Materials Sciences and Applications, 2013, 4, 751-760
Published Online November 2013 (htt p://www.scirp.org/journal/msa)
http://dx.doi.org/10.4236/msa.2013.411095
Open Access MSA
751
The Effect of Functionally Graded Materials into the
Sandwich Beam Dynamic Performance
Saber A. Rabboh1, Nadia E. Bondok2,3, Tamer S. Mahmoud1, Heba I. El Kholy4
1Mechanical Engineering Department, Shoubra Faculty of Engineering, Banha University, Banha, Egypt; 2Department of Technol-
ogy Development, Specified Studies Academy Worker’s University, Cairo, Egypt; 3Faculty of Design and Architecture, Jazan Uni-
versity, Jazan, KSA; 4Faculty of Engineering, Industrial Education, Beni-Suef University, Beni-Suef, Egy pt.
Received September 4th, 2013; revised October 17th, 2013; accepted November 5th, 2013
Copyright © 2013 Saber A. Rabboh et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
The original purpose of FGMs was the development of super resistant materials for propulsion systems. In the present
work, numerical and experimental techniques are used to investigate the dynamic behavior of generally laminated
composited beams. In the numerical analysis, the laminated beam is modeled u sing the commercial finite element soft-
ware ANSYS. In the experimental study the core and face materials of sandwich beam specimens are nylon/epoxy
FGMs and pure epoxy laminates respectively. The dynamic behavior of the sandwich composite beam specimens with
different fiber orientation was carried out using two dynamic excitation techniques, harmonic using harmonic response
and impulse using hammer. The specimens were prepared in the following configurations, different orientation angles,
different layers, and different thickness. The results reveal that the natural frequencies of sandwich beam were affected
directly by the face materials. The natural frequency decreases with increasing fiber orientations of the nylon/epoxy
face laminates. Increasing the thickness increases natural frequencies. This study concluded that it is useful for the de-
signers to select the fiber orientation angle to shift the natural frequencies as desired or to control the vibration level.
Keywords: Sandwich Beam; FGM; Nylon/Epoxy; Natural Frequency; Fiber Orientation
1. Introduction
FGMs are a new generation of engineered materials first
introduced by a group of Japanese scientists in 1984. The
original purpose of FGMs was the development of super
resistant materials for propulsion systems and air frame
of the space planes in decreasing thermal stresses and
increasing the effect of protection from heat.
The concept of FGMs emerged from the need to fab-
ricate a new composite for high temperature structural
applications by using a heat resistant ceramic on the high
temperature side and a metal on the low temperature side
to provide mechanical toughness. Anisotropy of these
composite allows the designer to tailor the material in
order to achieve the desired performance requirement, so
it is fundamental importance to develop tools that allow
the designer to obtain optimized designs considering the
structure requirement; and functional characteristics im-
posed by the production process. In engineering parties it
is of vital importance to induct thy dynamic analysis of
structures [1], and the dynamic analysis in mechanical
design is of great importance to control the vibration in
order to maintain the operating performance and to pre-
vent sudden failures in the structures. The occurrence of
resonance will decrease the life time of the structure and
cause unpredictable failures. A variety of structure com-
ponents made of FMGs such as turbine blades, aircraft
wings and aerospace can be approximated as laminated
composite sandwich beams, which require a deeper un-
derstanding of the vibration characteristics of the com-
posite sandwich beams [2]. Therefore, it is essential to
know characteristics of these structures, which may be
subject to dynamic loads in complex environmental con-
ditions. If the frequency the loads variation matches one
of resonance frequencies of the structure, large torsion
defections and internal stress can occur, which may lead
to failure of the structure components. To avoid the typi-
cal problems caused by vibrations it is important to de-
termine natural frequencies of the structure and modal
shapes to reinforce the most flexible regions, or damping
should be increased.

