Effect of the Thickness-wise Location Delamination on Natural Frequency for Laminate Plate

7/25/2019 Effect of the Thickness-wise Location Delamination on Natural Frequency for Laminate Plate

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International Journal of Applied Engineering Research

ISSN 0973-4562 Volume 8, Number 2 (2013) pp. 157-170

Research India Publications

http://www.ripublication.com/ijaer.htm

Effect of the Thickness-wise Location

Delamination on Natural Frequency for Laminate

Composite

R. Sultan, S. Guirguis, M. Younes and E. El-Soaly

*Libyan air force, [email protected]

Egyptian Armed Forces, Egypt

[email protected] Armed Forces, Egypt

[email protected]

thof Ramadan Higher Institute of Technology, Egypt,

[email protected]

Abstract

The laminated composite plates are basic structural components used in

a variety of engineering structures. An important element in the

dynamic analysis of composite laminate structure is the computation oftheir natural frequencies. The present study involves extensive

experimental works to investigate the free vibration of square wovenfiber Glass/Epoxy composite plates with two opposite simply supports

edges and the remaining two edges are free boundary conditions. The

specimens of woven glass fiber and epoxy matrix composite plates were

manufactured by the hand-layup technique. Elastic parameters of the

plate were also determined experimentally by tensile testing ofspecimens. Finite element modelling was employed to simulate the

dynamic response of composite laminates plates with delamination and

extract their vibration parameters. Present experiments were used tovalidate the results obtained from the FEM numerical analysis. In this

paper, the effect of delamination on free vibration through thickness-wise direction was introduced. First natural frequency was investigated

theoretically by using energy method and compared with numerical and

experimental results. Good agreement was found between theoretical,

numerical and experimental results. Results show that the delamination

has considerable effect on the natural frequencies.


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158 R. Sultan, S. Guirguis, M. Younes and E. El-Soaly

Keywords: Composite laminate plate, Finite element model, Energy

method, Natural frequencies, Delamination.

Nomenclature

a Distance from plate edge to delamination edge.

D11 Flexural rigidity of the healthy part in x-direction.

11D Flexural rigidity of the delaminated part in x-direction.

11E Youngs modules.

EX Experimental.

FEM Finite element model.

FRF Frequency Response Function.

h Thickness of plate.

L Length of square plate.

n Number of separated parts due to the delamination location.

THE Theoretical.

"y Second derivative of mode shape function with respect to x.

Mass per unit area of the plate.

Maximum deflection at x=2

L .

Length ratio.

Angular frequency.

2112 , Major and minor in-plane Poissons ratio.

1. IntroductionComposite materials are increasingly used in structural designs of aircraft,

helicopters, and spacecraft because of desirable properties like high strengthand stiffness, lightweight, fatigue resistance, and damage tolerance, etc. [1].

However, composites are very sensitive to the anomalies induced during their

fabrication or service life. Delaminations are found to be one of the important

defects in composite structures [2]. The presence of delaminations in a

composite structure affects its integrity as well as its mechanical properties

such as stiffness and strength. Reflection of the delamination in dynamic

response is the alteration of natural frequencies. In addition delamination modeswhich are related to the opening of the delaminated region depending on size

and location of delamination.


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Effect of the Thickness-wise Location Delamination 159

The use of vibration test as non destructive testing methods for defect

detection of laminated composite is a field attracting the interest of many

researchers [3-6].

Many authors have used the finite element technique to analyze the

dynamic of composite laminate. Ju et al. [7] presented a practical approach for

the vibration analysis of composite beams with multiple delaminations using

finite elements, and the results show that the effect of delamination on the

modal parameters depends on the mode number, the sizes, the locations and

the number of delaminations. Ramkumar et al. [8] in early 1979 presented a

simplified beam model to study the effect of delamination on the natural

frequencies of a delaminated beam. Gadelrab [9] used a finite element method

for modelling a composite laminated beam to obtain the effects of delamination

length and position on the natural frequencies. Zak et al. [10] presented finiteelement models to study the free vibration of cantilever plates with a through

width delamination. Their numerical results were compared quite well with

results from experimental investigation. Radu and Chattopadhyay [11] developed

a higher order shear deformation finite element to study the dynamic instability

of symmetric cross-ply cantilever plates with a through width delamination.

