Damage Identification- Curvature Mode Shape

333

Experimental Damage Identification of Carbon/

Epoxy Composite Beams Using Curvature

Mode Shapes

Cole S. Hamey,1 Wahyu Lestari,1 Pizhong Qiao1,* and Gangbing Song2

1Department of Civil Engineering, The University of Akron, Akron, OH

44325-3905, USA2Department of Mechanical Engineering, University of Houston, Houston, TX

77204-4006, USA

Many composite materials and structures are susceptible to defects, which can significantly reduce the

strength of structures and may grow to failure. To avoid the catastrophic failure of structures,

development of a reliable method of structural health monitoring is one of the most important keys in

maintaining the integrity and safety of structures. Dynamic response-based damage detection offers

a simple procedure as an alternative to the conventional nondestructive evaluation techniques.

However, this technique depends on the quality of measured data for its identification accuracy. In this

article, experimental aspects of dynamic response-based damage detection technique on carbon/

epoxy composites are addressed. Smart piezoelectric materials are used as sensors or actuators to

acquire the curvature modes of structures. These materials are surface-bonded to the beams. An

impulse hammer is used as an actuating source as well. Four types of damage detection algorithms

are evaluated for several possible damage configurations with two different excitation sources. The

quality of damage identification with the four different detection algorithms is discussed. These

experimental damage identification techniques using curvature modes and piezoelectric materials can

be effectively used in damage detection and health monitoring of composite structures.

Keywords dynamic response damage detection composite materials piezoelectricsensors and actuators composite beams

1 Introduction

Advanced composite materials have been

extensively used in structural applications, due to

their advantageous characteristics, such as high

stiffness and strength-to-weight ratios, improved

fatigue resistance, and superior damage tolerance

capability compared to metallic structures. Carbon/

epoxy composites have higher stiffness and

strength properties than other composites, such

as the commonly used E-glass/epoxy composites.

These advantageous properties have led to the

use of carbon/epoxy composites in structures that

undergo higher stresses, such as aircraft and

aerospace structures. However, the carbon/epoxy

composite laminates, like other composite mate-

rials and structures, are susceptible to defects,

which can originate from imperfections in

*Author to whom correspondence should be addressed.

E-mail: [email protected].

Copyright 2004 Sage Publications,Vol 3(4): 0333353

[1475-9217 (200412) 3:4;333353; 10.1177/1475921704047502]

Copyright 2004 Sage Publications,Vol 3(4): 0333353

[1475-9217 (200412) 3:4;333353; 10.1177/1475921704047502]

manufacturing process or develop during their

service life. Defects like fibre breakage, matrix

cracking, debonding between fibres and matrix,

and delaminations or interlayer cracks, are typical

damages in composite structures. These defects

can significantly reduce the strength of structures

and may eventually grow to failure. When the

failure occurs, it is often catastrophic, leading to

loss of human life and/or monetary losses. Such

failures often cause devastating effects on the

psychological state of the public as well.

The development of a reliable method of

structural health monitoring is one of the most

important keys in maintaining the integrity of

structures. Some of the nondestructive evaluation

equipment that utilise technologies such as X-ray

imaging or eddy current can identify damages;

but often these technologies are difficult to

implement on the site. In this study, dynamic

response-based damage detection techniques using

smart materials are explored for carbon/epoxy

composites. The dynamic response of structures

can offer unique information on defects that may

be contained within these structures. Changes in

the physical properties of the structure due to

damage will alter the dynamic responses such as

natural frequencies, damping and mode shapes.

These parameter changes can be extracted to

predict damage information, such as the presence,

location and severity of damage in a structure.

The dynamic response-based damage detec-

tion method is an interesting method due to its

simplicity of implementation. One method, in

which the dynamic response is utilised, is to use

the curvature mode shapes to detect damage. The

curvature mode shape change due to damage has

a local effect in nature; hence, it can be used

to locate damage properly, provided that the

changes of curvature are closely related to the

changes of physical properties in the structures.

The curvature mode shape methods have a poten-

tial to identify damage types that are hardly

visible or lay beneath the surface, such as delami-

nation. The challenge is to develop the ability to

identify the changes of response parameters (e.g.,

deformations and dynamic characteristics) and

interpret them in relation to the changes in phys-

ical properties of the structures. Moreover, the

ability to differentiate the types of damage in a

structure is also very important, since two differ-

ent types of damage may result in the same

changes in the parameters tested. For example,

a beam with large delamination and a beam

with two small delaminations may cause the same

frequency changes. Moreover, damage detection

in composite structures is more difficult com-

pared to the metallic structures due to the aniso-

tropy of the material, the conductivity of the

carbon fibre, and the fact that much of the

damage often occurs beneath the surface and is

hence hardly detectable or visible.

Some of the research studies related to

dynamic response-based techniques are sum-

marised here. Using a torsional spring to model

the change in stiffness at a crack location, an

analytical solution and damage identification to a

cantilever beam was developed by Rizos et al. [1].

The displacement mode shapes were determined

experimentally and analytically, and their com-

parison showed promising results. In a review of

frequency-based methods, Salawu [2] discussed

the effects of damage on the natural frequencies

of a structure. However, the frequency-based

methods might not confidently be able to deter-

mine the state of the structure if the change in

the natural frequencies was less than 5%. In

conclusion, the natural frequencies alone might

not be sufficient for a unique identification and

location of structural damage.