The Effect of Functionally Graded Materials into the Sandwich Beam Dynamic Performance 752
FGMs composed of two material constituents mixed
together with locally prescribed volume fractions have
been the focus of the majority of the literature concerning
FGMs and will be the focus of the study. Most authors
deal with epoxy and nylon. Hajime et al. [3] studied the
damping p ropert ies of carbon fi ber-re inforce d i nte rle aved
epoxy composites. Several types of thermoplastic-elasto-
meric films, such as polyurethane elastomers, polyethyl-
ene-based ionomers and polyamide elastomers, were
used as the interleaving materials. The damping proper-
ties of the composite laminates with/without the interleaf
films were evaluated by the mechanical impedance me-
thod. Also, the effects of the lay-up arrangements of the
carbon-fiber prepregs on the damping properties of the
interleaved laminates were examined. The stiffness of the
films at the resonant frequency of the laminates was an-
other important parameter that controlled the loss factor
of the interleaved laminate.
Khondker et al. [4] showed that the presence of fiber/
matrix interfaces strongly influences the overall me-
chanical properties of composites. Polyamide materials
were chosen and combined with Aramid fiber in an at-
tempt to achieve better interfacial bonding. Aramid/epo-
xy knitted composites were also fabricated to compare
them with aramid/nylon thermoplastic composites. Proc-
essing time, tensile modulus and strength of Aramid/
nylon composites have increased and decreased, respec-
tively. Aramid/nylon knitted composites have revealed
comparable strength property in the course direction,
albeit they have inferior tensile strength in the wale di-
rection when compared to that in Aramid/epoxy compos-
ites. In Aramid/nylon knitted composites, while tensile
modulus exhibited an increasing trend, there were clear
drops in tensile strengths with longer molding time. This
indicates that there could be an optimum molding condi-
tion at which maximum tensile properties can be ob-
tained.
In the work carried out by Meng-Kao et al. [5], the
faces of sandwich beams were graphite/epoxy laminates.
Epoxy and phenol resins served as a matrix material, and
multi-walled carbon annotates (MWNTs) provided rein-
forcement of the fabricated MWNT/polymer nanocom-
posites as core materials for sandwich beams. The finite
element method was used for free vibration analysis of
the sandwich beams; the natural frequencies and mode
shapes of the sandwich beams were calculated numeri-
cally. The experimental and numerical investigation of
the dynamic properties of sandwich beams with MWNT/
polymer nano composites as core materials, concluded
that the face laminate dominates the stiffness of the sand-
wich beams, and that the natural frequen cies of sandwich
beams were affected directly by the face materials and
decreased with increasing fiber orientations of the graph-
ite/epoxy face laminate.
A large number of investigators address the problem
of free vibration with free vibration analysis of FGMs.
Khalili et al. [6] studied the free vibration of three-lay-
ered symmetric sandwich beam which is investigated
using dynamic stiffness and finite element methods. To
determine the governing equations of motion by the pre-
sent theory, the core density has been taken into consid-
eration. Natural frequencies and mode shapes are com-
puted by the use of numerical techniques. After valida-
tion of the present model, the effect of various parame-
ters such as density, thickness and shear modulus of the
core for various boundary conditions on the first natural
frequency is studied. The study concluded that the face
properties like density, thickness are remained constant,
but the core properties are varied. Irrespective of the
boundary conditions, increasing the core/face density
ratio decreases the first natural frequency of the beam.
Galal et al. [7] studied the free vibration characteris-
tics of laminated composite beams (LCBs) which are one
of the bases for designing and modeling of industrial
products. In this study, the flexural vibrations of LCBs
are analyzed analytically using Bernoulli-Navier hy-
pothesis theory. The commercial finite element program
ANSYS 10.0 is used to perform a dynamic modeling to
the laminated beams. Mindlin eight-node isoperimetric
layered shell elements (Shell 99) are employed in the
modeling for describing the bending vibrations of these
laminated sandwich beams. The study concluded that
out-of plane bending frequencies decrease, in general, as
the fiber angle increases, in the case of the effect of fiber
orientation.
Simsek et al. [8] investigated the free vibration char-
acteristics and the dynamic behavior of a functionally
graded simply supported beam under a concentrated
moving harmonic load. Trial functions denoting the
transverse and the axial deflections of the beam are ex-
pressed in polynomial forms. The constraint conditions
of supports are taken into account by using Lagrange
multipliers. It is assumed that material properties of the
beam vary continuously in the thickness direction ac-
cording to the power-law form. The study concluded that
the effects of the different material distribution, velocity
of the moving harmonic load, the excitation frequency on
the dynamic responses of the beam are discussed. It is
observed from the investigations that the above-men-
tioned effects play very important role in the dynamic
behavior of the FG beam.
Xian-Kun et al. [9] deals with the small- and large-
amplitude vibrations of compressively and thermally
post-buckled sandwich plates with functionally graded
material FGM face sheets in thermal environments. Both
heat conduction and temperature-dependent material
properties are taken into account and the material proper-
ties of both FGM face sheets and a homogeneous sub-
Open Access MSA

