theoretical and experimental investigation of using...
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International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:01 70
162701-8585-IJMME-IJENS © February 2016 IJENS I J E N S
Theoretical and Experimental Investigation of Using
Date Palm Nuts Powder into Mechanical Properties
and Fundamental Natural Frequencies of Hyper
Composite Plate Dr. Abdulkareem Abdulrazzaq Alhumdany, Dr. Muhannad Al-Waily, and Mohammed Hussein Kadhim Al-jabery
Abstract— In this research the reinforcement of the resin
materials was made with two types of powder and short fiber to
produce an isotropic hyper composite material. So it is composed
of three materials, polyester resin material and two
reinforcements: short glass fiber and powder in the form of glass
or date palm nuts. The composite structure was studied to
estimate the mechanical properties (modulus of elasticity E, yield
stress y) experimentally and analytically, whereas the natural
frequencies were estimated theoretically, experimentally and
numerically. The theoretical method includes the solution of the
general equation of motion of the composite plate. The numerical
approach includes the estimation of the natural frequency of the
plate using finite element method operating on ANSYS software
version 11. The effects of powder type’s reinforcement for
different aspect ratios of plate were studied for different
boundary conditions. The results show that, when using the date
palm nuts powder, the yield stresses and the fundamental natural
frequency are increased. This encourage using this type of hyper
composite plate safely in the engineering applications where high
loads are encountered in a wide range of operating frequencies.
Finally, good agreement is obtained of the fundamental natural
frequency between the experimental and numerical results .The
maximum error is found 7.16 per cent..
Index Term-- Hyper Composite Materials, Isotropic Composite
Plate, Natural Frequency, Mechanical Properties, Date Palm
Nuts Powder..
I. INTRODUCTION
The first attribution of composite materials that has been
encouraged in the engineering applications is their
lightweight which has positive effects on efficiency, noise
and vibrations. In addition, composite materials are attaining
both high strength and high stiffness when compared with
metallic materials, which are favorable in the weight sensitive
applications (i.e. vehicles, aircrafts and aerospace
applications). Composite materials refer to materials having
strong fibers (continuous or discontinuous) surrounded by a
weaker matrix material.
Dr. Abdulkareem Abdulrazzaq Alhumdany
Head of Mechanical engineering Department /Kerbala University/Iraq.
alhumdany@ yahoo.com
Dr. Muhannad Al-Waily Mechanical Engineering Department/Al-Kufa University/Iraq.
Mohammed Hussein Kadhim Al-jabery
M.Sc. studentin Applied Mechanics, Department of Mechanical Engineering, Kerbala University/Iraq.
The matrix works to distribute the fibers and also to transmit
the load to the fibers. The bonding between fibers and matrix
is created in the manufacturing phase of the composite
material. This has an essential influence on the mechanical
properties of the composite material (E, G, and υ) [1]
Composite materials consist of two or more materials which
together produce desirable properties that cannot be achieved
with any of the components alone [2]. The desirable
characteristics of most fibers are high strength, high stiffness,
and comparatively low density. Glass fibers are the mostly
used ones in medium performance composites because of their
high tensile strength and low cost. Natural fibers such as hemp, flax, jute, wood, and several
waste cellulosic sources have been used as a suitable
alternative to synthetic fiber reinforcements for composite in
many applications. These fibers had specific benefits such as
low density, low pollutant emissions, biodegradability, high
specific properties and low cost. Furthermore, composites
made of friendly environment materials (e.g., biodegradable
materials) are getting particular attention for many interesting
applications. The key features of natural structural composites include
durable interfaces between hard and soft materials and
excellent bonding. A desirable combination of toughness,
strength, good fatigue resistance , resiliency, and a dramatic
influence of the presence of water, which can have notable
effects on mechanical and material properties [3],
Many studies were performed to examine the analysis of
natural frequencies and properties of composite plate, as:,
Parsuram Nayak (2008) [4], presented a combined
experimental and numerical study of free vibration of woven
fiber Glass/Epoxy composite plates. He determined
experimentally elastic parameters and natural frequencies of
woven fiber Glass/Epoxy cantilevered composite plates and
compared with the developed computer program based on
FEM and determined the natural frequency and mode shape of
the plate using ANSYS package. The experimental frequency
data is in fair agreement with those of the program
computation. The percentage of error between experimental
and ANSYS package results is within 15 per cent.