More effective methods of damage detection

using the curvature mode shapes have been

considered and proposed. Pandey et al. [3] were

among the first to develop the idea of damage

detection using the curvature mode shapes.

Although, the absolute difference between the dis-

placement mode shapes of damaged and undam-

aged beams was not discernable between the

damage location and other parts of the beam, the

curvature modes showed a significant change at

the damage location. Luo and Hanagud [4] devel-

oped a relationship between the dynamic proper-

ties of damaged and undamaged structures in the

form of an integral equation to identify damage.

The detection algorithm used the eigenvalues as

well as the eigenfunction information of the system

to identify the locations and corresponding sever-

ities simultaneously, with the input to the flaw

detection only based on the experimental data.

334 Structural HealthMonitoring 3(4)

Wahab and Roeck [5] conducted an experi-

mental damage detection study using the curva-

ture mode shapes of a real structure. Based on the

displacement data gathered during the razing of

bridge Z24 in Switzerland, the curvature mode

shapes were derived by a central difference approxi-

mation. The mode shape absolute difference aver-

aging noted as the curvature damage factor

(CDF) was used as a detection criterion. Wahab

[6] further examined a model updating in combi-

nation with the curvature mode shapes for

damage detection. In this method, an iterative

process was initiated which allowed the param-

eters of the simulated beam to converge to meet

the parameters of the actual beam. The conver-

gence of the model did not improve with the

inclusion of curvature data. The sensitivity of

results when the curvatures were included did not

change substantially. Lestari and Hanagud [7]

derived a mathematical relationship between

an intact beam and a damaged beam, to identify

the damage location and severity simultaneously.

Providing experimental data for both the healthy

and damaged beams were well acquired, the

damage could be identified by using a single

mode, based on the curvature mode shapes infor-

mation.

Wang and Wang [8] explored the feasibility

of using the piezoelectric materials for modal

testing on a cantilever beam. Different combina-

tions of sensors and actuators were simulated.

From a comparison of the modal damping

ratios and natural frequencies, it was demon-

strated that the PVDF sensors and the PZT

actuators were able to generate results that

were similar to those of an accelerometer and

an impulse excitation.

Building on the reliability of curvature

mode-based methods and considering the ease of

application of frequency-based methods, Sampaio

et al. [9] developed the frequency response func-

tion (FRF) curvature method. The benefit of this

method was that there was no need to perform

a complex modal analysis of the structure. The

central difference approximation was applied to

the FRF to obtain the second derivative FRF

curvature. Using data from the Interstate 40

bridge in New Mexico, the experimental results

of the FRF curvature method were demonstrated,

and the damage was located. In a comprehen-

sive experimental and numerical study on the

Interstate 40 bridge, different methods of damage

detection (i.e. damage index, curvature mode

shape, change in flexibility, change in uniform

load surface curvature, and change in stiffness)

were compared [10,11]. Comparisons of different

damage detection algorithms indicated that the

use of damage index yielded the best results,

whereas the flexibility method and the stiffness

method provided poor results.

The main goal of this study is to develop

damage detection techniques based on the

dynamic response and the utilisation of smart

materials. Most of the experimental curvature

data in literature were obtained by approximating

the second derivatives from displacement data.

Experimental determination of curvature mode

shapes by directly measuring the curvature modes

most likely yields better results than those

obtained from the displacement mode shapes.

With the availability of cost-effective and easy to

install piezoelectric materials, the curvature mode

shapes could more easily be obtained experimen-

tally. This paper will address some problems on

experimental aspects of structural health monitor-

ing based on dynamic response. In particular, the

changes of measured curvature in the form of

mode shapes or the frequency response functions

(FRF) are used to identify damage in composite

structures. Four damage detection algorithms

based on the curvature shapes and curvature FRF

are reviewed.

To aid in the detection of damage, smart

materials are often used. Piezoelectric materials

are the most commonly used smart materials in

structural health monitoring, due to their ability

to act both as an actuator and as a sensor and

their flexibility to be sized for specific applica-

tions. In this study, the piezoelectric materials in

the form of ceramic (leadzirconatetitanate,

PZT) and polymer film (polyvinylidenefluoride,

PVDF) are used as the actuator and the sensor,

respectively. Unlike the PZT ceramics, the PVDF

films are flexible which allows for more easy

bonding to curved and non-smooth surfaces.

With the use of double-sided tape, the PVDF

films can be attached to a structure and used

repeatedly.

C. S. Hamey et al. Experimental Damage Identification of Carbon/Epoxy Composite 335

2 Damage Detection

In this study, several existing detection

algorithms are employed to detect damage of

carbon/epoxy laminated composite beams.

Contrary to most results in the literature, the

directly measured curvature data are applied

to the method, and comparisons among differ-

ent algorithms are made and discussed. The

methods being considered include the absolute

difference of curvature mode shape method, the

curvature damage factor method, the damage

index method, and the FRF curvature method.

A brief review of these detection algorithms is

presented in the following.