The Effect of Functionally Graded Materials into the Sandwich Beam Dynamic Performance 753
strate are assumed to be temperature dependent. The re-
sults show that, as the volume fraction index increases,
the fundamental frequency increases in the pre-buckling
region, but decreases in the post-buckling region.
In the work carried out by Mohammed et al. [10,11], a
generalized model presenting the sandwich beams was
developed to calculate the flexural rigidity and sandwich
beams dynamic characteristics. Different cases such as
sandwich beams multi-layer cores, sandwich beams multi
cells, sandwich beams with holes in its cores having dif-
ferent shapes and different orientations were investigated.
The finite element code ANSYS 11 was used for free
vibration analysis of the sandwich beams; the natural
frequencies, mode shapes, and the static deflection of the
sandwich beams were calculated. The study concluded
that the finite element code ANSYS 11 was used fo r free
vibration analysis; the natural frequencies, mode shapes,
and the static deflection of the sandwich beams are cal-
culated. The investigation revealed that the static and
dynamic responses of the sandwich beams can be ad-
justed to the increasing of the number of cores or the
number of cells. Shapes and the static deflection of the
sandwich beams were calculated. The obtained results
from the finite element code ANSYS 11 such as static
deflections, static rigidity and natural frequencies were
compared with that obtained from the generalized equa-
tions according to the cases of investigations which ap-
pear to be in good agreement with each others, therefore
the generalized model can be used for the best design of
the sandwich beams.
In the present work, a FME model analysis and ex-
perimental techniques are used to investigate the dy-
namic behavior of generally laminated composited
sandwich beams, for different cases such as sandwich
beams FGM cores with different layers, different angles
and different thicknesses by using core and face materi-
als of sandwich beam specimens from Nylon/epoxy
FGMs and pure epoxy laminates respectively.
2. Materials
2.1. The Matrix
Epoxy resin was used as a matrix material. The type of
epoxy resin used in the present investigation is KE-
MAPOXY 150 manufactured by Chemicals for Modern
Buildings Company (CMB), Egypt. Epoxy resin is a
thermoses’ resin with good thermal and environmental
stability.
2.2. Nylon Fiber
In the present work Nylon fibers were used as reinforcing
agent. Nylons are semi-crystalline polymers. The amide
group (-CO-NH-) provides hydrogen bonding between
polyamide chains, giving nylon high strength at elevated
temperatures, toughness at low temperatures, combined
with its other properties, such as stiffness, wear and abra-
sion resistance, low friction coefficient and good chemi-
cal resistance.
3. Mould Preparation
Two different types of cuboids moulds were used to pre-
pare the FGMs sandwich beams. Each mould consists of
four sheets of plastic representing the wall sides. The
first mould was used to prepare four layers FGM sand-
wich beams while the second mould was used to prepare
the five layers sandwich beams. The dimension of each
mould is 25 × 100 × 100 mm3 (height (h) × length (L) ×
width (b)) as shown in Figure 1.
The sheets were punched into small holes using CNC
machine. Holes has 1 mm diameter. To change nylon
ratio inside the layers, the punches of each row are ar-
ranged as shown in Figures 2 and 3.
4. Specimens Preparation
The epoxy and hardener were mixed by a mechanical
mixer with speed 300 rpm for 3 minutes in a temperature
(a)
(b)
Figure 1. Moulds used to manufacture FGMs sandwich
beam specimens: (a) Four layers mould and (b) Five layers
mould. Dimensions in mm.
Open Access MSA

