Strojniški vestnik - Journal of Mechanical Engineering 69(2023)5-6, 224-234 Received for review: 2022-10-10
© 2023 The Authors. CC BY 4.0 Int. Licensee: SV-JME Received revised form: 2022-12-27
DOI:10.5545/sv-jme.2022.403 Original Scientific Paper Accepted for publication: 2023-03-20
*Corr. Author’s Address: Department of Technical Mechanical and Energy Engineering, Erbil Technical Engineering College,  
Erbil Polytechnic University, Erbil 44001, Iraq, ava.mohammed@epu.edu.iq
224
The Dynamic Behaviour of Symmetrical Laminated  
Nano-composite Containing Equal Numbers of Glass  
and Carbon Fibre Layers
Mohammed; A.A.K. – Hassan, G.I. – Khdir, Y .K.
Ava A.K. Mohammed
* – 
Gailan Ismail Hassan
 – 
Younis Khalid Khdir
Erbil Polytechnic University, Erbil Technical Engineering College,  
Department of Technical Mechanical and Energy Engineering, Erbil 44001, Iraq
Fibre-reinforced polymer composite has many uses in structural components that required high strength, stiffness, and damping capacity. 
Cross and quasi-laminated epoxy composites with and without nano Al
2
O
3
 were used in this investigation to determine flexural modulus, 
natural frequency, damping ratio, and mode shapes by using analytical, experimental, and numerical (ANSYS) methods. It was demonstrated 
that adding 2 % nano Al
2
O
3 
improved the flexural modulus and the damping ratio while decreased the natural frequency. Cross number 
2 and quasi number 2 had the highest natural frequency for cross and quasi laminate groups which are equal to 23.5 Hz and 20.25 Hz 
experimentally, respectively. On the other hand, the higher damping ratio was achieved for cross number 1 with nano Al
2
O
3
 and quasi number 
2 with nano Al
2
O
3
 for both cross and quasi laminates, which are equal to 0.707 % and 0.693 %, respectively. The flexural modulus and 
damping ratio are inversely related to each other. However, the novelty in this article is that by adding two glass plies at the outer surface of 
quasi group laminate the flexural modulus, natural frequency, and damping ratio are increased simultaneously, as in the configurations quasi 
number 2 and quasi number 2 with nano Al
2
O
3
 in comparison with quasi number 1 and quasi number 1 with nano Al
2
O
3
.
Key words: cross laminate, quasi laminate, natural frequency, damping ratio, nanoAl
2
O
3
Highlights
• 	 Adding 2 % nano Al
2
O
3
 decreases natural frequency and increases damping capacity and flexural modulus. 
• 	 Adding two glass plies at the outer surface of all laminated composite increases flexural modulus and natural frequency, but 
the damping ratio is also increased jointly in the quasi-laminated group.
• 	 Comparison between analytical, experimental, and numerical natural frequency for eight configurations of laminated 
composites.
0  INTRODUCTION
Multifunctional fibre-reinforced laminated polymer 
composites have been utilized in recent decades 
in structural applications, including automobiles, 
shafts, aircraft, bicycle frames, and tennis rackets, 
due to their superior properties, such as low density 
(low weight), high strength, high stiffness, and high 
damping capacity. The vibration energy dissipation 
of fibre-reinforced polymer composite (FRPC) can 
be achieved via increasing its viscoelastic behaviour 
[1]. FRPC damping capacity can be enhanced by 
increasing the numbers of interfacial regions, either 
by adding fibres or nano-fillers to its viscoelastic 
matrix, which then causes the vibrating energy to 
be dissipated by friction between the matrix and 
reinforcement. Hybridization is one of the means to 
increase the damping capacity of FRPC by adding 
high elongation to low elongation fibres [2] and [3].
Natural frequency and damping ratio represent 
the dynamic behaviour of materials. Glass and carbon 
fibres are widely use in structural applications. 
Researchers [4] to [8] have illustrated that the carbon 
fibre has a higher natural frequency than glass fibre 
due to the high bending modulus value of carbon 
fibre in a polymer matrix. In contrast, glass fibre has 
a higher damping ratio than carbon fibre in a polymer 
matrix, as shown in Table 1. The mechanical and 
dynamic properties of materials are related to each 
other. Zhang et al. [9] and Swolfs et al. [10] illustrated 
that a laminated fibre composite with equal numbers 
of glass and carbon fibres gives the best flexural 
strength and modulus. The high flexural modulus 
and low strain to failure carbon fabric is added to 
the low flexural modulus and high strain to failure 
glass fabric in order to benefit from the advantages 
of each ingredient and exclude the disadvantages of 
them. The natural frequency is related to the flexural 
modulus of the materials, increased with increasing 
flexural modulus, while the damping ratio is inversely 
related to the bending modulus. In order to increase 
interfacial boundary regions, nano-filler is added 
to the epoxy matrix of interply (G+C) hybrid fibre-
reinforced composite, so that more friction will occur 
when it vibrates; consequently, the damping ratio is 
increased.
Zhang et al. [11] investigated the tensile 
properties and damping characteristics in both 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)5-6, 224-234
225 The Dynamic Behaviour of Symmetrical Laminated Nano-composite Containing Equal Numbers of Glass and Carbon Fibre Layers  
vacuum and air environments of nine conditions 
of E-glass/polyurethane laminate composites by 
changing glass volume fraction (V
f
) 50 %, 55 %, 60 
% and angle of orientation 0°, 45°, and 90°. They 
deduced that the best damping capacity was for 
lower glass (V
f
) with a greater angle of orientation, 
which leads to lower tensile strength. The damping 
capacity in air is higher compared to that in vacuum 
for the same laminate. Navaneeth et al. [12] studied 
the tensile, flexural, and damping properties of woven 
glass/epoxy laminated composites with three different 
glass volume fractions: 50 %, 60 %, and 70 %. From 
collected experimental data, they found that the 
laminate with 60 % glass (V
f
) obtained the best tensile 
and flexural properties (strength and stiffness), while 
the laminate with 70 % glass (V
f
) obtained the highest 
natural frequency and lowest damping ratio. Hossein 
et al. [13] researched the effect of adding 1 %, 2 %, 
3 %, 5 %, and 7 % nano clay filler to 12-layer woven 
glass laminated epoxy composite and concluded 
that increasing the weight percentage of nano-filler 
to 5 % increased the natural frequency; after that, it 
decreased, but the damping ratio increased to 7 %. 
Khahaba [14] researched the impact of adding 1.5 
% nano SiC and 1.5 % nano Al
2
O
3
 on the damping 
properties of quasi-isotropic laminates with two 
stacking sequences [0/±45/90] and [90/±45/0]. They 
proved that the highest damping capacity is obtained 
for the second stacking configuration with and without 
nano glass/epoxy composite because the 90° first 
layer reduces the stiffness of the composites. Pujar 
et al. [15] examined the effect of introducing 0.1 %, 
0.5 %, and 1 % nano-graphene oxide on the damping 
properties of glass/epoxy composite by utilizing 0
o
 