Luay S. Al-Ansari et al. (2012) [5], presented a study
included an analytical and numerical vibration analysis of
hyper composite material of beam considering shear
deformation and rotary inertia. The hyper composite material
used consists of long reinforcement fiber and matrix with resin
International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:01 71
162701-8585-IJMME-IJENS © February 2016 IJENS I J E N S
and short fibers. Effects of volume fraction and types of fiber
and resin material on the natural frequencies are investigated.
The results show that the natural frequencies of the hyper
composite material of beam increases with increase of the
strength of fibers and volume ratio of the long fiber.
Muhannad Al-Waily (2013) [6], suggested an analytical
solution for dynamic analysis of hyper composite plate
combined from two reinforcement fiber, mat and powder or
short and powder, with polyester or epoxy resin matrix. The
effects of the volume fraction and types of reinforcement fiber
and matrix resin were studied theoretically. The suggested
analytical solution includes evaluation of the mechanical
properties of isotropic hyper composite material plate such as
E, G and υ. The results show that the natural frequencies
increases with the increasing of reinforcement fiber and with
the increasing of strength reinforcement fiber or resin matrix.
A comparison was made between the analytical and numerical
method using FEM operating on ANSYS software version 14.
Good agreement was obtained with maximum error about 1.8
per cent and minimum error about 0.75 per cent
Kanak Kalita and Abir Dutta (2013) [7], studied different
frequency modes for free vibration of isotropic plates using
the ANSYS computer package, considering several different
boundary condition cases involves clamped, simply-supported
and free. The analysis for isotropic plate is carried out for
uniform thickness and different aspect ratios (a/b= 0.4, 1.0, 1.5
and 2.0). The Square plate is analyzed for different boundary
conditions with different thickness ratio (a/h=5, 10, 20and 50).
The resulting analysis converted to non dimensional form for
ease of comparison with existing literature wherever possible.
In this work presents an experimental and theoretical study of
modal testing of two different short fiber Glass/Epoxy hyper
composite plates with two types of powder. One is made of
glass and the other is made of date palm nuts. A program
based on FEM is developed. The experimental results of the
program have been compared with that obtained from the
theoretical (analytical and numerical). Elastic properties of the
plates were determined experimentally from tensile test of the
models. Variation of natural frequency with different aspect
ratios and boundary conditions was studied.
II. ANALYTICAL STUDY
To evaluated the mechanical properties of hyper composite
materials assuming the reinforcement powder and resin
materials combined the isotropic composite matrix of
composite materials, and then, assuming the composite matrix
and mat or short reinforcement fiber combined isotropic
composite materials, as,
II.1. Mechanical properties of short reinforcement hyper
composite material plate
To evaluate the mechanical properties of short-matrix
composite materials assuming the short fiber as unidirectional
short fiber and evaluate the mechanical properties, then,
assuming the short fiber as random fiber. The density of hyper
composite plate combined from (resin matrix, power
reinforcement and short fiber) defined as,
(1)
Where, , are density of short fiber, powder, and
resin materials, respectively, (Kg/m3
). And, , are
percentage of volume of short fiber, powder, and resin
material respectively.
The Poisson ratio of hyper composite plate defined as,[8],
([
(
(
))
(
(
))]
[
(
(
))
(
(
))]
) (2)
Where af is the ratio of average fiber length to its diameter and
is taken 100.
The Young's modulus of elasticity and modulus of rigidity of
such a composite matrix are given by ,
[8],
(
(
))
(
(
)) (3)
(
(
))
(
(
)) (4)
Where, [1],
(
( )[ (
)
]
( ) [
(
)
])
(
( )[ (
)
]
( ) [
(
)
])
,
( )[ (
)
]
and, [9],
(
)
(
)
( )
( )
( (
))
( (
))
, (
)
(
)
( )
( )
( (
))
( (
))
Where is the modulus of elasticity and Poisson
ratio of resin material. Also Ecm and Esf is the modulus of
elasticity of composite material and short fiber respectively.
II.2. Vibration analysis of hyper composite plate
Consider now a plate element dx dy subject to a uniformly
distributed lateral load per unit area p, figure 1in addition to
the moments , , and .