The Effect of Functionally Graded Materials into the Sandwich Beam Dynamic Performance 754
Figure 2. Face of plastic sheet used to fabricate four layers
FGM sandwich beams showing two different holes layers.
Dimensions in mm.
Figure 3. Face of plastic sheet used to fabricate five layers
FGM sandwich beams showing three different holes layers.
Dimensions in mm.
in room temperature. After that the epoxy/hardner mix-
ture was poured in the plastic mould. The resin-contain-
ing nylon-fiber/epoxy was allowed to cure for about a
week. After curing, test specimens were cut using an
automatic saw with two different thicknesses, typically,
25 mm × 100 mm × 20 mm and 25 mm × 100 mm × 10
mm.
Nylon fibers having diameter of 0.5 mm were woven
into the holes of mould faces. Several specimens with
different nylon fibers orientations were prepared. Figure
4 show the nylon fibers orientations for the four and five
layers specimens. For each layer systems (i.e. four and
five layers) the volume fraction of the nylon fibers in
each layer varies. Six types of FGM sandwich beam
specimens were prepared as shown in Figures 5 and 6.
The total number of specimens was twelve (two speci-
mens each have thickness form each FGM sandwich
beam).
Figures 5 and 6 also shows the volume fractions of
both the epoxy and nylon fibers in the layers of four and
five layers specimens, respectively. In these Figures, the
(a)
(b)
Figure 4. Schematic illustration of fabricated laminated
composites with (a) four layers and fiber orientation (0/90)
and (b) five layers and fiber orientation (0/90/0).
Figure 5. Schematic illustration of sandwich FGM beams
having 4-layers showing the volume fraction of epoxy/ny lon
for specimens w ith fiber orientation.
layer 96/4 means that the volume fractions of the epoxy
matrix and the nylon fibers are 96% and 4%, respec-
tively.
5. Material Characterization
The material elastic properties of the lamina of test spe-
Open Access MSA

The Effect of Functionally Graded Materials into the Sandwich Beam Dynamic Performance 755
Figure 6. Schematic illustration of sandwich FGM beams
having 5-layers showing the volume fraction of epoxy/ny lon
for specimens w ith fiber orientation.
cimens are determined through the simple rule of mix-
tures. These properties are Young’s module (E1—in di-
rection 1, E2—in direction 2, E3—in direction 3). Pas-
sions’ ratios (υ12, υ13, υ23). In plane shear modulus (G12)
and transverse shear modules (G13 and G23) as referred in
Figure 7. This figure defines the material principal axes
for a typical woven fiber reinforced lamina. Axis 1 is
along the fiber length and represents the longitudinal
direction of the lamina; axes 2 and 3 represent the trans-
verse in plane and through the thickness directions re-
spectively. The tables in the Appendix indicated the Ma-
terial properties of core sandwich beam fiber orienta-
tion for three angles (0, 45, 90).
6. Calculation Percentage of Fiber
To calculate the ratio of nylon for each layer the area of
each hole, and t h e v o l ume fraction of fib e r an d matrix are
estimated by the following equations

f
f
fm
V
vVV  (1)
1
fm
vv (2)
where νf and νm are the volume fraction of the fiber, ma-
trix respectively.
By using densities of the fiber ρf, matrix ρm and com-
posite ρc, respectively, the fiber volume fraction νf can be
obtained by Equation (2)
cffm
vm v
 
 (3)
Using the relation of Equation (3) the fiber volume
faction νf is found according to the densities of fiber and
matrix present in Table 1 (Appendix). Then, the elastic
constants of the woven fabric composite material are
numerically estimated using the relation which are based
on their constituent properties .the young’s modulus and
the Poisson ratio o f th e fill and warp direction s are calcu -
lated and taken as an average of the longitudinal and
transverse values of thee corresponding unidirectional
layer.
Figure 7. Lamina reference axes.
Table 1. The mechanical properties of constituents of test
pecimens, nylon/e poxy.
Properties
Material Elasticity modulus
(Gpa) Density (kg/m3) Poisson ratio
Epoxy resin10 1800 0.4
Nylon fiber3 1130 0.2
The elastic constants and passion ratio of the unidirec-
tional composite are calculated using the simple rule of
mixtures by the relations of Equations (1)-(8) [10]
1
f
fm
EEvEv
m

 (4)



2
fm fmf
m
fm fmf
EE EEv
EE
EE EEv


 


 




(5)

12 11
23 212 11
1
11
mm
ff mf
mm m
EE
vv EE

 








 (6)



12 m
fm
GG G
fm fmf
fmf
GG GGv
GG Gv


 




(7)




22
23 23
21
E
G

 (8)


12 1
f
fm f
v   v
(9)
where indices m and f denote matrix and fiber, respec-
tively.
7. Experimential Dynamictesting Methods
7.1. Impulse Excitation Technique
The natural frequencies of the free vibration modes
where measured for boundary conditions, cantilever us-
ing the impact-testing method. The experimental setup is
schematically shown in Figure 8. The impulse was pro-
vided with Bruel & Kjaer (B&K) made impulse excita-
tion technique hammer of Type 8207 with steel tip hav-
Open Access MSA

