shm of composite plates: vibration based method by using pzt...

SHM of composite plates: Vibration based method by using PZT sensors

R. de Medeiros1,2, M. Sartorato1, D. Vandepitte2, V. Tita1 1 São Carlos School of Engineering, University of São Paulo, Department of Aeronautical Engineering

Av. João Dagnone 1100, 13563-120, São Carlos, São Paulo, Brazil

e-mail: [email protected]

2 KU Leuven, Department of Mechanical Engineering

Celestijnenlaan 300 B, B-3001, Heverlee, Belgium

Abstract This study presents experimental and numerical analyses about health monitoring metrics using vibration-

based method for damage detection in composite plates. Three composite plates, made of carbon fibre and

epoxy resin, were considered in this study, one intact, other damaged by manufacturing, i.e. a centre hole

(controlled damage) and the other damaged by low-velocity impact loading (uncontrolled damage).

Experimental and numerical analysis consists of vibration tests. In order to produce the excitation on the

structures, an impact hammer was used. Accelerometers and, in a second stage, piezoelectric transducers

were used for data acquisition. Firstly, the Frequencies Response Functions (FRFs) were obtained using

accelerometers. Then, secondly, piezoelectric transducers were used. Numerical analyses were carried out

through finite element modelling, considering the simulation of the piezoelectric transducers. Finally,

FRFs were analysed using appropriate metrics, which were compared in terms of their capability for

damage identification.

1 Introduction

Aircraft are composed by different complex systems, for example: structural, hydraulic, propulsion,

electronic and avionic elements. Damage detection on aircraft composite structures has been one of the

major concerns of operators during the last two decades. Vibration-based methods by using piezoelectric

sensors and/or actuators incorporated into composite structures offer a promising option to fulfil such

requirements and needs. These methods can use finite element analysis combined to experimental results

in order to detect damage. Thus, it is possible to identify, locate and estimate the damage events,

comparing dynamic responses between damaged and health structures. The basic idea of the vibration-

based damage detection method consists on assuming that damage is a combination of different failure

modes, which affect the local stiffness of the structure, and this modifies the dynamic characteristics of the

structure, i.e., the modal frequencies, mode shapes and modal damping values. Structural Health

Monitoring (SHM) can provide, all the time, during the aircraft life, a diagnosis of the material state and

the structure situation, as well as a prognostic like the residual strength of the structure. Thus, SHM can

reduce the maintenance costs, avoiding useless inspections.

Literature on vibration based method can been found in many conferences and journals. Salawu [1]

discussed the use of natural frequency as a diagnostic parameter in structural assessment procedures using

vibration monitoring. Doebling et al. [2] presented an overview of methods to detect, locate, and

characterize damage in structural and mechanical system by examining changes in measured vibration

response. Zou et al. [3] reviewed the model-based delamination detection methods for composite

structures using vibrations. Firstly, it describes the most commonly, model-based methods for damage

detection, used structural modelling techniques for delamination and the effects of delamination on

dynamic parameters. Then it focuses on the application of vibration-based model-dependent damage

3751

detection methods in composite structures. Finally, the review is devoted to the development of methods

with incorporated piezoelectric sensors and actuators for on-line delamination detection for composite

structures. Carden and Fanning [4] reviewed the state of the art in vibration-based conditioning monitoring

with particular emphasis on structural engineering applications. The review identified several different

approaches and categorized them. Montalvão et al. [5] reviewed the advances in structural health

monitoring and damage detection, with emphasis on composite structures. Ciang et al. [6] presented many

SHM methods for damage detection in a wind turbine system. Worden et al. [7] presented a review of

examples from nonlinear dynamical system theory and from nonlinear system identification techniques,

which are used for the feature-extraction portion of the damage detection process. It provides a number of

illustrations of complimentary approaches where damage-sensitive data features are based on nonlinear

system response. These features, in turn, can either be used as a direct diagnosis of damage or as input to

statistical damage classifier. Huang et al. [8] presented a review of the development of analytical,

numerical and hybrid approaches for modelling of the coupled piezo-elastodynamic behaviour in order to

use as a structural health monitoring system. Fan and Qiao [9] showed a review in order to identify

starting points for research in vibration-based damage identification and structural health monitoring.