The vibration of hyper composite plate could be evaluated
using solution of general equation of motion of composite
plate, with substation the boundary conditions of plate, and
then, evaluate the natural frequency of composite plate, by
using special plate equation, [9], as,
(5)
Where, are the bending moments (per unit length)
of plate, can be determined as, [9],
∫ ⁄
⁄, ∫
⁄
⁄ ,
∫ ⁄
⁄(6)
,
International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:01 72
162701-8585-IJMME-IJENS © February 2016 IJENS I J E N S
,
and, are strain fields determined with the
displacement fields as in the following equations [9],
,
,
Where w is the deflection of plate in z-direction.
Then, by substitution Eq. 6 in to Eq. 5, leads to
( )
( ) (7)
where
( ),
( ),
(8)
. For free vibration plate, the general equation of plate Eq. (7)
can be rewritten as the general equation of motion of
composite plate as [9],
( )
(9)
To evaluate the natural frequency of composite plate, solve
Eq. (9) with separation of variable method with substation the
boundary condition of plate. For simply supported boundary
condition [9], the displacement component in the z- direction
w is
( )
(10)
Where and are the number of half waves in the axial and
transverse (i.e. x and y) direction respectively. Whereas
is constant, while are the length and width of plate,
respectively.
(
) , on the edge
(11)
and
( ) , on the edge
(12)
Then, with substituting the boundary conditions of Eqs. (11)
and (12) into general equation of motion Eq. (9), and solving
the equation for time dependent leads to, [9],
[
(
( ) )
(
[ (
(
))
(
(
))
]
[ (
)
(
) ]
(
) ( )
[ (
(
))
(
(
))
]
)
]
[
]
(13)
This represents the natural frequency of short hyper composite
plate.
To evaluate the mechanical properties, Eqs. (2, 3 and 4), and
the natural frequency, Eq. 13, for isotropic hyper composite
simply supported plate, a computer program was built, using
Fortran Power Station ver. 4 program.
Fig. 1. Moment and shear forces per unit length on a plate
element and sign convention
III. EXPERIMENTAL WORK
The experimental work of composite materials includes study
of mechanical properties of two types of composite materials
with same volume fraction of short reinforcement glass fiber,
epoxy resin and two types of reinforcement powder, namely,
glass and date palm nuts.
III.1. Composite plates manufacturing processes
To test the mechanical properties of composite materials, the
samples are manufactured with the dimensions: 30 cm width,
40 cm length, and 5 mm thickness in the laboratory.
III.1.1. Making the date palm nuts powder
The steps of making date palm nuts powder are:-
1- Washing and drying the date palm nuts.
2- Breaking and crashing the seeds manually.
3- Using crushing machine to prepare powder of large
size.
4- Using Sieve shaker machine to screen the powder to
smaller size.
III.1.2. Evaluation the density
To predict the weight of composite components, the density of
each component (reinforcement glass fiber, powder ( glass and
date palm nuts), and polyester resin materials must be known.
The tools used are: dial phials and sensitive Libras.
The density can be calculated by dividing the material
weight to the difference in water volume as follows:
water
ightmaterialwedensity
(14)
Where, ∇ is the change of water volume after adding the
material to water as shown in Fig. 2. The measured weights,
change in volume and the calculated density of the
components are listed in Table 1 .
The steps of composite materials manufacturing are:-
1- Painting the upper wood block with insulated layers.
2- Preparing a glass frame.
3- Fixing the glass frame on the lower wood block.
4- Painting the insulated layers on the wood block and
glass frame.
5- Weighting the resin, powder and fibers.
6- Mixing the Resin and Powder.
7- Putting the resin mixture on fibers.
8- Putting the upper wood block.
9- Pressing upper block by heavy weights.
International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:01 73
162701-8585-IJMME-IJENS © February 2016 IJENS I J E N S
The final shapes of the two types of the composite plates are
shown in the Fig. 3. Noting that, the first type is with glass
powder whilst the second is with date palm nuts powder.
Fig. 2. Steps of evaluation density of powder.
Table I
Density of glass fiber, powder and polyester resin materials.
Materials Weight of
Fiber ( g ) ( mL )
Density
( kg/m3 )
Short fibers 150 75 2000
Glass powder 180 75 2400
Date palm nuts
powder 50 45 1111
Polyester resin 240 200 1200
The final shapes of the two types of the composite plates are shown
in the Fig. 3. Noting that the first type is with glass powder whilst the
second is with date palm nuts powder.
Fig. 3. The final composite plates.
III.2. Tensile test of the composite plates
The main objective of the tensile test is the determination of
the modulus of elasticity of the composite material in various
volume fractions of fiber and resin materials.