For comparison purposes between the

undamaged and damaged beam modes in curva-

ture mode-based damage detection methods, it

is best to first develop weights by comparing

the undamaged structure to the theoretical one

wij ij, theoreticalij

1

where wij is the weight, ij, theoretical is the theo-retical curvature, and ij is the experimentallymeasured curvature for ith mode shape at

location j. These weights are applied to both the

damaged and undamaged structures to allow for

greater ease in comparison

0ij wijij 2

0ij, damaged wijij, damaged 3

where 0ij and 0ij, damaged are, respectively, the

weighted undamaged and damaged curvatures

used for comparison. By applying the weight to

the undamaged specimen, it forces the measured

curvatures into the theoretical ones (Equation

(2)). The weighted shapes are also then normal-

ised such that

00 T 1 4

It is important to note that the weighting

function may cause large discrepancies at loca-

tions where the undamaged beam approaches

zero at modal nodes at different locations as

compared to the damaged structure. At this

particular location, a mode shape magnitude

divided by a small number of the weighting

function will produce large magnitude of the

weighted shape.

The Absolute Differences Method (ADM)

is the simplest method to employ. This method

takes the absolute difference in the magnitudes

of the curvature mode shape as:

0ij 0ij 0ij, damaged

5

where 0ij is the absolute difference in theundamaged and damaged modes. This method

examines each mode individually and is classified

as a single mode method. Results from this

method can vary depending on the boundary

conditions, damage locations, mode of interest,

and sensitivity. This variation led to the develop-

ment of other multiple mode methods such as

the curvature damage factor and damage index

methods.

The Curvature Damage Factor (CDF)

method involves a similar procedure as the

absolute difference method, where 0ij is deter-mined from the absolute differences. However,

the curvature damage factor was developed to

consider all of the modes at once [5],

CDFi 1N

XNj10ij 6

where CDFi is the curvature damage factor at

location i and N is the number of modes that will

be examined. This method is considered more

accurate than the absolute difference method

because it eliminates the problems caused by the

damage location in conjunction with certain

modes. Other problems still persist, in particular

the problem of sensitivity.

On the other hand, the Damage Index

Method (DIM) allows for greater sensitivity. This

method is also more complex as compared to

the other methods. In this study, the formulation

of the damage index is similar to that used by


Farrar and Jaurequi [10,11]

ij0ij,damagedn o2

Pimax1 0ij,damagedn o2

Pimax1 0ijn o2

0ijn o2

Pimax1 0ijn o2

Pimax1 0ij,damagedn o2

7

where ij is the damage index at location i formode j. Considering multiple modes, the sum-

mation of ij at one location for every mode isdefined as follows:

i Xj

ij 8

where i is the damage index at location i fromthe summation of the single mode damage

indices. This method is considered accurate and

valid for damage detection; however as with the

two previous methods, the modal analysis needs

to be conducted in order to employ these damage

detection algorithms.

Alternatively, the FRF Curvature Method

(FCM) offers a procedure without performing

modal analysis. Usually, the FRF is measured

from the displacement response. Then, the FRF

curvature for each location is calculated using a

central difference formulation.

00 ! ij 1

h2 ! i1, j 2 ! ij ! i1, j 9

where ! ij is the FRF measured at location ifrom an input force at location j. However, since

the FRF measured by the PZT ceramics or

PVDF films is already a function of curvature,

the numerical derivative in Equation (9) is not

necessary. Therefore, over a given frequency

range, the damage location will be indicated by

the following expression:

00 ! ijX!

00 ! ij 00 ! ij, damaged 10

where 00 ! ij is the absolute difference in theFRF curvatures. This method is fairly new and

only a few studies have reviewed the validity

of applying this method to experimental data.

Therefore, the accuracy of this method will be

determined by comparing the results with the

ones obtained by the other three methods.

3 Specimen Considerationsand Experimentation

In this study, six carbon/epoxy composite

beam specimens were tested. Each sample was

made of carbon fibre and epoxy resins and had a

[0/90]4T lay-up for a total of eight layers. The

thickness of each layer was 0.22mm (0.0086 in.)

for a total thickness of 1.75mm (0.0688 in.). Each

sample had a width of 25.4mm (1.00 in.) and a

length of 241.3mm (9.50 in.) (Figure 1). When

clamped in the cantilever configuration, the beam

samples had a free span length of 228.6mm

(9.00 in.). An 8mm 12mm piece of PZT ceramicwas attached to each composite sample as an

actuator. The PVDF films were used as sensors

and the beam sample was divided into 16 points

to best accommodate the films (Figure 2). Each

point was aligned with the centre of the PVDF

during the testing.

The experiment began with two undamaged

beams. Both of these samples were first tested,

and their undamaged mode shapes were obtained.

The undamaged mode shape used for comparison

Figure 1 An undamaged carbon/epoxy composite beam specimen.


was derived from an average of the two samples.

Later, one of the undamaged beams was artifi-

cially damaged by cutting a notch with a hand-

saw. The notch had around 1.6mm (0.0625 in.)

width and cut about 60% of the beam thickness

through the width of the beam. The other four

beams were already damaged, three samples

contained delamination at various locations and

the fourth had an impact damage. The delami-

nations were created during the fabrication of the

samples by inserting a piece of Teflon tape

between the second and the third layers of the

material at the desired locations. The impact dam-

age was created by dropping an 8.0 kg (17.6 lb)

mass from a height of 304.8mm (12.0 in.) onto an

undamaged carbon composite beam sample, thus

allowing for the testing and comparing of five

different damage conditions: one saw-cut notch,

three delamination types (A, B and C), and one

impact damage. The beam with a delamination

type A (Delam A) has a 25.4mm (1.00 in.)

delamination beginning approximately 31.75mm

(1.25 in.) from the fixed support or began at

sensor location 2 and ended at sensor location 4.