and 45°
 
fibre orientation and two boundary conditions 
(cantilever and free). They found that adding nano-
GO improves damping capacity, whereas 0.5 % 
GO gives the highest damping ratio. Increasing the 
angle of fibre orientation between 0°
 
and 45° leads to 
decrease natural frequency and increase damping ratio 
for cantilever boundary condition and vice versa for 
free condition. 
Table 1.  Comparative dynamic behaviour of glass and carbon fibre 
reinforced polymer composite [4] to [7]
FRPC Natural frequency [Hz] Damping ratio [%]
CFRPC High Low
GFRPC low High
Researchers [4] to [8], [16] to [19] investigated 
the mechanical and dynamic behaviour of hybrid 
glass/carbon laminated composite. Murrugan et al. 
[4] concluded that the presence of carbon fibre in 
the middle of the laminated composite H1[GCCG] 
increases tensile strength, tensile modulus, and 
damping ratio, while the presence of carbon fibre 
in the outer surface of the laminated composite 
H2[CGGC] increases flexural strength, flexural 
modulus, and natural frequency for (50 % carbon: 50 
% glass) fibre addition. Suman et al. [5] found that 
the interply hybridization of equal numbers of glass 
and carbon fibre in laminated composite affects the 
dynamic properties. As a result, the arrangement GC1 
[G/C/G/C/G/C/G/C]
s
 has a natural frequency of 46 
Hz and a damping ratio of 0.095. In contrast, altering 
the arrangement by putting the carbon fibre on the 
external surface for the arrangement CC1[C/G/C/G/C/
G/C/G]
s
 will slightly reduce both the natural frequency 
and damping ratio to 45 Hz and 0.088, respectively. 
Pujar et al. [6] investigated the tensile and dynamic 
properties for laminated composite that is fabricated 
from 80 % glass and 20 % carbon. They found that 
H3[G/G/G/G/C]
s
 has maximum tensile strength and 
modulus because of the presence of one carbon ply 
in the middle of the laminate. The dynamic properties 
were accumulated for free FFFF and cantilever CFFF 
boundary conditions. In the FFFF condition, a higher 
natural frequency was found in H1[C/G/G/G/G]
s
 