According to ASTM Number (D3039/D03039M), [11],the
shape and dimensions of tensile test specimen selected as
shown in figure 4.The samples are divided into three groups
for each type of composite plate.
Fig. 4. Shape and dimensions of tensile test specimen
The tensile test machine used to evaluate modules of elasticity
and yield stress for different reinforcement composite types is
with load capacity (0-540KN). The environmental conditions
of the laboratory are, temperature = 25 C⁰ and moisture = 40
per cent. The results of the tensile test are shown in Fig. 5.
a. glass powder
b. date palm nuts powder Fig. 5. Tensile test result of short reinforcement glass fiber, glass powder and
date palm nuts powder reinforcement, and polyester resin composite sample.
Weight of the powder volume of water with powder
1- The first type 2- The second type
Length=20
Thickness=
5 mm
International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:01 74
162701-8585-IJMME-IJENS © February 2016 IJENS I J E N S
III.3. Vibration test of composite plates
The vibration test involves evaluation the fundamental natural
frequency for two composite plate types and with same volume
fraction. The dimensions of vibration test plate samples are shown in
Fig. 6. Noting that a= 25 mm, b=25 mm and b=37.5 mm to get two values of
the aspect ratio (b/a) = 1 and 1.5
Fig. 6. Dimensions of vibration test sample.
The following boundary conditions are considered, Fig. 7, in
this research for two values of the aspect ratio:
1- All edges simply supported (SSSS)
2- Two edges simply supported and the others free
(SSFF)
3- Cantilever ( i.e. one edge clamped and the other
three edges free) (CFFF)
4- Two edges clamped supported and the others simply
(CCSS)
5- Two edges clamped and the others free (CCFF)
6- All edges clamped (CCCC).
Fig. 7. The boundary conditions of vibration test plate.
The vibration testing rig is shown in Fig. 8. while the flow
chart of the testing rig is shown in Fig. 9.
In the following a brief description to each element in the
testing rig :-
1- Frame on which the tested plate held made of steel
plate with (10 mm) thickness, Fig. 10(a).
2- Digital storage oscilloscope, model (ADS 1202CL+)
and serial No.01020200300012, Fig. 10(b)., with
maximum frequency (200 MHz), maximum read of
sample per second (500 MSa/s), Fast Fourier
Transformation (FFT) spectrum analysis and two
input channels.
3- Amplifier, type (480E09), Fig. 10 (c).
4- Impact hammer tool, model (086C03) (PCB
Piezotronics vibration division), Fig.10 (d), with
resonant frequency (≥ 22 KHz), excitation voltage
(20 to 30 VDC), constant current excitation (2 to 20
mA), output bias voltage (8 to 14 VDC), discharge
time constant (2000 sec), hammer mass (0.16 kg),
head diameter (1.57cm), tip diameter (0.63 cm), and
hammer length (21.6 cm).
5- Accelerometer, model (352C68), Fig. 10 (e), with
sensitivity (10.2 mV/(m/s2)), measurement range
(491 m/s2), mounted resonant frequency (≥35 kHz),
non-linearity (≤ 1per cent).
Two positions indicated on the tested plates: central and
terminal to apply five impulses on each position to excite the
plate by an impact hammer.
Impulse testing of the dynamic behavior of structure
involves striking the tested plate by the impact hammer, and
measuring the resultant motion with an accelerometer. Then
the signal is read from digital storage oscilloscope to FFT
function by using sig-view program to transform from
t-domain into -domain and get the fundamental natural
frequency of the plate as the average of ten readings, Fig. 11.
Fig. 8. The testing rig
5
mm
2.5
cm 2.5
cm
bt
at
b
a
2.5
cm
2.5
cm
𝒙
𝒚
Cantilever SSFF
CCFF CCCC
CCSS SSSS
Impact Hammer Accelerometer Storage Oscilloscope
Am
plif
iers
Output Signal Structure Rig Supported
Pla
te S
amp
le
International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:01 75
162701-8585-IJMME-IJENS © February 2016 IJENS I J E N S
Fig. 9. Flow chart of the testing rig.
a- Structure Rig for Vibration Test
b- Digital Storage Oscilloscope Part
c- Amplifier Part
d- Impact Hammer Part
Bolt to Install Accelerometer on Plate Specimen
e- Accelerometer Part
Fig. 10. Elements of the vibration testing rig.
Fig. 11. Sig-View Program for FFT Analysis Function.