Information of all five damaged-beam configura-

tions are summarised in Table 1, and the corres-

ponding geometry are presented in Figure 3. For

beam samples with delamination, a small bump

through width between sensor locations 10 and

11 was discovered. This imperfection was devel-

oped during the manufacturing process of the

composite plates with delamination before it was

cut into several beams.

The experimental set-up of dynamic testing is

presented in Figure 4. Two different sources of

excitation were employed, i.e., impulse excitation

and continuous excitation by using a PZT

actuator. For a testing with continuous excita-

tion, a sweep sine with a magnitude of 140V was

run through the actuators to excite the beams. A

Hewlett Packard 33120A waveform generator

was used to induce the sweep sine. The sweeps

took place over a frequency range from 1 to

2000Hz over a time of 120 s. The linear and logari-

thmic sweeps were used to excite each beam,

since an average of these two sweeps generates

the best mode shape results. The responses at

each point were recorded by a dSPACE data

acquisition system as time domain responses.

Two sets of sweep tests were conducted on the

damaged beams: one set had the sensors located

on the same side of the beam as the damage was

located, and in the other test the sensors were

located on the opposite side of the damage.

Table 1 Type and damage location of composite beam samples.

No. Damage type

Damage location,from the fixed end

(mm)Damage area

(mm)

Damage locationaccording to sensor

location

1 Delaminated A 31.7557.15 25.4 242 Delaminated B 31.7582.55 50.8 263 Delaminated C 69.8595.25 25.4 574 Impact 57.1582.55 25.4 465 Saw cut 80.5582.15 1.6 6

Figure 2 Schematic of the sensor layout for the carbon/epoxy composite samples.


For impulse excitation, a PCB impulse

hammer was used as the actuator. The impulse

location remained stationary and was located at

the free-end of the beams. A minimum of ten sets

of data was collected for each sensor location.

For all samples twenty data sets were acquired

at each point, except for the saw-cut sample and

the first undamaged sample that each had ten

data sets at a point. The FRF at each point were

averaged over all the measured data sets to help

eliminate noise interference recorded by the

sensors. These data sets were recorded at a range

from 1 to 2000Hz; however, one data set only

took one second to be conducted. The procedure

for data reduction of this method is the same as

that for the sweep sine methods once the FRF

has been determined. For both the tests, the

piezoelectric film sensors were roved along the 16

1. Del A

2. Del B

3. Del C

4. Impact

5. Saw-cut

Figure 3 Geometry of composite beam sample configurations.


measurement locations to allow direct generation

of the curvature mode shapes.

The procedure for the data reduction and

shape generation can be described briefly as

follows. Using MATLAB code, the time domain

responses are transferred into frequency response

functions (FRF) and extracted as vectors. These

vectors are then converted into I-DEAS functions

with the aid of IMAT interface program. Using

I-DEAS test module, the modal analysis of the

experimental results is performed and the curva-

ture mode shapes are generated. Once the mode

shapes are generated, the shapes are exported

back into MATLAB, where they are examined

thoroughly and weighted to the theoretical shapes.

4 Damage Detection Using PZT asActuator

There are two possibilities of attaching the

sensors into the specimens, i.e., on the same side

and on the opposite side of the damage, which

can be detailed as follows. A sensor is considered

on the same side as the damage if, in the case of

delamination, the sensors are bonded to a surface

which is closer to the plane of the delamination.

In the case of impact damage the sensors are

located on the concave side of the compression

caused by the impact. A sensor is opposite to the

damage when, in the case of delamination, the

sensors are located on the surface which is

farthest from the delamination plane. In the case

of impact damage, the sensor is located on the

convex side of the tension caused by the impact.

This idea is clearly illustrated in Figure 5. The

PZT ceramic patch bonded to the beams near the

cantilever end was used as an actuator to excite

the structure using a sweep sine.

Based on the results of both cases, there was

an insignificant change in the ability to detect the

damage, with delamination B being an exception.

In the case of the same side sensor/damage

configuration, it was difficult to detect large

Figure 4 Experimental set-up.

Figure 5 Illustration of same-sided and opposite-sided sensors.


delamination such as delamination B. This was

probably due to the fact that the delaminated

portion of beam has an apparent independent

vibration. When a sensor was located on the

delamination region as illustrated in Figure 6,

the same side sensor recorded the curvature of

the delaminated area as well, as if it were a short

fixedfixed beam over the delamination span.

The experimental results discussed in this

article are those with the sensor and the damage

on the same side, with exception of the delamina-

tion B case, of which the results from the opposite

side configuration are discussed. Complete experi-

mental results of the study can be found in

Hamey [12].

4.1 Frequency Measurements

The results of frequency measurements from

experiments with sweep sine excitation are pre-

sented in this section. The first three of the natural

frequencies of the damaged beams are compared

with the undamaged beam results. In these com-

parisons, an average of undamaged natural

frequencies is used. Both the undamaged beams

had slightly different natural frequencies for each

mode, of which the maximum difference is around

2.4% at the lowest natural frequency (the first

mode). These values are summarised in Table 2.

An examination of the natural frequencies

reveals a significant change for beams with

delaminations (Table 3) and saw-cut damage

(Table 4). For the beam with impact damage, the

frequencies are relatively unchanged by the pre-

sence of damage. In particular, the first natural

frequency demonstrates substantial changes,

between 11 and 20%. At the second and third

frequencies the percentage of change is smaller,

but it is still noticeable, with an average of

about 3%.