Kumar and Shrivastava [12] studied the effect of delamination on free

vibration response of square laminates with delamination around a central cut

out. It was found that the effect of delamination on natural frequencies is

mode dependent and in some cases delamination may have significant effect on

natural frequencies. Vibration tests were also carried out on an actual

specimen. It was concluded that the delamination results in the decrease innatural frequency, more predominantly for higher modes. Hu et al. [13]

proposed a FEM model to study the effect of delamination on the naturalfrequency and curvature of vibration mode of a clamped square plate with a

square delaminated region located at centre of the plate. They found that thenatural frequency decreases significantly with increasing delamination size. Yam

et al. [14] used a three-dimensional element to analyze the dynamics of

delaminated square laminates with free edges.

In present paper, a combined finite element and experimental approach

were used to characterize the vibration behaviour of composite laminate plates

with two opposite simply supports edges and the remaining two edges are free

boundary conditions. To this end, plates were made using the hand-lay-upprocess. Glass fiber was used as reinforcement in the form of bidirectionalfabric (0, 90) and epoxy resin as matrix. From the results, the influence of

thickness-wise delamination on natural frequencies was investigated. The firstnatural frequency was extracted theoretically by using energy method and the

results show good agreement with numerical and experimental results.

2. Preparation of test specimensThe composite laminate plate specimens used in present experiment were made

from 8 layers (0/90) woven E-Glass fiber with Epoxy matrix (

2

/75.3 mkg ).


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Fig. 2 Specimens with central thickness-wise delamination locations

3. Determination of Natural Frequency using Energy MethodThe laminate plate can be treated as onedimension analysis is that of the

investigation of cylindrical bending which concern plates those have boundary

condition, such as opposite two edges simply supported and the remaining two

edges are free as shown in Figure 3 and Figure 4.


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Fig. 3 Orthotropic composite laminate with two opposite simply supported

edges and other two edges are free

Fig. 4 Cylindrical bending deformation of square orthotropic laminate plate

3.1 Governing Equations

Consider the free vibration of laminated composite square plate of length (L)

with centrally delaminated part (L-2a), under cylindrical bending. The

convenient expression that represent the first mode shape of plate under

cylindrical bending showing below:

y SinL

x (1)

Where

The maximum potential strain energy Umax of the plate can be expressed

as:

Umax= dxyD

L

2"

0

11 )(2

1 (2)

After introducing equation (1) into equation (2) the Umax will be:


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Umax= )]()([

4

11113

32

SinDSinD

L

(3)

Where

D11=)1(12 2112

3

11

hE

11D =

)1(12 2112

1

3

11

n

i

ihE

L

a2

Similarly the maximum kinetic energy Tmax of the plate can be expressed

as:

Tmax= dxy

L

0

2)(2

1 (4)

After applying equation (1) into equation (4) and for conservative system

Umax= Tmax, this equality leads to the determination of the first fundamental

natural frequency of plate in the form:

411

3

2

LD

[ )])1((

11

11 SinDDSin

(5)

It may be observed that, for totally healthy plate at 1 and 1111 DD the

expression of equation (5) will be:

4

11

42

L

D

(6)

For delaminated plates with different interface locations in thickness

direction at 7.0 , the equation (5) can be expressed as follow:

11

112 217518171528D

D (7)

4. Tensile test

The material constants 11E , 22E , 12v and 12G of woven fiber Glass/Epoxy

composite plate were determined experimentally by performing unidirectional

tensile tests relevant to ASTM D3039 on specimens cut in longitudinal and

transverse directions, and at 45 to the longitudinal direction. The measured

experimental values of the elastic moduli are shown below:


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11E = 22E =19 GPa, 12v =0.256, 12G =2.8 GPa

5. Finite element model using ANSYSIn present research, the commercial finite element software ANSYS was used

to build finite element models and to study their vibration behaviour for both

healthy and delaminated cross ply 8-layered (0, 90) laminate plate. The 3-D

layered structural solid shell (SOLSH190) is 8 nodes element with three

degrees of freedom per node was used, this element type can be used for

simulating structure with wide range of thickness. The element allows 250

layers for modelling laminated composite. The layer information is input by

using section commands rather than real constant.

6. Experimental validation by vibration testThe results from present FE model and theoretical analysis validated with

experiments conducted on plates with two opposite simply supports edges and

the remaining two edges are free. Through vibration testing, it was determined

FRFs (Frequency Response Functions) which relate the response given by the

specimen when impacted by hammer, allowing for the determination of the

natural frequencies, this was done by fixing the laminate specimen in special

support locally manufactured as shown in Figure 5. The impact hammer was

used to give the input load (pulse) to the specimen, then output was capturedby the accelerometer and was amplified using a conditioning amplifier and

then read using the high resolution signal analyzer, giving the FRF. For everyspecimen multiple measurements were conducted Figure 6. The effect of

delaminations location through thickness wise direction on natural frequencies

was investigated.