The Effect of Functionally Graded Materials into the Sandwich Beam Dynamic Performance
Open Access MSA
756
7.2. Harmonic Response Technique
2
2
1
4
3
5
The natural frequencies of the free vibration modes were
measured for boundary conditions, cantilever using the
harmonic response method. The experimental setup is
schematically shown in Figure 10. The impulse was pro-
vided with vibration Exciter—Type 4809 with robust
titanium housing with integrated titanium connector. The
response was measured with B&K 4507 accelerometer
according to the previous conditions which using with
impulse excitation technique testing method. Figure 11
shows the frequency response of a typical sandwich
beam.
Figure 8. Impulse excitation technique apparatus. 1—power
amplifier—type 2706; 2—B & K portable PULSE 3560B
(analyzer); 3—heavy duty impulse excitation technique
hammers—types 8207; 4—4507 piezoelectric IEPE acceler-
ometers; 5—specimen. 8. Dynamic Modeling by the Finite Element
The beams were discretized using finite element (shell99)
as, this element has 8 nodes and is available in the com-
mercial package ANSYS. It is constituted by layers that
are designated by LN—Layer Numbers which, increas-
ing from the bottom to the top of the laminates; the last
number quantifies the existent total number of layers in
the laminates (NL—Total Number of Layers). The element
has six degrees of freedom at each node: translations in
the nodal x, y, and z directions and rotations about the
nodal x, y, and z-axes. The choice of shell99 element
type is based on layered applications of a structural shell
model, and the type of results that need to be calculated.
ing impulse excitation technique duration of 0.25 - 2 ms
and maximum frequency of 25 kHz. The response was
measured with B&K 4507 accelerometer having a weight
of 3 g, fixed on the beam surface with adhesive wax. The
signal from the accelerometer was fed into a five channel
Fast Fourier Transform (FFT) analyzer (B&K Pulse Ana-
lyzer 3560B) via a charge amplifier (B&K 2706). The
FFT of the time domain response from the accelerometer
was computed using the software Pulse computer, ver-
sion 6.0, to obtain the frequency response function
(FRF), whose peak locations give the natural frequencies
of various modes. The frequencies to 12 kHz were meas-
ured for all samples. To ensure that the accelerometer
signal is captured from the start of the impulse, the ana-
lyzer was set to a pre-trigger delay, so that it starts sam-
pling before the impulse excitation technique occurs.
Figure 9 shows the frequency response of a typical
sandwich beam.
Modal analysis will be carried out with ANSYS 11.0
finite element software. A modal analysis typically is
used to determine the vibration characteristics (natural
frequencies and mode shapes) of a structure in the design
stages. It can also serve as a starting point for another,
more detailed, dynamic analysis, such as a harmonic re-
sponse, or a spectrum analysis.
Fr equenc y R es pons e H1(R es pons e 1,Forc e) - Mark 11 (Magnit ude)
MODEL .me a : SA MPLE5 : In p u t : Mod a l F FT Anal y ze r 1
01k 2k 3k 4k5k 6k 7k 8k 9k10 k11k12 k
0
20
40
60
80
10 0
12 0
14 0
16 0
18 0
200
[Hz]
[(m/s² )/N]Fr equenc y R es pons e H1(R es pons e 1,Forc e) - Mark 11 (Magnit ude)
MODEL .me a : SA MPLE5 : In p u t : Mod a l F FT Anal y ze r 1
01k 2k 3k 4k5k 6k 7k 8k 9k10 k11k12 k
0
20
40
60
80
10 0
12 0
14 0
16 0
18 0
200
[Hz]
[(m/s² )/N]
Figure 9. Frequency response of a typical sandwich beam.