hybrid condition in the presence of one carbon fibre 
at the outer surface of the laminate. On the other 
hand, higher damping ratio was found in H3 hybrid 
condition in the presence of one carbon fibre in the 
middle of the laminate. In the CFFF condition, 
the natural frequency and damping ratio dropped 
in comparison with FFFF, with the higher natural 
frequency for first hybrid condition H1, while the 
higher damping ratio for H2[G/G/C/G/G]
s
 condition 
in which one carbon fibre is present after two glass 
fibres from the outer surface. Adyin et al. [7] predicted 
the dynamic properties for non-hybrid, interlayer, 
and intralayer hybrid composites for carbon, glass, 
and aramid fibre reinforced in an epoxy matrix and 
taking the angle of orientation, stacking sequence, 
and number of plies into consideration. They found 
the best arrangement of fibres for higher dynamic 
properties by using the Taguchi program. Karthik et 
al. [16] investigated the damping properties of E-glass 
chopped mat/woven carbon hybrid with four different 
volume fractions in epoxy matrix and polyester 
matrix. They demonstrated that the damping capacity 
increased with increasing glass volume fraction for 
both matrices; furthermore, the addition of 5 % carbon 
fibre gave the best damping behaviour and natural 
frequency for structural composite. Utomo et al. [17] 
studied the effect of increasing carbon layers and its 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)5-6, 224-234
226 Mohammed; A.A.K. – Hassan, G.I. – Khdir, Y.K.
position in eight-layer hybrid glass/carbon laminated 
unsaturated polyester composite and concluded that 
with increasing numbers of carbon layers near the 
outer surface of the laminate, the natural frequency 
increased and damping capacity (ξ) decreased. 
In contrast, by positioning carbon layers toward 
the centre of the laminate, the natural frequency 
decreased while the damping capacity increased. 
Finally, the natural frequency and flexural stiffness 
are directly proportional to each other. Singh et al [18] 
studied the effect of stacking sequence and angle of 
orientations on the natural frequency and damping 
ratio of four-layer glass/carbon epoxy laminates and 
found that the laminate [0c/90g]
s
 acquired the highest 
natural frequency, while [90c/0g]
s
 obtained the 
lowest one. The highest damping ratio is attained for 
both laminates [90g/90c]
s
 and [90c/90g]
s
, while the 
laminate [0c/0g]
s
 obtained the lowest damping ratio. 
Pingulkar et al. [19] utilized ANSYS software package 
to evaluate natural frequency and mode shapes of 
eight-layer glass/carbon hybrid laminated cantilever 
plates and concluded that important change in natural 
frequency can be obtained by hybridization, change of 
angle of orientation, and stacking sequence more than 
change in volume fraction. Bulut et al. [20] inspected 
the effect of adding Kevlar fibre into the glass fibre in 
hybrid laminated epoxy composite with various hybrid 
ratios through tensile and damping tests. They deduced 
that H4 (G2K8) had maximum tensile strength and 
maximum damping capacity; both factors improved, 
by 124 % and 145 %, respectively, in comparison 
with glass/epoxy laminate. Alsaadi et al. [21] studied 
the effect of adding (0.5 %, 1 %, 1.5 %, 2.5 % and 
3%) nano-SiO
2
 on the tensile, flexural, and damping 
properties of carbon/Kevlar intraply hybrid epoxy 
composite. They obtained that the highest tensile 
modulus and flexural modulus are at 0.5 % nano SiO
2
, 
while the highest tensile strength and flexural strength 
at 3 % and 1.5 % nano SiO
2
, respectively. The flexural 
modulus and natural frequency are directly related to 
each other. Therefore, the highest natural frequency at 
0.5 % nano-silica which gave 20.5 % improvement, 
while the damping capacity (damping ratio) decreased 
by 37 %. Fairlie and Njuguna [22] investigated the 
impact of stacking sequence and angle of orientation 
on the tensile and damping capacity of interply hybrid 
carbon/flax epoxy laminated composite and attained 
that the outer layer in the laminate is the important 
layer to control the damping capacity of the laminate. 
By adding one flax layer at the exterior of the carbon/
epoxy laminate, the damping ratio increased by 53.6 
% and by adding two flax layers, it increased by 94 
%. Alexander et al. [23] studied the effect of boundary 
conditions, material properties, and laminate 
thickness on the natural frequency of glass/epoxy 
and basalt/epoxy laminated composite and reached 
to the conclusion that the damping capacity of basalt/
epoxy composite is higher than that for glass/epoxy 
composite. Erkliğ, et al. [8] inspected the dynamic 
behaviour of interply FRPC by using carbon, Kevlar, 
and glass fibres and determined that [(0G/90G)3]
s
 