Output Signal
Accelerometer
Input Signal
Impact Hammer
Amplifiers
Digital
Storage
Oscillosc
USB Memory
Frame on which the
tested plate held
Plate
B- Natural Frequency
A- Accelerometer single
International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:01 76
162701-8585-IJMME-IJENS © February 2016 IJENS I J E N S
IV. NUMERICAL ANALYSIS STUDY
The numerical study of natural frequency of hyper
composite plate evaluated by using the finite elements method
was applied by using the ANSYS program (ver.11). The three
dimensional model were built and the element type
(SHELL93) were used, figure 12. The following assumptions
and restriction are considered, [12]
1- Zero thickness element or element tapering down to a
zero thickness at any corner is not allowed.
2- Shear deflections are included in this element.
3- The out-of plane (normal) stress for this element
varies linearly through the thickness.
4- The transverse shear stresses (SYZ and SXZ) are
assumed to be constant through the thickness.
5- The transverse shear strains are assumed to be small
in a large strain analysis.
The size of mesh is the most important characterization in
the finite element analysis. It is found that an increase in the
element's number leads to accurate results, but, sometimes that
increase gives inaccurate results. To avoid this problem, a
convergence study was done to get the appropriate size of
mesh to be used. The chosen mesh must achieve two
purposes: accurate results and minimum time consumption in
both feeding the data and the execution time. The convergence
study is illustrated in table 2 for a plate with aspect ratio 1 and
in table 3 for a plate with aspect ratio 1.5. The mesh type 3 is
used in this research for the two cases.
Fig. 12. Shell93-8 Node Element Geometry, [12]
Table II
The mesh types of the composite plate for AR=1.
Table III
The mesh types of the composite plate for AR=1.5.
V. RESULTS AND DISCUSSIONS
The results of isotropic hyper composite plate included
evaluation of the effect of the adding two types powder (glass
and date palm nuts) reinforcement on the mechanical
properties and natural frequency. The composition of the
composite plate, as percentage of volume is short glass fiber
= 30 per cent, epoxy resin matrix material
and powder (glass or date palm nuts)
. Two aspect ratios (AR=1 and 1.5) and different
boundary conditions are considered.
V.1. Mechanical Properties of Composite Plates
The mechanical properties and density of glass reinforcement,
powder or short glass fiber and resin epoxy material used to
combine the isotropic hyper composite plate are shown in
table 4, [1] and the mechanical properties of hyper composite
plate studied are shown in table 5.
Table IV
Density of glass fiber and resin material, D. Gay et al. [1].
Table V Mechanical properties of hyper composite plate composed of different
reinforcement powder, glass fiber and resin matrix
Mesh
Type
Length *width
Divisions
Number of
elements
Natural
Frequency (Hz)
1 18*12 216 352.93
2 36*24 864 352.91
3 74*48 3552 352.91
4 92*62 5704 352.91
5 102*68 6936 352.91
6 112*74 8288 352.91
Mesh
Type
Length
*width
Divisions
Number of
elements
Natural
Frequency (Hz)
1 12*12 144 458.3
2 24*24 57 458.26
3 48*48 2304 458.248
4 96*96 9216 458.249
5 144*144 20736 458.249
6 192*192 36864 458.249
Materials
(kg/m3)
E (GPa) G
(GPa)
Glass Powder or Fiber 2066 74 30 0.25
Polyester Resin 1200 4.5 1.6 0.4
Composit
e type
%
%
E
(GPa)
G
(GPa)
(kg/m3)
glass
powder 30 10 60
16.86
9 5.814
0.38
51 1560
date
palm
nuts
powder
30 10 60 13.25
8 /
0.38
51 1111
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162701-8585-IJMME-IJENS © February 2016 IJENS I J E N S
From table 5, it can be concluded that the hyper composite
plate with date palm nuts powder has less weight, ( ) and
more flexible or less stiffness, (E) as compared with that of
using glass powder. The percentage of decreasing the weight
is 40.4. This is attributed to the fact that the date palm powder
is lighter than the glass powder. The percentage of decreasing
the stiffness (E) is 27.2 .
The exact value of the modulus of elasticity of short glass
fiber, glass powder reinforcement and epoxy resin composite
type listed in table 6, is the theoretical value determined by
equation 3. This value was compared with the averaged
experimental value of tensile test results and the error found to
be acceptable as illustrated in table 6. Knowing that three
samples of composite plate were tested and one of them failed
in the tensile test. The remaining successful samples are S1
and S2. While the three samples of the tested plate composed
of fiber glass, date palm nuts powder and epoxy resin are
succeeded S1, S2 and S3.