Also, they guided researchers in better implementing available damage identification algorithms and

signal processing methods for beam- or plate-type structures. The review is organized by the classification

using the features extracted for damage identification methods. Pérez et al. [10] presented the results of an

experimental campaign conducted to investigate the feasibility of using vibration-based methods to

identify damages sustained by composite laminated due to low-velocity impacts. The experimental

programme include an evaluation of impact damage resistance and tolerance according to ASTM test

methods, characterization of damage by ultrasonic testing and quantification of the effects on the vibration

response. The experimental results indicate that impact-induced damages result in detectable changes in

the vibration response of coupons. Medeiros et al. [11-14] presented experimental and numerical results in

vibration-based damage detection and structural health monitoring for beam- cylinder- plate- or bonded

joints. The results demonstrated the potentiality of this technique in detecting damage.

Regarding numerical approaches, in general, the problem is to model correctly structures with

piezoelectric transducers, either attached or embedded [15]. In general, the results for different models of

finite elements can be used to identify damage by using electro-magnetic coupling of piezoelectric

sensors. Several theoretical models exist in the literature. However the mostly common used commercial

finite element packages contain only solid finite elements with piezoelectric capabilities [16]. Hence,

simulations of complex shell or large structures become computationally unfeasible, especially for thin or

curved structures, in which shell elements would be preferred. Also, for curved structures, some effects

are more important than for quasi-planar structures, such as the non-linear shearing relative distortions

terms on the normal strains and the electrical field-strain coupling [17]. Usually, the existing studies

propose ways to include higher order shell theories [18] or a lagrangean solution to the non-linear

geometric problem by including Green strains or von Karman strains [19]. In particular, Gabbert et al. [20]

and Nasser et al. [21] created non-linear models, which characterize better the electrical field-strain

coupling by using a first order electrical field solution that naturally fulfils Gauss’ Law. Moreover, most of

the works existing in the literature model the electrical-mechanical coupling innate via the first order

electrical field theories, which uses the continuous electrodes constitutive equations and Faraday induction

law solution.

In practical, for the large and complex structures, as well as for structures with hard access, it is very

difficult to detect damage by using local damage detection methods (e.g. ultrasonic), because this type of

methodology can be only used to inspect accessible components of a structure. In order to detect damage

throughout the whole structure, especially some large structure, a methodology, which uses global

vibration based, has been more adequate. Recently, this type of methodology has been used for composite

structures. Therefore, this present study shows experimental and numerical analyses about health

monitoring metrics by using vibration-based method for damage detection in composite plates. Three

composite plates, made of carbon fibre and epoxy resin, were considered in this study, one intact, other

damaged by manufacturing, i.e. a centre hole (controlled damage) and the other damaged by low-velocity

impact loading (uncontrolled damage). Experimental and numerical analysis consist of performed

vibration tests. In order to produce the excitation on the structures, an impact hammer was used.

Accelerometers and, after that, piezoelectric transducers were used for data acquisition. Firstly, the

3752 PROCEEDINGS OF ISMA2014 INCLUDING USD2014

Frequencies Response Functions (FRFs) were obtained by using accelerometers. Then, secondly, by using

piezoelectric transducers. Numerical analyses were carried out via Finite Element Method, considering the

simulation of the piezoelectric transducers. Regarding the finite element analyses, a mathematical

formulation of a non-linear shell finite element for piezoelectric active composite was proposed. The

formulation contemplates both the problem of the electrical-mechanical coupling problem, by introducing

first order electrical field polarization theory and electrical field-strains coupling. Due to the objective of

SHM simulations, a linear, first order shear theory element was preferred over more complex models due

to the efficiency of such elements and the fact that modal and frequency analysis require only

displacement solutions. The final formulation was implemented using an eight nodes serendipity quadratic

finite element. The element was implemented in a Fortran subroutine and compiled through the finite

element commercial package AbaqusTM using its User Element (UEL) subroutine. Finally, FRFs were

analysed by using some metrics, which were compared in terms of their capability for damage

identification.

2 Experimental Analyses

The experimental analyses were carried out via vibration tests on composite plates. The plates are made of

8 plies stacked in [0]8 lay-up configuration. The specimens are manufactured by filament winding. The

composite plates are made of carbon fibre with epoxy resin (Carbon Fibre Reinforced Polymer – CFRP).