and [(0C/90C)3]
s
 had minimum and maximum 
natural frequencies, respectively. The laminates 
[(0C/90C)3]
s
 and [(0K/90K)3]
s
 had the minimum 
and maximum damping capacity, respectively. To 
increase natural frequency, add higher stiffness 
fibre at the outer surface, like carbon; however, to 
increase the damping ratio of the structure, add higher 
viscoelastic fibre at the surface like Kevlar. Hybrid 
[(0C/90C)/(0K/90K)/(0G/90G)]
s
 had the maximum 
natural frequency compared to other hybrids, and the 
[(0/90)3]
s
 fibre orientation had the maximum natural 
frequency compared to other orientations. Moreover, 
[24] showed that the large cut-out size decreases the 
natural frequency, while the small cut-out size had a 
trivial effect on the natural frequency. Bulut et al. [25] 
investigated the influence of adding S-glass interply 
to woven carbon-aramid intraply on the natural 
frequency and found that higher natural frequency 
can be obtained by positioning glass in the middle 
and (C+A) at the outer surface of the laminate, where 
the configuration [CA2G2]
s
 had the highest natural 
frequency. Kröger et al. [26] increased the damping 
capacity of unidirectional carbon fibre/epoxy laminate 
by adding vectran, aramid, and cellulose in intraply 
form. In contrast, tensile, flexural strength, and 
stiffness were reduced.  
Senthamaraikannan and Ramesh [27] decided 
to increase the damping capacity of woven carbon 
laminated structure by adding 11 % nano SiO
2
 with 9 
% micro CTBN rubber to the epoxy matrix, despite the 
slight drop in tensile and flexural modulus. Bulut et 
al. [28] investigated the dynamic behaviour of basalt/
epoxy laminated composite by adding (0.1, 0.2, and 
0.3) nano-graphene and determined that 0.1 % and 0.2 
% of nano-pellets increased the natural frequency and 
damping ratio, but 0.3 % decreased both of them. 
According to the above literature review, it is 
clear that increasing flexural modulus is accompanied 
by increasing the natural frequency and decreasing the 
damping ratio. One way to increase flexural modulus 
is by adding equal numbers of glass and carbon fibre 
layers to the composite matrix and then rearranging 
them to obtain a higher damping capacity. Another 
way to increase flexural modulus and damping 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)5-6, 224-234
227 The Dynamic Behaviour of Symmetrical Laminated Nano-composite Containing Equal Numbers of Glass and Carbon Fibre Layers  
capacity is by adding nearly 2 % nano-filler to the 
matrix of fibre-reinforced polymer composite.
The aim of this investigation is to increase flexural 
modulus, natural frequency, and damping capacity 
simultaneously by using a new special arrangement of 
glass and carbon fibres that are different from the cited 
studies and by adding 2 % nano Al
2
O
3
 to the epoxy 
matrix of G/C hybrid composite. Eight configurations 
for eight layers of glass/carbon epoxy laminated 
composite with and without nano Al
2
O
3
 were 
fabricated. Analytical, experimental, and numerical 
(ANSYS) methods were used to evaluate the flexural 
modulus, natural frequencies, damping ratio, and 
shape modes, in addition to compare between them.
1  ANALYTICAL WORK
Knowledge of the dynamic properties of FRPC is just 
as important as that of the static ones. It is suitable to 
utilize static stiffness to estimate the natural frequency 
of laminated composite [2]. Classical laminate plate 
theory (CLPT) was used to evaluate the theoretical 
flexural modulus and fundamental natural frequency 
for all laminates (shown in Table 2) by using the 
mechanical properties for unidirectional glass and 
carbon fibres with and without nano-Al
2
O
3
 (shown in 
Table 3).
The flexural stiffness matrix and theoretical 
flexural modulus for each laminate can be calculated 
by using Eqs. (1) and (2) [29]. 
 DQ
ij ij