Compared to the undamaged beams, the first

natural frequency of delamination B, where the

sensor was located at the opposite side of the

delamination (oppDelam B), has the highest

change of 20.6%. This might be due to the lack

of the sensors near the fixed end, where the first

mode readings were typically analysed. Overall,

the values of the frequency changes of Delam C

are comparable to those of Delam A, since the

delamination length in both the cases are the

same, although their locations are different. In

the impact damage case, the natural frequencies

are actually increased slightly instead of being

decreased or relatively unchanged (Table 4). The

first natural frequency demonstrated less than

3% of increase. For the saw-cut damage case,

the natural frequencies changed quite dramati-

cally. The first is reduced by about 15%, the

second changed by 6.4% and the third by almost

4%; these changes are substantial when compared

to the changes by the other damage conditions.

4.2 Mode Shapes

The undamaged beam curvature mode shapes

were generated by averaging the mode shapes

from two undamaged beam samples to provide

the best representative shape as a base for later

comparison. The average mode shapes are shown

in Figure 7(a), which are better than either of

the other two individually. Even before being

Figure 6 Illustration of the sensors when placed on a large delamination

Table 2 A comparison of the natural frequencies for theundamaged beams.

Mode Undam. 1 Undam. 2 Ave. Undam. % Change

1st 33.2 32.4 32.8 2.422nd 182.2 179.3 180.8 1.573rd 502.5 498.4 500.5 0.81


weighted, the average shapes more closely resem-

ble the theoretical shapes.

Based on a visual inspection of the curvature

mode shapes (Figure 7(b) and (c)), the damage

location of delamination A and B cannot be

discerned. The mode shapes are not as smooth as

the ones obtained from the undamaged beams,

even after weighting them, the damage location

is still not recognisable. For Delam C, the

damage location could be somewhat discerned

(Figure 7(d)). In all three modes there was some

distinct pattern of shapes around the locations of

sensors 5, 6 and 7. This became more evident

after the shapes were weighted. In particular, at

point 5 where the delamination began, the change

could be easily recognised. Similar indication is

also noticed at the curvature mode shapes of

impact-damaged beam (Figure 7(e)). The impact

damage location could be predicted around loca-

tion 5. For the saw-cut damaged beam, the

damage location could be somewhat discerned

from mode 1, around location 6 (Figure 7(f )). It

is clearly evident that in the first mode there was

some mode difference at location 6. Yet, in the

second and third modes, there is no distinction

around location 6, from which a prediction of the

damage location could be made.

4.3 Damage Identification Analysis

In this section, damage identification results are

presented. The four damage detection algorithms

introduced in Section 2 are used to locate the

damage in the composite beams.

4.3.1 Delaminated Beam A Applying the ADM

to the data of Delam A indicated that around the

damage location (sensor 3) there is a peak in the

first mode (Figure 8(a)). However, there are also

peaks at locations 6 and 7 and at imperfection

location (sensor 10). Thus any single mode

cannot detect the location of damage in this

instance. The CDF also failed to properly locate

the damage for Delam A (Figure 8(a)). Neither

the DIM nor the FCM fared any better on this

damage condition (see Figure 8(b)). Although

both the methods did show peaks at the location

of sensor 4, other peaks were also recognisable.

Hence, all the methods failed to exclusively

locate the damaged area for beam Delam A.

Some of the methods did have peaks around the

damage location; however peaks at other non-

damaged location were also present. The inability

to locate the delamination may be due to the fact

that the damage location lies near modal nodes

in two of the three modes examined. Acquiring

additional modes by refinement of sensors and

thus the ability to more properly judge higher

modes may aid in alleviating this problem.

4.3.2 Delaminated Beam B For the delaminated

beam B, the application of ADM resulted in

some peaks within the damaged area (sensors

26) for all three modes (Figure 9(a)) and around

the imperfection (locations 10 and 11). The peak

that was located near sensor 14 in the third mode

caused concern, since there was no explanation

for this peak. The CDF estimated that locations

6 and 10 (Figure 9(a)) as possible damage and

Table 3 Comparisons of the natural frequencies of delaminated beams: Delam A, oppDelam B andDelam C.

Mode Undam. Delam A %Change oppDelam B %Change Delam C %Change

1st 32.8 29.12 11.34 39.61 20.60 29.23 11.012nd 180.8 175.45 2.96 171.54 5.13 179.06 0.973rd 500.5 481.89 3.72 492.84 1.53 489.01 2.30

Table 4 Comparisons of the natural frequencies of impact and saw-cut damaged beams.

Mode Undam. Impact %Change Saw-cut % Change

1st 32.8 33.82 2.97 27.99 14.772nd 180.8 181.78 0.53 169.23 6.403rd 500.5 505.06 0.91 481.99 3.70


(a) (b)

(c) (d)

(e) (f)

Sensor location

Sensor location

Sensor location

Sensor location

Sensor location Sensor location

Sensor location

Sensor location

Sensor location

Sensor location


Figure 7 The first three curvature mode shapes, from sweep sine excitation experiment, of (a) the average undamagedbeam; (b) Delam A beam; (c) oppDelam B beam; (d) Delam C beam; (e) impact-damaged beam and (f) saw-cutdamaged beam.


imperfection locations, respectively. The CDF

captured a peak at location 14 as well. Both the

DIM and FCM (Figure 9(b)) were able to locate

the damage and the imperfection. The DIM had

two peaks around the damage boundaries: one

at location 4 and the other at near location 6,

although false indication at location 14 was also

captured. The FCM also had two peaks, one

large gradual peak spanning between locations 4

and 6 where the delamination was located and

the other peak was around location 10. In

conclusion, the location of delamination B that

spanned locations 2 to 6 was identified by all

three multiple mode methods. The delamination

was recognised around locations 4, 5, 6 and 7.