The Effect of Functionally Graded Materials into the Sandwich Beam Dynamic Performance 757
4
1
3
2 5
Figure 10. Harmonic response testing equipment. 1—power
amplifier—type 2706 ; 2—portable PULSE 356 0B (anal y zer ) ;
3—vibration exciter—type 4809; 4—specimen; 5—4507 pie-
zoelectric IEPE accelerometers.
Finite Element Modeling
The finite element code ANSYS 11 was used for free
vibration analysis of the sandwich beams; the natural
frequencies and mode shapes and the static deflection of
the sandwich beams were calculated. Element shell99
having eight nodes and six degrees of freedom per node,
was used. The obtained results such as natural frequen-
cies were compared with the sandwich beam are made
face of isotropic materials and core of many plies of
orthotropic materials as shown in Figure 12. In the
analysis the material properties of the core and face ma-
terials of sandwich beams indicate to (Appendix (a)) the
sandwich beam width = 100 mm, length L = 100 mm and
thickness b = 20. A perfect bonding at the interface be-
tween the face and the core materials was assumed. The
sandwich beam is considered to be cantilever type, i.e.
fixed at one end.
9. Result and Discussion
Table 2 show the comparison between the experimental
and FE mode results for the impulse excitation technique
damped natural frequencies obtained by free vibration
test for all types of laminated sandwich beam previously
mentioned also Figure 13 indicated this comparison of
the natural frequencies, equivalent to the damping char-
acteristics for the laminated sandwich beam with thick-
ness 20 mm of fiber angle 0˚, 45˚, 90˚.
9.1. Influence of Number of Layer on Vibration
of Sandwich Beam
The influence of increase the number of layers and
amount of fiber for the same total thickness of the free
vibration for the laminated sandwich beam is investi-
gated. The analysis is preformed using experimental test
and finite element method. The results indicated that in-
crease the number of layer increase natural frequencies
of the sandwich beam as shown in Figure 13.
Variation of flexural frequencies with respect to fiber
angle change of woven roving laminated beams are pre-
sented in Figure 13. The experimental frequencies are
plotted with the ANSYS results against fiber angle of
woven roving laminated beams.
This is due to possibility is present in symmetric angle
ply laminated and the regularity of the distribution of the
proportion of the different fiber in each layer .This is
possibility makes one or more of these materials very
attractive since due possibility is present in symmetric it
makes possibility to obtain the desired natural frequen-
cies without increasing mass or changing geometry. In
practical application, it means that if a natural frequency
excites the structure, the designer changes the material
properties by changing parentage of fiber in each layer,
changing geometry.
9.2. The Influences of Fiber Orientation Are
Investigated
The material properties of the core laminate of sandwich
beams were varied through the fiber orientations in core
Fr equenc y R es po ns e H1(Res po nc e,Fo rc e) - Mark 1 (Magnitude)
Wor k ing : s am ple5 : Input : F FT Analyzer
01k 2k 3k 4k5k 6k 7k 8k 9k 10 k11k12 k
0
10
20
30
40
50
60
[Hz]
[(m/s² )/N]Fr equenc y R es po ns e H1(Res po nc e,Fo rc e) - Mark 1 (Magnitude)
Wor k ing : s am ple5 : Input : F FT Analyzer
01k 2k 3k 4k5k 6k 7k 8k 9k 10 k11k12 k
0
10
20
30
40
50
60
[Hz]
[(m/s² )/N]
Figure 11. Frequency r e sponse of a typic al sandw ic h be am.
Open Access MSA

The Effect of Functionally Graded Materials into the Sandwich Beam Dynamic Performance 758
X
Y
Z
Figure 12. Sketch of five layers symmetric of sandwich
beam.
0
2000
4000
6000
8000
10000
1234
Natualfequencies(Hz)
modeno
twolayers
experimntal
twolayers
FEM
three layrs
experimental
(a)
0
2000
4000
6000
8000
10000
1234
Natualfequencies(Hz)
modeno
twolayers
experimntal
two layers
FEM
th reelayrs
experimental
(b)
Figure 13. Experimental test and theoretical variation natu-
ral frequencies, of four layers and to five layers versus,
mode of variation using (impulse). (a) At fiber orientation θ
= 0˚ and (b) At fiber orientation θ = 90˚.
nylon/epoxy laminates. Figure 14 shows the natural fre-
quencies of the bending modes of sandwich beams with
an epoxy face and varied fiber orientation in the ny-
lon/epoxy core laminate; the fiber orientations in ny-
lon/epoxy core laminates are fabricated with angles
(0/90), (45/90) and (90/-90). According to Figure 14, the
natural frequencies of the sandwich beams decrease with
increasing fiber orientation of the core laminate.
From these results, it is possible to verify the influence
of fiber orientation on the free flexural vibration of lami-
nated beams. It is found that the maximum flexural fre-
quency occurs at θ = 0˚ and the minimum occurs at 90˚.
This can be explained by the fact that the fibers oriented
at 0˚ are more appropriate to flexural loads.
Variation of flexural frequencies with respect to fiber
angle change of woven roving laminated beams are pre-
sented in Figure 14. The experimental frequencies are
plotted with the ANSYS results against fiber angle of
woven roving laminated beams.
Table 2. Comparison of natural frequencies (Hz) between
ANSYS and experimental (impulse excitation technique,
harmonic response technique) for woven FGM laminated
sandwich beams.
ORINTATION (20) impulse excitation technique
ANSYSexp ANSYS exp ANSYSexp
0 0 45 45 90 90
1504 2528 1460 2448 1470 880
4001 5400 3921 5120 3881 4600
6960 6744 6858 7024 6762 6000
7957 8992 7719 9016 7969 8520
12123 13000 11876 1186011475 9328
ORINTATION (20) harmonic response technique
ANSYSexp ANSYS exp ANSYSexp
0 0 45 45 90 90
609 544 559 544 609 160
1209 800 1659 800 1209 736
4806 5728 4406 5344 4806 4544
9602 9536 8802 8928 9602 7360
1200 12480 10450 114901200 9512
Figure 14. Natural frequencies of sandwich beam from FE
model and Harmonic response method for five layers.
With relation to the deviations of the FE modal results
in relation to the experimental ones, come possible meas-
urement errors can be pointed out such as: measurement
noise, positioning of the accelerometers and their mass,
non-uniformity in the specimens properties (voids, varia-
tions in thickness, non uniform surface finishing). Such
factors are not taken into account during the numerical
analysis, since the model considers the specimen entirely
perfect and with homogeneous properties, what rarely
occurs in practice. Another aspect to be considered is that
the input properties in the model came from the applica-
tion of the rule-of mixtures and they do not take into ac-
count effects of the fiber-matrix interface as well as the
irregular distribution of resin on the fibers. Also, these
models did not include damping effects, which can have
a large influence on the structure behavior. Also, the
Open Access MSA