Table VI
Comparison between the experimental and theoretical values of the modulus
of elasticity of short hyper composite materials of glass reinforcement powder
and fiber and resin matrix.
The experimental values of tensile test results showed that the
yield stress of short glass fiber, date palm nuts powder
reinforcement and polyester resin composite type increased
more than the yield stress of short glass fiber, glass powder
reinforcement and epoxy resin composite (with same volume
fraction components), however the modulus of elasticity of
date palm nuts powder composite type decreased as compared
to that of glass powder composite type, as shown in table 7.
According to our knowledge, no attempt was carried out in
using the date palm nuts powder as reinforcement agent in
hyper composite plates. The first important finding of this
research is that using the date palm nuts powder increases the
yield stress as compared with the traditional glass powder.
This property is preferable in the design point of view.
Table VII Experimental values of modulus of elasticity and yield stress of Short Hyper
Composite Materials Combined of different reinforcement powders and fiber
and resin matrix.
Sample
No.
Short Fiber, Glass
Powder and Resin
Short Fiber, Date palm
nuts Powder and Resin
E (GPa) Y (MPa) E (GPa) Y (MPa)
S1 17.116 111.94 13.314 155.5
S2 16.623 122.62 12.469 143.02
S3 / / 13.991 161.74
AVR 16.869 117.28 13.258 153.42
V.2. Vibration results
The Vibration study of isotropic hyper composite plate
includes evaluation the fundamental natural frequency
( ) of composite plate structure with different aspect
ratios (AR=1 and 1.5), and different boundary conditions
(SSSS, CCSS, SSFF, CCFF, SFFF, and cantilever)
experimentally, numerically and analytically.
The numerical and analytical results of the fundamental
natural frequency of short glass fiber, glass powder
reinforcement and polyester resin were compared and
tabulated in table 8. As mentioned in article 2.2 the exact
analytical method is only available in a plate with all its edges
simply supported (i.e. SSSS case). The error is 7.16 per cent
for aspect ratio of (AR=1) and 6.17 per cent for (AR=1.5)
which is acceptable.
Table VIII
Comparison between numerical and analytical results of natural frequency of short hyper composite glass fiber , glass powder reinforcement and resin.
Results AR= 1 AR= 1.5
Ana (rad per sec) 1460.216 1068.67
Num (rad per sec) 1572.99 1138.95
Error(per cent) 7.16 6.17
From table 9, it is observed that the fundamental natural
frequency increases when using the date palm nuts powder as
compared with that of using the glass powder as a
reinforcement agent. This trend can be seen for both AR=1
and 1.5 experimentally and numerically for SSSS case. This
can be attributed to the fact that the hyper composite plate has
less weight and less stiffness. But the percentage of decreasing
the weight (40.4) is more than the percentage of decreasing
the stiffness (27.2) as shown in article 5.1. The natural
frequency is the ratio of stiffness to the mass. So it is
reasonable for the fundamental natural frequency to be
increased.
This is the second important finding of this research which
is preferable from the dynamic of structure point of view.
Table IX Comparison between the experimental and numerical results of natural
frequency of short hyper composite materials composed of different
reinforcement powders , glass fiber and resin matrix.
The experimental values of the fundamental natural frequency
were measured from vibration test and averaged from ten
experimental values by indicating two positions: central and
terminal on the tested plates and applying five impulses to
excite the plate on each position by an impact hammer. The
values were tabulated in table X for SSSS boundary condition.
Sample No. Exp E (GPa) Exact E (GPa) Error %
S1 17.116
16.107
6.3
S2 16.623 3.2
AVR 16.869 4.7
Sample
No.
Short Fiber, Glass
Powder and Resin
Short Fiber, Date palm
nuts Powder and Resin
AR=1 AR=1.5 AR=1 AR=1.5
Exp
(rad/sec)
1514.
6 1093.36 1623.54 1187.21
Num
(rad/sec)
1572.
9 1138.95 1691.05 1224.46
Error % 3.71 4 3.99 3.13
International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:01 78
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Table X
The experimental values of fundamental natural frequency of short hyper composite materials composed of different reinforcement powders, glass fiber
and resin matrix with SSSS boundary condition.
It is important to mention that the sequence of the boundary
condition number in Figs. 13 & 14 is as the same that
mentioned in article 3.3.