The imperfection discussed earlier was also

detected at locations 9 and 10.

4.3.3 Delaminated Beam C The ADM on each

mode of Delam C identified the damage location

(a)

(b) Sensor location

ABS

diff

CDF

Sensor location

Dam

age

inde

x

FRF

curv

atur

e

Damage indexFRF curvature

Figure 9 Detection results based on curvature shapes experimental data for oppDelam B beam from (a) absolutedifference and CDF methods, and (b) damage index and FRF curvature methods.

(a)

(b) Sensor location

ABS

diff

CDF

Sensor location

Dam

age

inde

x

FRF

curv

atur

e


Figure 8 Detection results based on curvature shapes experimental data for Delam A, from (a) absolute difference andCDF methods, and (b) damage index and FRF curvature methods.


in the area between locations 4 and 8, which are

close to the actual location (57) (Figure 10(a)).

The first mode depicts the delamination area by

showing two peaks at the locations of sensors 4

and 8. The CDF also displays a large peak along

the damaged area (Figure 10(a)). Similar peaks

were also displayed at the imperfection location

of sensor 10. The DIM was able to accurately

determine the location of the whole delamination

by displaying a peak through locations 6, 7 and 8

(Figure 10(b)). A small peak was also located at

point 10 as expected. The FCM was partially

able to detect the damage (location 7). However,

several peaks were also located in other areas

as well.

All the methods discussed were capable of

locating the delamination C, with the exception of

the FCM. The location of this damage condition

made it possible to generate the first three mode

shapes without having a modal node within the

vicinity of the delamination. It is demonstrated

that the DIM could more accurately detect the

damage location compared to the other methods.

4.3.4 Impact Damaged Beam In the case of

impact beam, all three modes from the ADM

showed peaks around location 6 (Figure 11(a)).

Only the third mode had multiple peaks, with the

second peak being located at sensor 11. Hence, it

can be said confidently that the impact damage

location was around location 6. The CDF and

FCM also displayed a significant peak around

the damaged area (Figure 11(a)) with a small

peak at the imperfection location. The DIM

estimated accurately the location of the whole

damage by displaying a peak through locations

6 and 7 (Figure 11(b)). The location of impact

damage was identified properly by all the

methods. The ADM and CDF methods gave

a better estimation of the damage location

(within 12.7mm or 0.5 in. of the actual location);

whereas the DIM and the FCM were both off by

25.4mm (1.0 in.).

4.3.5 Saw-Cut Damaged Beam For the saw-cut

beam, only the ADM was able to display the

damage location by demonstrating peaks around

location 6, especially in the first and second

modes (Figure 12(a)), although, for mode 3,

peaks at other locations were also significantly

large. In all of the other methods, the identifica-

tions near the damage location were overshad-

owed by peaks at other locations. The CDF

displayed a large plateau over the damage

location. However, it failed to accurately locate

the damage since the most prominent peak was

found at location 9. The DIM and FCM were

unable to determine the damage location. Peaks

at locations 9, 10 and 14 (Figure 12(b)) were

more significant.

(a)

(b) Sensor location

ABS

diff

CDF

Sensor location

Dam

age

inde

x

FRF

curv

atur

e


Figure 10 Detection results based on curvature shapes experimental data for Delam C, from (a) absolute differenceand CDF methods, and (b) damage index and FRF curvature methods.


5 Damage Detection Using ImpulseHammer Excitation

Experiments using the impulse hammer had

the same damage configuration specimens

described earlier. The tests were conducted with

the sensors mounted on the same side of the

beam where the damage was located. The FRF

for impulse hammer excitation often contains a

large amount of noise at locations where the

natural frequencies do not exist. Due to the high

amounts of noise in these regions, the FRF

curvature method cannot effectively be applied to

the FRF data obtained from impulse hammer

excitations. For this reason, no FRF curvature

method data is presented in this section.

5.1 Frequency Measurements

The results of natural frequencies from

experiments with the impulse hammer excitation

are comparable to the test results using the sweep

sine excitation, although all the first three natural

frequencies excited by impulse hammer are a little

higher. Summary of the results of the two

(a)

(b) Sensor location

ABS

diff

CDF

Sensor location

Dam

age

inde

x

FRF

curv

atur

e


Figure 11 Detection results based on curvature shapes experimental data for impact-damaged beam from (a) absolutedifference and CDF methods, and (b) damage index and FRF curvature methods.

(a)

(b) Sensor location

ABS

diff

CDF

Sensor location

Dam

age

inde

x

FRF

curv

atur

e


Figure 12 Detection results based on curvature shapes experimental data for saw-cut damaged beam from (a) absolutedifference and CDF methods, and (b) damage index and FRF curvature methods.


undamaged beams and their averages are pre-

sented in Table 5.