Fig. 5 Test rig

F i x tu re C o m p o s i te lam in a te p la te


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Fig. 6 Experimental modal analysis

7. Result and discussionsAfter validating the present FEM in previous work [15], the experimental,

numerical and theoretical results for free vibration study of healthy and

delaminated laminate composite plates are presented. The variation of natural

frequencies with thickness-wise delamination location was investigated.

Frequencies were found for four modes and tabulated for comparison anddiscussion Table 1.

Table 1 The natural frequencies comparison between the theoretical analysis,

finite element model and measured experimental results of square compositelaminate plate in Hz.

Delamination

position

First mode Second mode Third mode Fourth mode

THE FEM EX FEM EX FEM EX FEM EX

Healthy 99.4 96.3 92.7 124.4 119.9 299.1 285.1 381.6 373.1

1-7 89.8 89.9 85.5 113.4 106.9 247.7 230.1 320 303.9

2-6 82.4 82.7 79.8 102 97.5 224.1 212.2 266.1 254.8

3-5 77.3 77.2 75.3 93.3 89.6 198.8 190.5 226.4 217.6

4-4 75.9 75.2 73.8 90.2 86.9 189.2 181.9 211.3 205.2

All interfaces 66.8 66.1 68.4 74.8 78.9 77.6 80.9 96.5 101.1

From Figure 7 it was observed that the decrease in natural frequencies for

a delamination at mid plane more significant than other three interfaces except

the case when the delamination located between all interfaces, which reveal

more decrease in natural frequencies. When the delamination was located closeto the free surface (1-7), the discrepancy between present FE model and

experimental data was substantial. This is likely to be due to the opening and

closing behaviour of delamination during vibrations will result in a decrease of

stiffness Figure 8. In the case of specimens containing multi delaminations

between all interfaces, the experimental frequencies higher than that of the


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other results, the possible reason could be the small deviation in the

manufacturing process because these samples have been specially manufactured

for the present study.

a) First mode

b) Second mode

c) Third mode

d) Fourth modeFigure. 7 Comparison between theoretical, FEM, and experimental measured

natural frequencies

0

40

80

120

Healthy plate Interface 1-7 Interface 2-6 Interface 3-5 Interface 4-4 All interfaces

Naturalfrequencyin(Hz)

Theoretical

FEM

Experimental

0

40

80

120

160



FEM

Experimental

0

40

80

120

160

200

240

280

320



FEM

Experimental

0

40

80

120

160

200

240

280

320

360

400

440



FEM

Experimental


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be contributed to the fact that delamination at inner interface may cause

a greater decrease in global stiffness than at outer interfaces.

3.

Greatest reduction in natural frequency occurs, when delaminationlocated between all interfaces.

4. It is also found that the mode shapes of delamination at the top freesurface vary significantly.

5. When the delamination was near the plate surface, the mode shape

displays an opening and that the opening was more obvious at the

delamination region near the free ends of the plate. Furthermore, when

mode shape hardly displays an opening, the finite element and

experimental frequencies were close to each other, and when the mode

shape displays an opening, the results show different frequencies.

6.

The above results show that the influence of delamination on naturalfrequencies varies with vibration modes.

7. As can been seen, the FE results comparing with experimental data fordelaminations located at the inner interfaces, the maximum difference

was 5.3%. But when the delamination was located close to the free

surface (1-7), the discrepancy between our FE model and experimental

data was 7.1%. Generally the present results obtained from free

vibration of the composite laminate plates of both experiment and FEM

were in good agreement and capable to provide accurate predictions for

natural frequencies of delaminated composite.

8. The current theoretical analysis is helpful to get results of first

fundamental natural frequency of the healthy and delaminated compositelaminate by using assumed mode shape function in energy method.

9.

The validity of present theoretical procedure is demonstrated by using

FEM and experimental work. The data from FEM is also used as test

case to assess the validity and accuracy of the proposed theoretical

analysis. The difference between the values computed with the present

analytical method and the finite element values for healthy plate is

3.1% and for delaminated plates is less than 1%.