The plate geometries consist of 305 mm length, 245 mm width and 2.16 mm total thickness (Fig. 1). Three

versions of nominally similar plates were investigated in this study, one intact, another one damaged by

drilling a centre hole (controlled damage), which has diameter equal 5mm, and the other one is damaged

by low-velocity impact loading (uncontrolled damage). Due to fibre orientation, this damage has length

equal 130mm in the fibre direction. Firstly, the Frequencies Response Functions (FRFs) were obtained

using accelerometers (Fig. 1(a)). The accelerometers were model 352C22 lightweight. Accelerometer 1

(sensitivity 9.00 mV/g) was set on the position 1, accelerometer 2 (sensitivity 9.31 mV/g) was set on the

position 2, accelerometer 3 (sensitivity 9.57 mV/g) was set on position 3 and accelerometer 4 (sensitivity

9.94 mV/g) was set on position 4, which can be seen in Fig. 2. Then, secondly, piezoelectric transducers

were used (Fig. 1(b)) M2814-P1 type MFC (Macro Fibre Composite) manufactured by Smart Material

Inc., which use the 33 mode of piezoelectricity. The piezoelectric geometries consist of 38 and 28 mm

overall and active length, respectively, 20 and 14 mm overall and active widths, respectively, and 0.305

mm total thickness (Fig. 3). The excitation for both sets of vibration tests was applied by using an impulse

signal through an impact hammer PCB Model 0860C3 (Piezotronics).The input was set on the position 1

in the back side of the plate.

(a) (b)

Figure 1: Schematic experimental set (a) with accelerometers and (b) with MFCs

STRUCTURAL HEALTH MONITORING 3753

Six experimental and three computational models were studied in this work. The first, second and third

models (P1A, P2A and P3A) represent the intact plate (P1), centre hole plate (P2) and impacted plate (P3)

which are experimentally measured using accelerometers. The fourth, fifth and sixth models (P1P, P2P

and P3P) represent the intact plate (P1), centre hole plate (P2) and impacted plate (P3) which are

experimentally measured using piezoelectric transducers. The dataset contains FRFs, including

information on natural frequencies and damping factor, which can be used to identify the presence of

damage at the structure. However, sometimes, it is necessary to use appropriate metrics in order to identify

the damage.

Fig. 2 to Fig. 4 show all data acquisition set-ups used in the experimentation. The specimen is suspended

on elastomeric wires to simulate “free-free” boundary condition, the accelerometers (Fig. 4(a)) and MFCs

transducer (Fig. 5(a)) and the hammer linked to a LMS SCADAS equipment, which was controlled by the

Test.Lab software (LMS Test.Lab). The LMS SCADAS is a plug and play equipment and it has

multifunction analog, digital and timing I/O board for USB bus computers.

(a) (b) (c)

Figure 2: Experimental Setup with accelerometers: (a) intact; (b) damaged by central hole and (b)

damaged by impact

(a) (b) (c)

Figure 3: Experimental Setup with MFCs: (a) intact; (b) damaged by central hole and (c) damaged by

impact


(a) (b)

Figure 4: Experimental layout by using (a) accelerometers and (b) piezoelectric sensors

The input signals are generated by an impact force hammer in the position 1 (Fig. 1(a) and Fig. 1(b)). This

type of input provides an excitation over a wide range of the required frequencies. This is important

because different types of damage can affect different frequency ranges, and the resonant and anti-

resonant characteristics of a structure may be good indicators of damage. This approach, which uses

impulse vibration, is a more global damage indicator compared to other methods, which uses single

frequency tone bursts and wave reflection. The FRF can indicate damage, which is inside the structure.

However it is important to highlight that they may not be as sensitive to small damage on the surface as

compared to wave propagation methods. Each signal consists of 2048 points and sampling occurred at

1024 Hz. The number of averaging individual time records was selected to be five.

3 Numerical Analyses

Modal and frequency simulations of Plate 1 (intact) and Plate 2 (with centre hole) were developed using a

finite element proposal, which was implemented in AbaqusTM via UEL (User Element Subroutine).

Figure 5: Numerical finite element model for Plate 2.


The material elastic properties of the plates were obtained from previous research work by the authors [22-

23]. The elastic, piezoelectric coupling and dielectric properties of the transducers were obtained based on

data from the sensors manufacturer and the methodology proposed by the authors [24]. Figure 5 shows the

finite element model used for the analysis of Plate 2, highlighting the mesh density, boundary conditions,

loads, and positions of the transducers. The mesh for Plate 1 and 2 contains respectively 5448 and 5712

quadratic elements. More details about the finite element proposal are addressed in the next section.

Using the aforementioned material properties and models, undamped direct solutions for a frequency

domain from 0 Hz to 1024 Hz were performed using 2048 equidistant steps (0.5Hz frequency step). The

same impact points, load type and FRF measurements (H11, H12, H13 and H14) used for the experimental

tests were used in the numerical simulations. The undamped approach was used for the numerical studies

to make sure experimental and numerical data were independent from each other.

3.1 Finite Element Proposal

This section gives a summary of the mathematical formulation of the finite element, including the

mechanical and electrical assumptions and the constitutive equations. This formulation is an improved

version of previous work by the authors [12], and it includes the electrical-mechanical coupling innate to

the first order electrical field theories [20-21].