In general, the changes in natural frequencies

due to damage measured by impulse hammer

experiment are much smaller than those with

sweep sine excitation (Tables 6 and 7). The

percentage of change is between 1.4 and 8.8%,

ignoring changes below 1%. Some changes in the

second mode are not significant (0.78% and

lower) due to the fact that the location of

damage is near to or at the location of modal

nodes, in this case delamination A, B and impact

damage. Similarly, for the third mode of saw-cut

damaged beam, the location of damage is near

the node of mode 3.

The impact damage relatively unchanged

the natural frequencies (Table 7). Results of

hamDelam C indicated a different trend than

those presented in hamDelam A or Delam C.

The frequency changes due to saw cut also

exhibited a different trend from the test using

sweep sine excitation. The inconsistency in the

frequency changes might be due to the measure-

ment of natural frequency, which could slightly

drift depending on the measuring equipment,

weather conditions, background noise, ambient

vibrations, and the inability to accurately repeat

the initial boundary conditions.

5.2 Mode Shapes

The curvature mode shapes generated for

each undamaged beam were also averaged to

generate the best shape. The average mode

shapes from undamaged beams 1 and 2 are

displayed in Figure 13(a)). The curvature mode

shapes generated by measurement with impulse

hammer excitation were less smooth compared to

the curvatures generated by sweep sine excitation.

The lack of smoothness in the mode shapes

increases the difficulty in determining a location

solely based on their appearance.

Based on visual inspection, a flattening at

locations 24 in the first mode and small peak at

location 3 may indicate the location of delamina-

tion A (Figure 13(b)). However, this observation

is not conclusive. Especially after weighting

them, the damage location is not recognisable.

For delamination B, the indication of damage

location is more pronounced (Figure 13(c)). There

Table 5 Comparison of the natural frequencies for the undamaged beams excited by impulse hammer.

Mode hamUndam. 1 hamUndam. 2Ave.

hamUndam. %Change

1st 29.17 30.18 29.67 3.382nd 178.38 177.27 177.82 0.633rd 469.47 487.46 478.47 3.76

Table 6 Comparisons of the natural frequencies of delaminated beams from impulse hammer experiments:hamDelam A, hamDelam B and hamDelam C beams.

Mode hamUndam. hamDelam A %Change hamDelam B %Change hamDelam C %Change

1st 29.67 30.43 2.53 32.29 8.81 32.08 8.102nd 177.82 177.73 0.05 176.43 0.78 184.81 3.933rd 478.47 493.11 3.06 517.35 8.13 501.33 4.78

Table 7 Comparisons of the natural frequencies of delaminated beams from impulse hammer experiments: hamImpactand hamSaw-Cut damaged beams.

Mode hamUndam hamImpact %Change hamSaw-Cut %Change

1st 29.67 29.26 1.41 29.60 0.252nd 177.82 177.04 0.06 170.62 4.053rd 478.47 495.59 3.58 478.90 0.09


(a) (b)

(c) (d)

(e) (f)

Sensor location

Sensor location

Sensor location

Sensor location


Sensor locationSensor location

Sensor location

Sensor location

Sensor location

Sensor location

Figure 13 The first three curvature mode shapes, from impulse hammer excitation experiment, of (a) the averageundamaged beam; (b) hamDelam A beam; (c) hamDelam B beam; (d) hamDelam C beam; (e) hamImpact damagedbeam and (f) hamSaw-Cut damaged beam.


are clear peaks in the first and second modes

at locations 3 or 4. This became less evident

after the shapes were weighted; but it was still

recognisable. Additionally, the second mode

clearly indicates the existence of imperfection at

location 10.

The minor indications of delamination C were

exhibited by all the three mode shapes (Figure

13(d)), between locations 5 and 7. This became

more evident after the shapes were weighted. In

particular at point 5, the change could easily be

recognised. Small inconsistencies in all three

modes around locations 5 and 6 (Figure 13(e))

indicate the location of impact damage. Saw-cut

damage effect on the first mode shape (Figure

13(f )) was quite obvious, where there were some

variations at locations 5, 6 and 7, which surround

the damage location. However, in the second and

third modes, there is no distinction around the

point from which a prediction of the damage

location could be made.

5.3 Damage Identification Analysis

5.3.1 Delaminated Beam A Similar to the

results from sweep sine excitation, all the

methods could not properly locate the damaged

area (Figure 14). A large peak at location 6 in

all the three modes gave a false indication of

damage location since the actual location is

between sensors 24. Yet, the location of the

imperfection was identified quite properly by

all the methods except the absolute difference of

the first mode. These results reinforce the earlier

remarks that the location of the damage, which

lies near the modal nodes in two of the three

modes examined, made damage identification to

be not feasible. Refinement of sensor configura-

tion may solve this problem.

5.3.2 Delaminated Beam B The first and third

modes of ADM showed partial damage boundary

locations (Figure 15(a)), at locations 4 and 7,

respectively. The location of the damage fell at

or near the modal node of the second mode

and made it difficult for one to detect the

damage using this mode. The CDF also displayed

a double peak situated at the beginning and

end of the delamination (Figure 15(b)). The DIM

for hamDelam B had peaks at locations 2 and 7,

which corresponded with the limits of the delami-

nation. A peak near location 10 was not very

recognisable. Although, the three methods pre-

sented in this article were able to locate some part

of the delamination B, such large delamination

may be difficult to detect completely, considering

the probability that some part of damage is

located at the vicinity of modal nodes.