 
1
3
1
3
1
3
k
n
k
kk
hh, (1)
 E
hD
b
=
12
3
11
*
. (2)
Table 2.  Stacking sequence G: C configuration of hybrid laminated 
epoxy composite
Symbol Laminates Stacking sequences Hybrid ratio G:C
C1 Cross no. 1 [G0/C90/C0/G90]
s
4:4
C1WN
Cross no. 1
with nano Al
2
O
3
[G0/C90/C0/G90]
s
4:4
C2 Cross no. 2 [G0/G90/C0/C90]
s
4:4
C2WN
Cross no. 2 
with nano Al
2
O
3
[G0/G90/C0/C90]
s
4:4
Q1 Quasi no. 1 [G0/C90/C45/G-45]
s
4:4
Q1WN
Quasi no. 1 
with nano Al
2
O
3
[G0/C90/C45/G-45]
s
4:4
Q2 Quasi no. 2 [G0/G90/C45/C-45]
s
4:4
Q2WN
Quasi no. 2 
with nano Al
2
O
3
[G0/G90/C45/C-45]
s
4:4
Table 4 demonstrates the [D] matrix, theoretical 
flexural modulus E
b
, and fundamental natural 
frequency wn for all laminated epoxy composites. The 
fundamental frequency is the smallest frequency for 
the structure; for the case of a cantilever beam, wn can 
be calculated from Eq. (3) [30]
 wn
l
EI
A
by y







1
2
1 875
2

.
. (3)
Table 3.  The mechanical properties of unidirectional glass and 
carbon with and without nano alumina
Laminates
Density 
[kg/m³]
E
1
 
[MPa]
E
2
 
[MPa]
ν
12
G
12
 
[MPa]
UD glass/epoxy 1658 31802 12804 0.22 4271
UD carbon/epoxy 1484 99438 6273 0.25 4031
UD glass/epoxy Al
2
O
3
1883 33507 13344 0.27 4500
UD carbon/epoxy Al
2
O
3
1574 105044 6626 0.3 4260
The results in Table 4 show that cross-laminate 
has higher flexural modulus than quasi-laminate, 
similar to the results of [7] and [17]. It is apparent 
that C2WN and Q2WN laminates have maximum 
flexural modulus E
b
 in the cross and quasi groups, 
respectively. In spite of the presence of two glass 
layers on the exterior of both laminates, it is in 
contrast with the results of [16] because of the effect 
of element Q11, Q12, and Q66 in [Q
ij
] matrix of the 
90º
 
glass layer. By adding 2 % nano Al
2
O
3
, the natural 
frequency for all laminates slightly dropped despite 
the increase in flexural modulus, similar to the results 
of research [14]. The maximum natural frequency had 
been obtained for C2 in the cross-group, while in the 
quasi-group, Q2 had the maximum natural frequency. 
2  EXPERIMENTAL
2.1  Materials
The matrix material used in this study is the 
laminating epoxy resin MGS L285 with hardener 
H285 in a 100:40 mixing ratio (resin: hardener), for 
which the density for resin and hardener are equal to 
1.18 g/cm³ to 1.23 g/cm³ and 0.94 g/cm³ to 0.97 g/cm³ 
respectively, while the viscosity for them is equal to 
600 mPa·s  to 900 mPa·s and 50 mPa·s to 100 mPa·s, 
respectively. Unidirectional carbon and E-glass fabric 
were used as fibre reinforcement with weights equal 
to 300 g/cm² and 330 g/cm², respectively. Both the 
matrix and fibre were supplied by the DOST KIMYA 
Company, Turkey. Finally, spherical aluminium oxide 
(Al
2
O
3
) nano-powder/nano-particle with a size of 48 
nm, which was used as a filler reinforcement, was 
supplied by Nanografi Nanotechnology Company, 
Turkey.