3.2 Mechanical Hypothesis

The kinematics for degenerated shells and the First Order Shear Theory (FOST) were used to describe the

displacements of a given shell, based on the displacement of its reference section (ui) and its rotations (θθθθo),

as shown in Eq. (1). The matrix Tij is the transformation matrix from the global coordinate system (x1, x2,

x3) to the local coordinate system in the shell (s1, s2, s3), in which the composite principal directions are

defined. The FOST was used to increase the computational efficiency of the model. Also, as most

applications of smart composites only require displacement calculations (modal analysis, explicit dynamic

analysis), higher order theories are not necessary.

( )kjk3jijjiji HsuTuTu θ+==

,

−=

00

01

10

H

, 2..1k;3..1j,i ==

(1)

The iso-parametric coordinate system (ξ1, ξ2, ξ3) is related to the local coordinate system through Eq. (2),

where -0.5 ≤ η ≤ 0.5 is the ratio of the distance of the reference section relative to the mid-section to the

whole thickness. The engineering strains are calculated through Eq. (2).

( )η−ξ= 2

2

hs 33

,

θδ+

∂

θ∂+

∂

∂=

∂

∂+

∂

∂=ε oklj3

j

okl3

j

kik

i

j

j

iij H

2

h

sHs

s

uT

s

u

s

u

2

1

, 2..1o;3..1k,j,i ==

(2)

3.3 Electrical Hypothesis

The electrical assumptions used are: the piezoelectric layers are transversal isotropic; the transversal

normal stress is not significant (i.e. σ3≈0); and the electrodes are either continuous or inter-digitals with

symmetric polarization, i.e. E1=E2≈0, such as the M2814-P1 PZT used in the experiments. The electrical

field is assumed to evolve linearly through the thickness of a given piezoelectric layer. By using Eq. (3),

the introduced electrical-mechanical coupling naturally fulfils the Gauss law.


hss

d

ed

C

eCe

sE3

2

3

1

11

2

33

33

E

33

33

E

13

31

33

ϕ∆−

∂

ε∂+

∂

ε∂

−

−

−=

ε

ε

(3)

3.4 Constitutive Equations

A piezoelectric active lamina constitutive equation is written as Eq. (4) or in reduced form Eq. (5) using

the e-form constitutive equations for a piezoelectric material with kinematic and electrical assumptions.

+−−

+

+

−−−−

−−−−

=

3

13

23

12

22

11

11

2

33

33

33

3313

31

33

3313

31

11

2

15

44

11

2

15

44

66

33

3313

31

33

2

13

22

33

2

13

12

33

3313

31

33

2

13

12

33

2

13

11

3

13

23

12

22

11

000

00000

00000

00000

000

000

E

d

ed

C

eCe

C

eCe

d

eC

d

eC

C

C

eCe

C

CC

C

CC

C

eCe

C

CC

C

CC

D

E

E

E

E

E

E

E

E

E

E

E

E

E

E

E

E

E

E

E

E

E

E

E

γ

γ

γ

ε

ε

τ

τ

τ

σ

σ

ε

ε

(4)

γ

ε

−

=

τ

σ

3

offplane

plane

s

t

b

3

offplane

plane

Ed0e

0C0

e0C

D (5)

3.5 Finite Element Equations

Using the Hermite serendipity shape functions ϕn [17], the displacements, rotations and electrical voltages

are calculated based on nodal values using the expressions in Eq. (6).

nnonnoinni uu ϕφϕθφθφ ˆ,ˆ,ˆ === (6)

Using these expressions and the strains and electrical fields, Eqs. (7) are derived.

uBsB

BsB

1s30s

1b30b

+

+=ε

, uBsˆBE 130 ϕϕ +ϕ=

(7)

The variational equilibrium equation of a single element is found in Eq. (8), where U is the volume

integration over the element of the specific electric-mechanical enthalpy, also called Gibbs’ piezoelectric

energy, given by Eq. (9) and P is the work from the external loads.

(8)

(9)

Using the simplification matrices B from Eq. (7), and the constitutive equation; the final finite elemental

equilibrium equations main be written as Eq. (10).

0PU =δ+δ=Πδ

∫Ω ⋅δ−σ⋅δε=δ DEU


QKuK

FKuK

u

uuu

=ϕ⋅+⋅

=ϕ⋅+⋅

ϕϕϕ

ϕ

(10)

Where the Kuu, Kϕu, Kuϕ and Kϕϕ matrixes were obtained using the hypothesis of a parabolic distribution

of off-plane distortions and the common development for finite elements.

