measurement points willdefine the maximum number of mode shapes generated.

The larger number of measurement points is, the more

mode shapes can be generated. However, using the

lower curvature modes yields better results than using

the higher modes, as at higher modes the nodal curva-

ture points of damaged modes shifting from the original

position of undamaged modes. In addition, this curva-

ture mode-based method offers information on localeffects of damage. Piezoelectric smart sensors provide

direct extraction of the modal curvature conveniently,

without estimation calculation using central difference

method as for the modal displacement measurement.

Acknowledgements

The test samples were provided by the KSCI, and we

thank Dr. Jerry Plunkett of KSCI and Prof. Julio F.

Davalos of West Virginia University for their technical

contribution and support. Partial financial support for

this study is received from the National Science Foun-

dation––Partnerships for Innovation program (EHR-

0090472) and the Ohio Aerospace Institute––Collabo-

rative Core Research Program (OAI-CCRP#2002-04).

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