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)5-6, 224-234
228 Mohammed; A.A.K. – Hassan, G.I. – Khdir, Y.K.
Table 4.  Flexural stiffness matrix, theoretical flexural modulus E
b
, 
and fundamental natural frequency wn
Lami- 
nates
Flexural stiffness matrix [D] 
[Pa·m³]
Theoretical 
flexural 
modulus, 
E
b
 [GPa]
Fundamental 
natural 
frequency, 
wn [Hz]
C1
21 21 56 0
15 62 56 0
00 27 8
..
..
.










31.6 23.254
C1WN
22 46 20 10
20 12 70 50
00 29 4
..
..
.










33.5 22.75
C2
22 43 18 10
18 11 29 50
00 28 3
..
..
.










33.3 23.78
C2WN
23 79 23 30
23 31 37 10
00 29 8
..
..
.










35.1 23.29
Q1
16 21 32 11 65
32 12 72 61 65
16 51 65 44 3
...
.. .
...










23.0 19.78
Q1WN
17 24 37 41 75
37 42 88 31 75
17 51 75 46 6
...
.. .
...










24.4 19.42
Q2
17 73 62 14 6
36 21 40 71 46
14 61 46 46 4
.. .
.. .
...










24.75 20.52
Q2WN
18 84 23 15 5
42 31 49 11 55
15 51 55 48 8
.. .
.. .
...