As the final finite element was implemented within AbaqusTM UEL, and modal and frequency analysis

solvers were used in the solution phase, with the external forces F and Q taken to be concentrated nodal

forces.

Γ= ]F[F , Γ= ]Q[Q (11)

4 Vibration-Based Metrics

Different modal parameters can be used in order to identify the damage in the structure, such as resonance

frequencies, amplitudes, phases and vibration modes. These parameters must be chosen taking into

account several factors, such as the type of analysis used, previously known experimental data of the

structure, the type of sensors attached to the structure, as well as their location and the type and extent of

damage, which is required to be detected. Hence, in the present work, different metrics were compared

based on FRFs magnitude and frequency.

Maia et al. [25] presented a metric that use the FRF curves differences between two FRFs, which are

measured at specific positions. This metric will be used in order to determine the influence of the MFCs in

the free-free vibration analysis. This method can be defined as:

( ) ( ) ( )ωαωαωα D

ki

H

kiik −=∆ (12)

If more than one frequency and force are considered, the index is the sum of the damage indices from each

frequency and force. The researchers divided by the sum of the FRF of the healthy structure in order to

obtain a ratio rather than an absolute value. This method can be defined as:

( )

( )∑∑

∑∑∆

=

ω

ω

ωα

ωα

k

H

ki

k

ki

iMSFRF _ (13)

where the superscripts H and D represent the healthy and damaged structures, respectively, the subscripts i

and k denote the location of measure and force, respectively. α(ω) denotes the frequency response

function, and ω denotes the frequency range. The D expression returns value “zero”, if there is no

variation in the structural dynamic behaviour.

Silva et al. [26] showed a damage metric chart obtained by frequency response from input-output data.

The damage metric is an index based on the root-mean-square deviation (RMSD). This feature is

computed with data in the frequency domain. This damage index is used for electrical impedance signal,

but in this present work, it is adapted in order to use in vibration analysis and investigated range of

frequency. So, this metric can be defined as:

( ) ( )[ ]

∑−

=ω

ωαωα

nMFRF

D

ki

H

ki

i

2

_ (14)

Where n is the number of frequency lines. These values once collected for different sensor/actuator pairs

can roughly quantify the amount of damage in a structure. The D expression returns values greater than

zero if any variation in the structural response occurs, and D will return “zero”, if there is no damage in

the structure.

Zang et al. [27] presented the global shape correlation function (GAC) and global amplitude correlation

function (GSC) for structural health monitoring. Similar to the definitions in [27], it can be defined as:


( )[ ] ( )[ ]

( )[ ] ( )[ ]( ) ( )[ ] ( )[ ]( )ωαωαωαωα

ωαωα

D

ki

TD

ki

H

ki

TH

ki

D

ki

TH

ki

iGAC⋅⋅⋅

⋅=

2

(15)

∑=ω

ii GACFRFGACFRF __ (16)

( )[ ] ( )[ ]

( )[ ] ( )[ ]( ) ( )[ ] ( )[ ]( )ωαωαωαωα

ωαωα

D

ki

TD

ki

H

ki

TH

ki

D

ki

TH

ki

iGSC⋅+⋅

⋅⋅=

2 (17)

∑=ω

ii GSCFRFGSCFRF __ (18)

Where the superscript T is a transpose column vector, Δω is the frequency increment between

measurement points. ω1 is the lower frequency and ω2 is the upper frequency of the range of interest.

Based on Eq. (15) and Eq. (17), it can be seen that GACi and GSCi are a real-valued function of frequency

between zero and unity. Also, the shape correlation coefficient is sensitive to mode shape differences but

not to relative scales. On the other hand, the amplitude correlation coefficient uses damaged response

amplitudes. Moreover, The FRF_GACi and FRF_GSCi will be a real constant between zero and unity to

indicate total/zero change of structural responses [27].

Prada et al. [28] presented metrics in order to compare the normalized FRFs magnitudes in specific

frequencies: the change in measured ratio metric (CMRM) and the transmissibility ratio metric (TRM).

These metrics can be defined as:

2

1_

sensor

D

i

H

sensor

D

i

H

iCMRMFRF

=

α

ϕα

ϕ

α

ϕα

ϕ

(19)

2

1_

sensor

D

i

sensor

D

i

iTRMFRF

=

α

ϕ

α

ϕ

(20)

Where φ is the natural frequency of the structure. The Eq. (19) compares the ratio between two different

sensors. Eq. (20) uses the transmissibility ratio between the normalized magnitudes of the FRF of a given

frequency obtained from two different sensors for a given parameter. This approach does not require

previously known data, but requires more sensors to work. These sets of expressions returns values “1”, if

there is no variation in the structural behaviour, but they will return other value, if any variation occurs.

