Effect of the Thickness-wise Location Delamination on Natural Frequency for Laminate Plate
Transcript of 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
1/14
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
thof Ramadan Higher Institute of Technology, Egypt,
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.
-
7/25/2019 Effect of the Thickness-wise Location Delamination on Natural Frequency for Laminate Plate
2/14
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.
-
7/25/2019 Effect of the Thickness-wise Location Delamination on Natural Frequency for Laminate Plate
3/14
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 ).
-
7/25/2019 Effect of the Thickness-wise Location Delamination on Natural Frequency for Laminate Plate
4/14
-
7/25/2019 Effect of the Thickness-wise Location Delamination on Natural Frequency for Laminate Plate
5/14
Effect of the Thickness-wise Location Delamination 161
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.
-
7/25/2019 Effect of the Thickness-wise Location Delamination on Natural Frequency for Laminate Plate
6/14
162 R. Sultan, S. Guirguis, M. Younes and E. El-Soaly
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:
-
7/25/2019 Effect of the Thickness-wise Location Delamination on Natural Frequency for Laminate Plate
7/14
Effect of the Thickness-wise Location Delamination 163
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:
-
7/25/2019 Effect of the Thickness-wise Location Delamination on Natural Frequency for Laminate Plate
8/14
164 R. Sultan, S. Guirguis, M. Younes and E. El-Soaly
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
-
7/25/2019 Effect of the Thickness-wise Location Delamination on Natural Frequency for Laminate Plate
9/14
Effect of the Thickness-wise Location Delamination 165
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
-
7/25/2019 Effect of the Thickness-wise Location Delamination on Natural Frequency for Laminate Plate
10/14
166 R. Sultan, S. Guirguis, M. Younes and E. El-Soaly
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
Healthy plate Interface 1-7 Interface 2-6 Interface 3-5 Interface 4-4 All interfaces
Naturalfrequencyin(Hz)
FEM
Experimental
0
40
80
120
160
200
240
280
320
Healthy plate Interface 1-7 Interface 2-6 Interface 3-5 Interface 4-4 All interfaces
Naturalfrequencyin(Hz)
FEM
Experimental
0
40
80
120
160
200
240
280
320
360
400
440
Healthy plate Interface 1-7 Interface 2-6 Interface 3-5 Interface 4-4 All interfaces
Naturalfrequencyin(Hz)
FEM
Experimental
-
7/25/2019 Effect of the Thickness-wise Location Delamination on Natural Frequency for Laminate Plate
11/14
-
7/25/2019 Effect of the Thickness-wise Location Delamination on Natural Frequency for Laminate Plate
12/14
168 R. Sultan, S. Guirguis, M. Younes and E. El-Soaly
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
-
7/25/2019 Effect of the Thickness-wise Location Delamination on Natural Frequency for Laminate Plate
13/14
Effect of the Thickness-wise Location Delamination 169
(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
-
7/25/2019 Effect of the Thickness-wise Location Delamination on Natural Frequency for Laminate Plate
14/14
170 R. Sultan, S. Guirguis, M. Younes and E. El-Soaly
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.