Fig. 13 shows comparisons between the experimental and
numerical values of the fundamental natural frequency when
using glass powder for the six boundary conditions and for
AR=1 and 1.5.While Fig. 14 show the same comparison but
when using date palm nuts powder.
Figs. 15, 16. Show a comparison between experimental and
numerical natural frequency results of short hyper composite
glass fiber and glass powder reinforcement and polyester resin
(sample 1) and short hyper composite glass fiber and date
seeds powder reinforcement) and polyester resin numerical
(sample 2) for aspect ratio of composite plate (AR=1). The
figures confirmed the natural frequency results of simple 2
were greater than that of simple 1. Same confirm was
achieved for aspect ratio of (AR=1.5) as Figs. 17, 18.
Figs. 19, 20. shown the effect of aspect ratio on the
experimental, and numerical natural frequency results for two
different aspect ratios of composite plate short glass fiber and
glass powder reinforcement and polyester resin (sample 1
(AR=1, 1.5). shown that the natural frequency results were
increased with the aspect ratio decreasing since the natural
frequency results were more for (AR=1) than that of
(AR=1.5).
From these figures one can conclude the followings :-
1- The experiments predict low values rather than the
numerical method results,
2- The deviation between the experimental and the
numerical results decreases as the aspect ratio
increases,
3- The maximum deviation occurs at the boundary
condition No. 4 (i.e. CCSS) while the minimum
deviation occurs at the boundary condition No. 2 (i.e.
SSFF) and the boundary condition No. 6 (i.e. CCCC)
as the aspect ratio increases,
4- The fact that using date palm nuts powder as a
reinforcement agent increases the fundamental
natural frequency of the hyper composite plate is
again emphasized,
5- For AR=1,the maximum fundamental natural
frequency occurs at the boundary condition No. 6
(i.e. all edge clamped CCCC) while the minimum
occurs at the boundary condition (B.C) No. 3 (i.e.
cantilever). This is attributed to the fact the CCCC
B.C appears high stiffness while the cantilever B.C
appears the low and
6- As the aspect ratio increases, the minimum value of
the fundamental natural frequency occurs at the B.C.
No. 5 (i.e. CCFF) while the boundary condition at the
maximum value does not change.
a- Aspect ratio =1
b- Aspect ratio =1.5
Fig.13. Comparison between numerical and experimental values of the fundamental natural frequency with six boundary conditions of short hyper
composite glass fiber, glass powder reinforcement and polyester resin for two
aspect ratios (AR=1, 1.5).
NO. of
pulses
Using glass powder
Exp (Hz)
Using date palm nuts
powder Exp (Hz) AR=1 AR=1.5 AR=1 AR=1.5
1 247.8 190.06 289.18 221.74
2 251.46 179.5 261.13 190.06
3 238.89 176.11 267.21 183.105
4 244.14 183.56 272.58 188.59
5 229.49 180.97 256.34 182.18
6 241.39 189.85 241.39 194.33
7 242.9 188.26 275.87 198.36
8 226.31 180.36 276.35 189.81
9 253.9 177.53 281.64 195.92
10 248.99 178.79 227.6 201.17
AVR
(Hz) 242.527 182.499 264.92 194.526
AVR
(rad\sec) 1523.84 1146.67 1664.54 1222.24
International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:01 79
162701-8585-IJMME-IJENS © February 2016 IJENS I J E N S
a- Aspect ratio =1
b- Aspect ratio =1.5
Fig.14. Comparison between numerical and experimental values of the fundamental natural frequency with six boundary conditions of short hyper
composite glass fiber, date palm nuts powder reinforcement and polyester
resin for two aspect ratios (AR=1, 1.5).
Fig. 15. Comparison between experimental natural frequency results of
sample 1 and sample 2 for aspect ratio (AR=1).
Fig. 16. Comparison between Numerical natural frequency results of sample
1 and sample 2 for aspect ratio (AR=1).
Fig. 17. Comparison between experimental natural frequency results of
sample 1 and sample 2 for aspect ratio (AR=1).
Fig. 18. Comparison between Numerical natural frequency results of sample
1 and sample 2 for aspect ratio (AR=1).
International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:01 80
162701-8585-IJMME-IJENS © February 2016 IJENS I J E N S
Fig. 19. The effect of aspect ratio on the numerical natural frequency results
of sample 1 for two different aspect ratios of composite plate (AR=1, 1.5).