26.0 20.05
2.2  Laminates Manufacturing
In this investigation, four hybrid glass/carbon 
laminates were used without nano-particles and the 
other four with it. The 2 % nano Al
2
O
3
 were added 
to epoxy matrix by using dual mixing method, which 
includes both ultrasonic vibration and magnetic 
stirring mixing simultaneously. After that, the bubbles 
produced are removed by degassing the suspension 
mixture. The glass and carbon fibre fabrics were cut 
into the required angles and dimensions, and then 
arranged according to the design stacking sequence 
in order to start the vacuum assisted resin infusion 
method (VARIM) by drawing the epoxy mixture into 
the closed system of arranged fibres and VARIM 
accessories [31]. A flow chart for the purpose of each 
fabrication stages is shown in Fig. 1.
Fig. 1.  Stages of laminated composite fabrication
2.3  Free Vibration Test
The dynamic properties of FRPC beam with 
dimensions are 250 mm length × 25 mm width and 
2 mm thickness; they were measured by using the 
experimental set up shown in Fig. 2, which consist of 
the following apparatuses. Firstly, an impact hammer 
transducer was used to excite an impulsive force and 
measure it at the midpoint of the beam (Brüel & Kjær, 
type 8206). Secondly, a piezoelectric accelerometer 
was used to measure the vibration response of the 
excited beam (Brüel & Kjær, type 4507 B30515) 
positioned at the free end of the beam. Finally, the 
both hammer and accelerometer were connected to 
the Brüel & Kjær controller modules type 7539A, 
5-channels, in order to analyse the collected data by 
using fast Fourier transform (FFT) Analyzer to obtain 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)5-6, 224-234
229 The Dynamic Behaviour of Symmetrical Laminated Nano-composite Containing Equal Numbers of Glass and Carbon Fibre Layers  
the dynamic response of the free vibration test, in 
terms of time domain and frequency domain.  
a)    b) 
c)    d) 
Fig. 2.  Free vibration test set up and its parts;  
a) free vibration set up, b) impact hammer,  
c) accelerometer sensor, and d) blank module
Due to FRPC beam free vibration, the dynamic 
behaviour of the glass/carbon epoxy laminated 
composite can be found in terms of time domain 
(displacement-time envelope) and frequency domain 
(acceleration-frequency envelope). The original aspect 
of this paper is that the frequency response is neither 
represented in terms of input impulsive force with 
respect to frequency nor within output acceleration 
with respect to frequency; the new representation was 
in terms of output over input (acceleration/impulsive 
force) in the y-axis against the frequency in the x-axis, 
as shown in Fig. 3. The red curser position in Fig. 3 
represents the resonant frequency, for the range of 
frequency is between 0 Hz and30 Hz, as represented 
by the critical frequency for the laminates and not 
necessarily the maximum frequency. If the laminate is 
subjected to force with excited frequency equal to this 
a)
Acceleration [m/s
2
] /  
Force [N]
Frequency Response(acc,force) - Input (Real Part)
Working : Input : Input : FFT Analyzer
20 22 24 26
-80
-40
0
40
80
[Hz]
[(m/s²)/N] Frequency Response(acc,force) - Input (Real Part)
Working : Input : Input : FFT Analyzer
20 22 24 26
-80
-40
0
40
80
[Hz]
[(m/s²)/N]
Frequency [Hz]
b)
Acceleration [m/s
2
] /  
Force [N]
Frequency Response(acc,force) - Input (Real Part)
Working : Input : Input : FFT Analyzer
20 22 24 26
-80
-40
0
40
80
[Hz]
[(m/s²)/N] Frequency Response(acc,force) - Input (Real Part)
Working : Input : Input : FFT Analyzer
20 22 24 26
-80
-40
0
40
80
[Hz]
[(m/s²)/N]
Frequency [Hz]
c)
Acceleration [m/s
2
] /  
Force [N]
Frequency Response(acc,force) - Input (Real Part)
Working : Input : Input : FFT Analyzer
21.5 22 22.5 23 23.5 24 24.5
-200
-100
0
100
200
[Hz]
[(m/s²)/N] Frequency Response(acc,force) - Input (Real Part)
Working : Input : Input : FFT Analyzer
21.5 22 22.5 23 23.5 24 24.5
-200
-100
0
100
200
[Hz]
[(m/s²)/N]
Frequency [Hz]
d)
Acceleration [m/s
2
] /  
Force [N]
Frequency Response(acc,force) - Input (Real Part)
Working : Input : Input : FFT Analyzer
21.6 22 22.4 22.8 23.2
-40
0
40
[Hz]
[(m/s²)/N] Frequency Response(acc,force) - Input (Real Part)
Working : Input : Input : FFT Analyzer
21.6 22 22.4 22.8 23.2
-40
0
40
[Hz]
[(m/s²)/N]
Frequency [Hz]
e)
Acceleration [m/s
2
] /  
Force [N]
Frequency Response(acc,force) - Input (Real Part)
Working : Input : Input : FFT Analyzer
17 17.5 18 18.5 19 19.5
-8
-4
0
4
8
[Hz]
[(m/s²)/N] Frequency Response(acc,force) - Input (Real Part)
Working : Input : Input : FFT Analyzer
17 17.5 18 18.5 19 19.5
-8
-4
0
4
8
[Hz]
[(m/s²)/N]
Frequency [Hz]
f)
Acceleration [m/s
2
] /  
Force [N]
Frequency Response(acc,force) - Input (Real Part)
Working : Input : Input : FFT Analyzer
18.4 18.6 18.8 19 19.2 19.4 19.6
-40
-20
0
20
40
[Hz]
[(m/s²)/N] Frequency Response(acc,force) - Input (Real Part)
Working : Input : Input : FFT Analyzer
18.4 18.6 18.8 19 19.2 19.4 19.6
-40
-20
0
20
40
[Hz]
[(m/s²)/N]
Frequency [Hz]
g)
Acceleration [m/s
2
] /  
Force [N]
Frequency Response(acc,force) - Input (Real Part)
Working : Input : Input : FFT Analyzer
18 19 20 21 22
-40
-20
0
20
40
[Hz]
[(m/s²)/N] Frequency Response(acc,force) - Input (Real Part)
Working : Input : Input : FFT Analyzer
18 19 20 21 22
-40
-20
0
20
40
[Hz]
[(m/s²)/N]
Frequency [Hz]
h)
Acceleration [m/s
2
] /  
Force [N]
Frequency Response(acc,force) - Input (Real Part)
Working : Input : Input : FFT Analyzer
15 16 17 18 19 20
-80
-40
0
40
80
[Hz]
[(m/s²)/N] Frequency Response(acc,force) - Input (Real Part)
Working : Input : Input : FFT Analyzer
15 16 17 18 19 20
-80
-40
0
40
80
[Hz]
[(m/s²)/N]
Frequency [Hz]
Fig. 3.  Frequency responses of laminated epoxy composites with and without nano Al
2
O
3
;  
a) C1, b) C1WN, c) C2, d) C2WN, e) Q1, f) Q1WN, g) Q2, and h) Q2WN