5 Results and Discussion

The feasibility of using vibration-based NDT for damage identification in laminated composites is

assessed by comparing the experimental results for both healthy and damaged structure. Also, different


types of damage were considered. Moreover, special attention is paid to the relation between the damage

metrics. Figures 6 and 7 show the experimental and numerical FRFs using accelerometers and

piezoelectric sensors for all measured points. Indeed, it is difficult to identify the damage by visual

inspection of the FRFs only; so it is necessary to introduce metrics in order to identify the presence or not

of the damage.

(a) (b)

Figure 6: FRFs obtained for (a) Plate 1 and (b) Plate 2 by using accelerometers experimental data and

MFCs experimental and computational data

(a) (b)

Figure 7: FRFs obtained for (a) Plate 1 and (b) Plate 3 by using accelerometers experimental data and

MFCs experimental and computational data


Table 1 shows the different resonance frequencies measured by accelerometers and piezoelectric

transducers experimentally and just piezoelectric transducers computationally for health and damaged

composite plates. First, it can be observed that the values obtained for the different types of damage do not

exhibit large changes. This fact is associated to the small magnitude of the exciting pulse loading, which

was selected to avoid that the structures would go in a non-linear regime, making the resonance

frequencies remain practically unaltered. Therefore, an SHM metric, which takes into account only the

variation in the frequencies, might not be the best strategy for this type of damage. However, when it was

compared the intact structure (Plate 1) to the damaged by impact loading (Plate 3), it was possible to

observe significant differences between the second and third modes. This is because the presence of

damage changes the stiffness of the structure.

ω1 [Hz] ω2 [Hz] ω3 [Hz] ω4 [Hz] ω5 [Hz] ω6 [Hz]

Position Mode type /

Measure

1st

torsion

1st

flexural

2nd

torsion

2nd

flexural

3rd

torsion

3rd

flexural

Plate 1

H11

AExp 61.5 153.8 163.8 226.0 254.8 333.0

PExp 61.7 154.8 165.3 226.0 255.0 336.0

PComp 56.5 158.4 169.9 244.4 268.4 332.8

H12

AExp 61.2 153.8 163.3 226.0 255.5 333.0

PExp 62.0 154.8 163.5 226.3 255.8 334.8

PComp 56.5 158.4 169.9 244.4 268.4 332.8

H13

AExp 61.2 153.8 163.8 226.3 254.3 333.0

PExp 61.7 154.8 165.0 226.3 255.3 335.3

PComp 56.5 158.4 169.9 244.9 268.4 332.8

H14

AExp 61.5 153.8 163.3 226.3 254.5 333.0

PExp 62.0 154.8 163.8 226.3 255.0 335.3

PComp 56.5 158.4 169.9 244.9 268.4 332.8

Plate 2

H11

AExp 60.5 149.5 161.0 224.5 253.3 334.8

PExp 61.2 150.8 162.8 224.8 253.8 330.8

PComp 56.5 158.4 169.4 241.4 268.4 331.8

H12

AExp 60.2 149.8 160.8 224.5 253.8 328.5

PExp 61.0 150.5 161.3 225.0 254.3 328.5

PComp 56.5 158.4 169.4 240.9 268.4 331.8

H13

AExp 60.2 149.5 161.0 224.8 252.5 334.8

PExp 60.7 150.5 162.3 225.0 253.8 337.5

PComp 56.5 158.4 169.4 241.4 268.4 332.3

H14

AExp 60.5 149.8 160.8 224.8 252.8 333.5

PExp 60.7 150.5 160.8 225.0 253.8 330.0

PComp 56.5 158.4 169.4 241.4 268.4 331.8

Plate 3

H11 AExp 60.5 150.0 130.5 225.5 251.8 327.5

PExp 60.5 151.8 132.3 225.5 252.0 331.3

H12 AExp 60.2 149.8 130.5 225.8 252.5 327.8

PExp 61.0 150.5 132.0 225.8 252.5 330.3

H13 AExp 60.2 150.3 130.5 226.0 251.3 327.5

PExp 60.7 151.5 132.0 225.8 252.0 330.5

H14 AExp 60.5 149.8 130.5 225.8 251.5 327.8

PExp 61.0 150.5 132.0 225.8 252.0 330.8

* Subscripts Exp. and Comp. are experimental and numerical data, respectively.