The Effect of Functionally Graded Materials into the Sandwich Beam Dynamic Performance 759
computational package ANSYS does not allow for the
consideration of the fibers interweaving present in the
fabric used.
10. Conclusions
In this work, the dynamic characteristics of generally
laminated FGM composites sandwich beam with differ-
ent fiber orientations were tested experimentally and
theoretically. The main conclusions that can be drawn
from this investigation are:
1) The changes in fiber angle yield to different dy-
namic behaviors of the component, which has, different
natural frequencies for the same geometry, mass and
boundary conditions, as the fiber angle increases, and the
flexural natural frequencies damp, with range 48% to 8%
related to the change of fiber angle (0˚ to 90˚) of im-
prove fiber orientation of the epoxy/nylon core FGM
laminate.
2) Increasing the thickness leads to the improvement
of natural frequencies according to the moment of interia
of the sandwich beam cross section.
3) Increasing the number of the layers leads to the im-
provement of the natural frequencies with range 9% to
44% related to the change of fiber angle (0˚ to 90˚).
REFERENCES
[1] L. Qi, V. P. Iu and K. P. Kou, “Three-Dimensional Vi-
bration Analysis of Functionally Graded Rectangular
Plates,” Journal of Sound and Vibration, Vol. 311, 2006,
pp. 362-381.
[2] M. Koizumi, “Concept of FGM,” Ceramic Transactions,
Vol. 34, 1993, pp. 3-10.
[3] K. Hajime and K. Manabu, “Damping Properties of Ther-
moplastic-Elastomeric Interleaved Carbon Fiber-Rein-
forced Epoxy Comp osites,” Composites Science and Tech-
nology, Vol. 64, No. 16, 2004, pp. 2517-2523.
http://dx.doi.org/10.1016/j.compscitech.2004.05.006
[4] T. Khondker, M. Fukui, A. Inoda and H. Nakai, “Fabrica-
tion and Mechanical Properties of Aramid/Nylon Plain
Knitted Composites,” Composites: Part A, Vol. 35, No.
10, 2004, pp. 1195-1205.
http://dx.doi.org/10.1016/j.compositesa.2004.03.004
[5] Y. Meng-Kao and H. Tsung-Han, “Dynamic Properties of
Sandwich Beams with MWNT/Polymer Nanocomposites
as Core Materials,” Composites Science and Technology,
Vol. 68, No. 14, 2008, pp. 2930-2936.
http://dx.doi.org/10.1016/j.compscitech.2007.10.010
[6] S. M. R. Khalili, N. Nemati, K. Malekzadeh and A. R.
Damanpack, “Free Vibration Analysis of Sandwich Be ams
Using Improved Dynamic Stiffness Method”, Composite
Structures, Vol. 92, No. 2, 2010, pp. 387-394.
http://dx.doi.org/10.1016/j.compstruct.2009.08.020
[7] A. Galal and F. Mohammed, “Effects of Orientation and
Laminate Stacking Sequence on Out-of-Plane and In-
Plane Bending Natural Frequencies of Laminated Com-
posite Beams,” Composite Structures, Vol. 82, 2009, pp.
146-156.
[8] M. Simsek and T. Kocaturk, “Free Vibration Analysis of
Beams by Using a Third-Order Shear Deformation The-
ory,” Vol. 32, 2007, pp. 167-179.
[9] X. Xian-Kun and S. Hui-Shen, “Vibration of Post-Buck-
led Sandwich Plates with FGM Face Sheets in a Thermal
Environment,” Journal of Sound and Vibration, Vol. 314,
No. 1-2, 2008, pp. 254-274.
http://dx.doi.org/10.1016/j.jsv.2008.01.019
[10] M. A. Salam and N. E.Bondok, “Free Vibration Charac-
teristic for Different Configurations of Sandwich Beams,”
Journal of Sound and Vibration, Vol. 10, 2009, pp. 1-14.
[11] M. A. Salam and N. E.Bondok, “Free Vibration Charac-
teristics for Different Configuratio ns of Sandwich Be ams ,”
International Journal of Mechanical & Mechatronics, Vol .
10, 2010, pp. 41-54.
Open Access MSA