Fig. 20. The effect of aspect ratio on the experimental natural frequency
results of sample 1 for two different aspect ratios of plate (AR=1, 1.5).
VI. CONCLUSION
The main conclusions that can be withdrawn from this work
are:-
1- Using the date palm nuts powder as a reinforcement
agent in the hyper short glass fiber composite plate is
the first attempt in this research.
2- The yield stress of hyper short glass fiber composite
plate using date palm reinforcement powder is
increased as compared with that of using glass
powder reinforcement by 30.8 per cent. This increase
in the yield stress encourages using this type of hyper
composite plate in the engineering applications,
where high loads are applied.
3- The modulus of elasticity of hyper short glass fiber
composite plate using date palm reinforcement
powder is decreased as compared with that of using
glass powder reinforcement by 27.2per cent. This
leads to use this type of hyper composite plate in the
engineering applications, where flexibility is
preferred.
4- The fundamental natural frequency of hyper short
glass fiber composite plate using date palm
reinforcement powder is increased as compared with
that of using glass powder reinforcement. This is
preferable from the dynamic point of view to allow
this type to be used safely in a wide range of
frequencies.
5- Increasing the aspect ratio leads the fundamental
natural frequency to be decreased for two types of
powder and for all the boundary condition discussed.
6- When compared the value of the fundamental natural
frequency experimentally and numerically, for
different types of the boundary conditions and for the
two types of aspect ratio, it is found that the
maximum error (7.16 per cent) occurs at the CCSS
B.C, AR=1 and when using glass powder. While the
minimum error (0.67 per cent) occurs at SSSS B.C,
AR=1.5 and when using glass powder.
7- The maximum value of the fundamental natural
frequency occurs at CCCC B.C for two aspect ratios
(AR=1, 1.5), and the minimum occurs at cantilever
B.C for aspect ratio (AR=1), and CCFF B.C for
aspect ratio (AR=1.5).
ACKNOWLEDGMENT
The authors express sincere thanks to the staff of
laboratories in the mechanical engineering department of Kufa
University.
REFERENCES 1- D. Gay, S. V. Hoa and S. W. Tsai, “Composite Materials Design
and Applications” Book, CRC Press LLC, 2003.
2- J. N. Reddy, “Mechanics of Laminated Composite Plates and
Shells,” Book, CRC Press LLC, 2004. 3- H. Ehrlich and H. Worch, "Sponges as natural composites: from
biomimetic potential to development of new biomaterials," in
Porifera Research: Biodiversity, Innovation &Sustainability , University of Technology, Germany, 2007.
4- Parsuram Nayak, “Vibration Analysis of Woven Fiber
Glass/Epoxy Composite Plates,” M.Sc. Thesis of Technology in Civil Engineering (Structural Engineering), Department of Civil
Engineering, National Institute of Technology Rourkela, Orissa,
India, 2008. 5- Luay S. Al-Ansari, Muhannad Al-Waily and Ali M. H. Yusif,
“Vibration Analysis of Hyper Composite Material Beam Utilizing
Shear Deformation and Rotary Inertia Effects,” International Journal of Mechanical & Mechatronics Engineering IJMME-
IJENS, 12(4), 76-87, 2012.
6- Muhannad Al-waily, “Theoretical and Numerical Analysis Vibration Study of Isotropic Hyper Composite Plate Structural,”
International Journal of Mechanical and Production Engineering Research and Development IJMPERD, 3, 5, 145-164, 2013.
7- KanakKalita and AbirDutta, “Free vibration Analysis of Isotropic
and Composite Rectangular Plates,” International Journal of Mechanical Engineering and Research, 3, 301-308, 2013.
8- Muhannad Al-Waily, “Analytical and Numerical Buckling and
Vibration Investigation of Isotropic and Orthotropic Hyper Composite Materials Structures,” Book, International Energy and
Environment Foundation, 2015.
9- J. S. Rao, “Dynamics of Plates,” Book, Narosa Publishing House, 1999.
10- Muhannad L. S. Al-Waily, "Analysis of Stiffened and Unstiffened
Composite Plates Subjected to Time Dependent Loading," M. SC. Thesis, Kufa University, 2004.
11- ]D3039/D03039M], “Standard Test Method for Tensile Properties
of Polymer Matrix Composite Materials,” Annual Book of ASTM Standards, 15, 1995.
12- ANSYS, “Release 11.0 Documentation for ANSYS," ANSYS
Help, 2011.