theoretical and experimental investigation of using...

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.

[email protected]

Mohammed Hussein Kadhim Al-jabery

M.Sc. studentin Applied Mechanics, Department of Mechanical Engineering, Kerbala University/Iraq.

[email protected]

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

mailto:[email protected]

mailto:[email protected]



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)

,



,

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.



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



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



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



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



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



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



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).



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.

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