5.3.3 Delaminated Beam C Using the first

mode of the ADM, the damage was estimated

(a)

(b) Sensor location Sensor location

ABS

diff

CDF

Dam

age

inde

x

i

Figure 14 Detection results based on curvature shapes experimental data for hamDelam A beam, from (a) absolutedifference methods, and (b) damage index and CDF methods.


at locations 3 and 6, whereas from both the

second and third modes at locations 5, 7 and 8

(Figure 16(a)). When combined together in the

CDF method (Figure 16(b)), there was a large

peak spanning through these four locations. This

provided a good indication of the damage, since

the actual damage location is between locations 5

and 7. In addition, the imperfection at location

10 was also identified.

The DIM identified the location of the whole

delamination by displaying peaks through loca-

tions 6, 7 and 8. This result was off by one

location, since the actual damage is located

between locations 5 and 7. A peak indicating that

the imperfection was located at location 10 was

obtained as expected. These results corresponded

closely with the results from the sweep sine

excitation tests for beam Delam C.

5.3.4 Impact Damaged Beam The ADM

showed that all the three modes produced peaks

around location 6 (Figure 17(a)). Only the third

mode had multiple peaks with the second

peak located at location 11. Because the peak

at location 6 appeared in all the three modes,

it was determined reliably that the damage is

(a)


ABS

diff

CDF

Dam

age

inde

x

i

Figure 15 Detection results based on curvature shapes experimental data for hamDelam B beam, from (a) absolutedifference methods, and (b) damage index and CDF methods.

(a) (b) Sensor location Sensor location

ABS

diff

CDF

Dam

age

inde

x

i

Figure 16 Detection results based on curvature shapes experimental data for hamDelam C, from (a) absolutedifference methods, and (b) damage index and CDF methods.


located near location 6. The CDF also dis-

played a large peak along the damaged area

(Figure 17(b)), while the other peaks were quite

small. The DIM was also able to determine the

damage location by displaying a peak through

location 6. In this damage configuration, the

damage location was identified accurately by

all the three methods with a similar trend of

indication.

5.3.5 Saw-Cut Damaged Beam The ADM indi-

cated that the first and third modes showed

peaks around damage location (i.e., location 6)

(Figure 18(a)), although peaks at other locations

were quite significant as well. The second mode

had undulation with the highest peak at location

11. The CDF displayed a peak over the damage

location (Figure 18(b)). However, it generated

peaks at locations 9 and 11. The DIM identified

the damage location more accurately by display-

ing a substantially more dominant peak at loca-

tion 6. All the methods were able to moderately

localise the damage around location 6 for beam

hamSaw-Cut.

6 Conclusions

In general, the damage detection methods with

an impulse hammer excitation generated better

identification results compared to the continuous

excitation using PZT. Delamination C, the impact

damage, and the saw-cut damage were identified

properly by the curvature mode-based damage

detection technique presented in this study.

However, for delamination A and delamination B,

the results are limited and inconclusive. Damage

configuration and location affect the ability of the

method.

From this study of using both the sweep sine

and impulse hammer excitations, the following

concluding remarks can be drawn:

1. Condition delamination A does not contain

a damage configuration that is conducive

to identification of the damage appropriately.

This limits the method to properly identify

damages that are in close proximity to

the clamped end and/or modal node points.

2. The Damage Index Method (DIM) detects and

isolates the damages better than any of the other

methods studied. The FRF Curvature Method

(FCM) does not seem to work as well as the

other methods. However, the FCM may work

better with a system that generates smooth FRF

curves.

3. A large delamination, as in the condition of

delamination B, might be identified by multiple

peaks at the edges of the delamination by all the

methods under study. However, this could cause

(a)


ABS

diff

Dam

age

inde

x

CDF

i

Figure 17 Detection results based on curvature shapes experimental data for hamImpact damaged beam, from(a) absolute difference methods, and (b) damage index and CDF methods.


misleading interpretations, such that the peaks

are viewed as a multiple instance of some highly

localised damage.

4. For the large delamination configuration (e.g.,

in delamination B), identification procedure will

generate better results when the sensors were

located opposite to the delamination side. This

will reduce the effect of vibration of the

delaminated part. In the cases of relatively

localised damage, such as the impact damage

or saw-cut damage, the location of the sensor

with respect to the damage side has little effect

on the identification results.

5. The frequency changes varied widely from one

test to another and from sample to sam-

ple, especially at low natural frequencies.

Thus, frequencies are inadequate to be used

as a parameter in the damage magnitude

prediction.

6. Finally, all the methods presented exhibited that

the curvature modes measured by the piezo-

electric sensors can be used as promising

alternatives in damage detection techniques.

The excitation sources used in this study,

impulse hammer and continuous sweep sine

excitations, work equally well, and the results

were often nearly identical. Therefore, each

excitation type with its own benefits, is a good

candidate for being an excitation source in the

implementation of a detection method.

Acknowledgements

The carbon/epoxy composite test samples used in this study

were provided by Honeywell, Inc. This study was partially

supported by the College of Engineering at the University

of Akron and Ohio Aerospace Institute Collaborative

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

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(a)


ABS

diff

CDF

Dam

age

inde

x

i

Figure 18 Detection results based on curvature shapes experimental data for hamSaw-Cut damaged beam, from(a) absolute difference methods, and (b) damage index and CDF methods.


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Damage Identification- Curvature Mode Shape