Table 1: Experimental and numerical resonances frequencies

Furthermore, one of the first conclusions, which can be obtained from this data, is that the simulation of

damage in the structure by drilling a hole cannot be representative for the case of stiffness degradation of

the material. In fact, this damage does not change the total mass such as debonding of layers in composite

materials or degradation of the structural resistance due to aging. However, the impact damage brings

about changes in the dynamic behaviour. As observed from the FRFs (Fig.6 and 7 and Table 1), it is very


complicated to identify the damage in the composite plates, because it depends on the size and location of

the damage, as well as the interest frequency range and the mode shape. On the other side, the FRF is

desirable from the viewpoint of applications for SHM systems, because structural FRFs are sensitive to

small changes and damage in a structure. To quantify this sensitivity, a damage indicator was used in

order to calculate the difference in the FRF responses between health (intact) and damaged structures.

Using the data from the FRFs, both numerical and experimental, tables 2 to 4 were obtained using the

calculated damage metrics shown previously. Different metrics based on the magnitude of the amplitude

of the FRFs in specific frequencies were calculated using relations between the response from either

sensors or both. As the numerical analysis was done with zero damping, the magnitudes at the resonance

frequencies may go up to infinite. As such, for the numerical case, the chosen frequencies are close to, but

not coinciding with the resonance peaks. Only the real part of the signal is analysed, because it is more

sensitive to structural modifications than the imaginary part. This last term is dominated by capacitive

response of the sensor and, therefore, it is less sensitive to structural damage effect [24].

Damage Position Measure FRF_MS FRF_M FRF_GAC FRF_GSC

Centre

Hole

H11

AExp. 0.5428 11.2756 0.3303 0.5747

PExp. 0.3759 1.3747 0.5630 0.7483

PComp. 0.7953 4.1464 0.0459 0.1983

H12

AExp. 0.5411 11.0456 0.3353 0.5789

PExp. 0.4687 1.4727 0.4708 0.6822

PComp. 0.7868 4.1474 0.0452 0.1969

H13

AExp. 0.4466 11.0403 0.4120 0.6413

PExp. 0.4514 1.4345 0.4806 0.6877

PComp. 0.7871 4.7066 0.0472 0.2011

H14

AExp. 0.5353 10.5568 0.3613 0.6004

PExp. 0.4994 1.4916 0.4753 0.6763

PComp. 0.7776 4.7079 0.0462 0.1992

Impact

H11 AExp. 0.9545 15.2700 0.0664 0.2573

PExp. 0.5833 1.5647 0.4327 0.6576

H12 AExp. 0.9260 14.0921 0.0932 0.3053

PExp. 0.6985 1.5303 0.3416 0.5823

H13 AExp. 0.7142 14.9227 0.1365 0.3684

PExp. 0.6641 1.6666 0.2670 0.5167

H14 AExp. 0.8743 13.7689 0.0983 0.3134

PExp. 0.6928 1.6112 0.2828 0.5318

Table 2: Damage indicators for different types of damaged and sensors position

Table 2 shows that the metrics are sensitive to different types of damage. As expected, the impact damage

is more severe than the centre hole. This is probably due to the fact that the damage by low-velocity

impact causes a higher changes in the stiffness of the composite plates. In fact, values of FRF_MS and

FRF_M are “zero” for healthy state while those for damaged states are greater than “zero”. However,

values of FRF_GAC and FRF_GSC are near unity for healthy state while those for damaged states are

sharply reduced. Clearly, damage indicators are sensitive to damaged states and they can be used for

damage identification purposes in structural health monitoring systems. Furthermore, all damage metrics

present in table 2 can be presented in a graph in order to show the damage variation for each frequency

value.

Based on tables 3 and 4, it can be concluded that metrics, which use data from more than one sensor, were

more reliable. These metrics, as the other, are sensitive to different types of damage. As expected, the

impact damage is more severe than the centre hole. Table 4 shows that there is an advantage when it does

not need previously known data (healthy structure). This metric relates the transmissibility between the

sensors.


Comparing the numerical and experimental results, the differences in the damage metrics can be verified.

This difference can be explained because the numerical simulations did not use a damping model. Thus,

the FRFs present different orders of magnitude. Indeed, it presents the same behaviour for both the

experimental and numerical results.