The Effect of Functionally Graded Materials into the Sandwich Beam Dynamic Performance 760
Appendix. Material properties of three core layers sandwich beam. (a) Fiber orientation (0/90/0); (b) Fiber orientation
(45/90/45); (c) Fiber orientation (90/90/90).
(a)
Properties Symbol Unit Layer 1 Layer 2 Layer 3
Fiber volume fra c t i on Vf Vol% 3% 10% 15%
Lamina longitudinal modulus E1 GPa 9.8 9.3 8.95
Lamina transverse elastic modulus E2 GPa 9.35 8.1 7.4
Lamina transverse elastic modulus E3 GPa 9.35 8.1 7.4
Lamina major Poisson’s ratio υ12 0.39 0.38 0.37
Lamina major Poisson’s ratio in plane υ13 0.39 0.38 0.37
Lamina major Poisson’s ratio in plane υ23 0.37 0.36 0.37
Shear modulus in plane G12 GPa 3.35 3.176 2.692
Shear modulus in plane G13 GPa 3.35 3.176 2.692
Shear modulus in plane G23 GPa 3.35 3.176 2.692
Density of composite ρc Kg/m3 1392 1384 1360
(b)
Properties Symbol Unit Layer 1 Layer 2 Layer 3
Fiber volume fra c t i on Vf Vol% 4% 16% 22%
Lamina longitudinal modulus E1 GPa 9.7 8.88 8.46
Lamina transverse elastic modulus E2 GPa 9.12 7.28 6.6
Lamina transverse elastic modulus E3 GPa 9.12 7.28 6.6
Lamina major Poisson’s ratio υ12 0.39 0.368 .356
Lamina major Poisson’s ratio in plane υ13 0.39 0.368 .356
Lamina major Poisson’s ratio in plane υ23 0.37 0.368 .356
Shear modulus in plane G12 GPa 3.28 2.65 2.4
Shear modulus in plane G13 GPa 3.28 2.65 2.4
Shear modulus in plane G23 GPa 3.28 2.65 2.4
Density of composite ρc Kg/m3 1389 1357 1341
(c)
Properties Symbol Unit Layer 1 Layer 2 Layer 3
Fiber volume fra c t i on Vf Vol% 5% 20% 30%
Lamina longitudinal modulus E1 GPa 9.65 8.6 7.9
Lamina transverse elastic modulus E2 GPa 9.0 6.82 5.88
Lamina transverse elastic modulus E3 GPa 9.0 6.82 5.88
Lamina major Poisson’s ratio υ12 0.39 0.36 0.34
Lamina major Poisson’s ratio in plane υ13 0.39 0.36 0.34
Lamina major Poisson’s ratio in plane υ23 0.36 0.36 0.34
Shear modulus in plane G12 GPa 3.28 2.49 2.16
Shear modulus in plane G13 GPa 3.28 2.49 2.16
Shear modulus in plane G23 GPa 3.28 2.49 2.16
Density of composite ρc Kg/m3 1388 1346 1319
Open Access MSA