10.Analytical methods to predict changes in the natural frequencies are of

dubious worth in more complex mode shapes of higher modes ofvibration and limited to a number of particular shapes of plates with

particular boundary conditions, and the experimental methods used toobtain the natural frequencies are difficult to set up, because we have

to use a proper manufacturing boundary condition. So far, finite element

method was shown to be more realistic for application.

11.Present finite element method can be successfully applied further to

analyze the natural frequencies of healthy and delaminated composite

plates. The FEM provides an alternative and convenient way to model

delamination in more complex structures.

12.The deviation of numeric results in relation to experimental ones, somepossible measurements error can be pointed out such as: measurement

noises, position and mass of accelerometer, non uniformity of specimens


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(bubble, voids, variation of thickness, bad surface finish), additionally

the lack of complete fixity provided by the experimental supporting

structure will have a significant effect on the experimental resonances.Also there may be variation of elastic properties of the plate, as the

sample cut from the plate was different from the plate used in the casevibration testing, tensile properties may vary with specimen preparation

and with speed and environment of testing causing variation in stiffness

which affect the values of natural frequency. Such factors are not taken

into account during numerical analysis, since the finite element model

consider the model entirely perfect and homogeneous properties, what

rarely occurs in practice. Also, the computational package ANSYS

(version 12.1) does not allow for the consideration of the fibers

interweaving present in the fabric used.

9. References

[1] Shokrieh. M., Najafi. A., Experimental evaluation of dynamic behaviour

of metallic plates reinforced by polymer matrix composites, Composite

Structures, pp. 472478, 75, 2006.

[2] Garg, A.C., . Delamination-a damage mode in composite structures.

Engineering Fracture Mechanics 29, pp.557-584. 1988.

[3] Salawu OS. Detection of structural damage through changes in

frequency: a review. Eng Struct;19:71823. 1997.[4] Gomes AJMA, Silva JMME. On the use of modal analysis for crack

identification. In: Proceedings of the 8th International Modal AnalysisConference, FL USA, p. 110815. 1991.

[5] Sanders D, Kim YI, Stubbs RN. Non-destructive evaluation of damage

in composite structures using modal parameters. Exp Mech;32:24051.

1992.

[6] Tenek LH, Henneke II EG, Gunzbhurger MD. Vibration of delaminated

composite plates and some applications to non-destructive testing.

Composite Structures;23(3):253262. 1993.

[7]

Ju F, Lee HP, Lee KH. Free-vibration analysis of composite beams

with multiple delaminations. Composites Engineering;4(7):715730. 1994.[8] Ramkumar, R. L., Kulkarni, S. V. and Pipes, R. B., Free Vibration

Frequencies of a Delaminated Beam, 34th Annual Technical

Conference Proceedings, Society of Plastic Industry Inc., Sec. 22-E, pp.

15 (1979).

[9] Gadelrab, R. M., The Effect of Delamination on the Natural Frequencies

of a Laminated Composite Beam, Journal of Sound and Vibration,

197, pp. 283292 1996.

[10] Zak, A., Krawczuk, M. and Ostachowicz, M., Numerical and

Experimental Investigation of Free Vibration of Multilayer Delaminated


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Composite Beams and Plates, Computational Mechanics, 26, pp.

309315.2000.

[11]

Radu, A. G. and Chattopadhyay, A., Dynamic Stability Analysis ofComposite Plates Including Delaminations Using a Higher Order Theory

and Transformation Matrix Approach, International Journal of Solidsand Structures, 39, pp. 19491965.2002.

[12] Kumar, A. and Shrivastava, R. P., Free Vibration of Square Laminates

with Delamination Around a Central Cutout Using HSDT, Composite

Structures, 70, pp. 317333. 2005.

[13] Hu, N., Fukunaga, H., Kameyama, M., Aramaki, Y. and Chang, F. K.,

Vibration Analysis of Delaminated Composite Beams and Plates Using

Higher Order Finite Element, International Journal of Mechanical

Science, 44, pp. 14791503 2002.[14]

Yam, L. H., Wei, Z., Cheng, L. and Wong, W. O., Numerical Analysis

of Multi-Layer Composite Plates with Internal Delamination, Computersand Structures, 82, pp. 627637. 2004.

[15] R Sultan, S Guirguis, M Younes and E El-Soaly.International journal of

mechanical engineering and robotics research Vol. 1, No. 3, October

2012.

Effect of the Thickness-wise Location Delamination on Natural Frequency for Laminate Plate

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