Damage Position Measure ω1 [Hz] ω2 [Hz] ω3 [Hz] ω4 [Hz] ω5 [Hz] ω6 [Hz]

Centre

Hole

H11 – H12

AExp. 0.7767 0.6911 1.354 1.0432 1.1658 1.5444

PExp. 1.6440 0.8432 1.0732 0.9555 1.0802 2.1662

PComp. 0.9999 1.0004 0.8279 2.2417 1.0009 1.5680

H11 – H13

AExp. 0.7914 0.9850 1.0409 0.9677 1.4731 0.9550

PExp. 0.7791 0.8340 0.4602 0.9457 1.2815 1.3949

PComp. 1.0017 0.9996 1.0361 2.2700 1.0052 1.8398

H11 – H14

AExp. 0.8344 0.7648 1.3985 0.9587 1.3586 1.4195

PExp. 0.1758 1.0184 0.0940 15.9357 1.2191 4.4862

PComp. 1.0042 1.0003 0.8267 0.5661 1.0039 0.8343

Impact

Loading

H11 – H12 AExp. 0.8189 0.7877 1.0143 1.0011 1.0844 1.1634

PExp. 0.4411 2.4198 0.5796 1.0646 1.0470 1.2494

H11 – H13 AExp. 0.8162 1.1109 1.1447 0.9764 1.2133 1.0023

PExp. 6.4325 2.3616 0.5008 1.0081 1.1137 1.1152

H11 – H14 AExp. 0.8151 1.0223 1.2040 0.9601 1.0835 1.2099

PExp. 2.3104 1.8590 0.7283 0.9403 1.0758 1.0764

Table 3: FRF_CMRM damage indicator

Damage Position Measure ω1 [Hz] ω2 [Hz] ω3 [Hz] ω4 [Hz] ω5 [Hz] ω6 [Hz]

Centre

Hole

H11 – H12

AExp. 0.9935 1.2203 0.7283 0.9800 0.8562 0.2321

PExp. 0.1987 1.0841 0.4038 1.0630 1.0508 0.2850

PComp. 1.1355 1.1399 1.1907 0.9939 1.1434 0.8361

H11 – H13

AExp. 1.1503 1.1212 1.1131 0.9993 1.0769 1.0169

PExp. 0.5383 1.0591 0.7789 1.1346 0.8491 0.8817

PComp. 0.9992 0.9968 0.9905 0.8989 1.0134 0.7914

H11 – H14

AExp. 0.9588 1.3314 0.8035 0.9912 0.7494 0.2334

PExp. 0.7482 0.9975 6.2569 0.0624 0.9372 0.4941

PComp. 1.1325 1.1390 1.1915 1.1063 1.1343 1.2656

Impact

Loading

H11 – H12 AExp. 0.9422 1.0707 0.9726 1.0212 0.9204 0.3081

PExp. 0.7404 0.3777 0.7477 0.9541 1.0841 0.4941

H11 – H13 AExp. 1.1154 0.9941 1.0122 0.9904 1.3075 0.9689

PExp. 0.0652 0.3740 0.7159 1.0644 0.9770 1.1028

H11 – H14 AExp. 0.9814 0.9960 0.9333 0.9897 0.9397 0.2738

PExp. 0.0570 0.5465 0.8078 1.0571 0.9837 0.6805

Table 4: FRF_TRM damage indicator

6 Conclusions

Different metrics are used to identify damage in composite plates by monitoring the vibration response of

the structure. Accelerometers and piezoelectric transducers are used for data acquisition. The analyses

were carried out to obtain modal parameters of both an undamaged and a damaged specimen of a

nominally identical structure. Damaged metrics were compered. The metrics were calculated for data

retrieved from each sensor alone and by the ratio of the data retrieved by each sensor. Experimental and

numerical analyses were presented. For the numerical analyses, a non-linear shell finite element for

piezoelectric active composite was implemented in Abaqus via UEL subroutine. The analyses were

performed to obtain modal parameters of both healthy and damaged structures, simulated in the structure


by drilling a centre hole. The experimental and numerical results showed that the vibration-based damage

identification methods combined to the metrics can be used in SHM systems. This method has the

advantages that it can be to implement and has low cost. Also, it gives information on the overall

condition of the system. The experimental analyses combined to the damage metrics diagnose if the

structure is damaged or not. These metrics show that the impact damage is more severe than the centre

hole. Finally, it is possible to conclude that there is a great future perspective for the application of

vibration-based methods by using MFCs sensors on SHM systems for composite structures.

Acknowledgements

The authors would like to thank São Paulo Research Foundation (FAPESP process number: 2012/01047-

8), as well as Coordination for the Improvement of the Higher Level Personnel (CAPES process number:

011214/2013-09), National Council for Scientific and Technological Development (CNPq) and

FAPEMIG for partially funding the present research work through the INCT-EIE. The authors also would

like to thank Navy Technological Centre (CTM – Brazil) for manufacturing specimens and Prof.

Reginaldo Teixeira Coelho (University of Sao Paulo) for kindly providing the use of the AbaqusTM

license.

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