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)5-6, 224-234
230 Mohammed; A.A.K. – Hassan, G.I. – Khdir, Y.K.
resonance frequency, then the amplitude of vibration 
pulse will be magnified and cause failure and presence 
of crack in the same laminate. The dynamic responses 
of all laminates are illustrated in Fig. 4 in terms of 
time domain. The number of peaks for cross- and 
quasi-group vibration response to a 400 ms time are 
5 and 4 peaks respectively; this is due to the increase 
of natural frequency of cross group in comparison 
with quasi group as shown in Tables 4 and 5, similar 
to the results of studies [7] and [18]. The maximum 
natural frequency for the laminate C2 is equal to 23.5 
Hz in cross group. On the other hand, the maximum 
one in the quasi group is for the laminate Q2 and 
equal to 20.25 Hz as shown in Fig. 5 because the 
flexural modulus of the arrangement of GGCCCCGG 
organized by two glass plies at the outer surface is 
higher than that of the arrangement GCCGGCCG as 
shown in Table 5 which is different from the results of 
studies [6] and [17]. The element Q11, Q12, and Q66 
of [Q
ij
] matrix for 90º glass fibre is higher than that for 
90
o
 carbon. Therefore, the presence of 90º glass as a 
second layer in the laminate leads to increase the first 
element of [D] matrix and then the flexural modulus. 
By adding 2% nano Al
2
O
3
 to all laminated composites, 
the amplitude of the vibration response decreased in 
comparison with the original state as shown in Fig. 4. 
This is due to the increase of the damping ratio for 
the nano particle addition case in comparison with the 
non-addition case, similar to the results of researches 
[11], [13] to [17], [21], [27], and [28] as shown in Table 
5 and Fig. 6. This is occurred because of the increase 
of the interfacial regions in composite leading to more 
a)
Displacement [m]
Time(transient) - Input
Working : Input : Input : FFT Analyzer
0 100m 200m 300m 400m
-8m
-4m
0
4m
8m
[s]
[m] Time(transient) - Input
Working : Input : Input : FFT Analyzer
0 100m 200m 300m 400m
-8m
-4m
0
4m
8m
[s]
[m]
Time [s]
b)
Displacement [m]
Time(transient) - Input
Working : Input : Input : FFT Analyzer
0 100m 200m 300m 400m
-8m
-4m
0
4m
8m
[s]
[m] Time(transient) - Input
Working : Input : Input : FFT Analyzer
0 100m 200m 300m 400m
-8m
-4m
0
4m
8m
[s]
[m]
Time [s]
c)
Displacement [m]
Time(transient) - Input
Working : Input : Input : FFT Analyzer
0 100m 200m 300m 400m
-8m
-4m
0
4m
8m
[s]
[m] Time(transient) - Input
Working : Input : Input : FFT Analyzer
0 100m 200m 300m 400m
-8m
-4m
0
4m
8m
[s]
[m]
Time [s]
d)
Displacement [m]
Time(transient) - Input
Working : Input : Input : FFT Analyzer
0 100m 200m 300m 400m
-8m
-4m
0
4m
8m
[s]
[m] Time(transient) - Input
Working : Input : Input : FFT Analyzer
0 100m 200m 300m 400m
-8m
-4m
0
4m
8m
[s]
[m]
Time [s]
e)
Displacement [m]
Time(transient) - Input
Working : Input : Input : FFT Analyzer
0 100m 200m 300m 400m
-8m
-4m
0
4m
8m
[s]
[m] Time(transient) - Input
Working : Input : Input : FFT Analyzer
0 100m 200m 300m 400m
-8m
-4m
0
4m
8m
[s]
[m]
Time [s]
f)
Displacement [m]
Time(transient) - Input
Working : Input : Input : FFT Analyzer
0 100m 200m 300m 400m
-8m
-4m
0
4m
8m
[s]
[m] Time(transient) - Input
Working : Input : Input : FFT Analyzer
0 100m 200m 300m 400m
-8m
-4m
0
4m
8m
[s]
[m]
Time [s]
g)
Displacement [m]
Time(transient) - Input
Working : Input : Input : FFT Analyzer
0 100m 200m 300m 400m
-8m
-4m
0
4m
8m
[s]
[m] Time(transient) - Input
Working : Input : Input : FFT Analyzer
0 100m 200m 300m 400m
-8m
-4m
0
4m
8m
[s]
[m]
Time [s]
h)
Displacement [m]
Time(transient) - Input
Working : Input : Input : FFT Analyzer
0 100m 200m 300m 400m
-8m
-4m
0
4m
8m
[s]
[m] Time(transient) - Input
Working : Input : Input : FFT Analyzer
0 100m 200m 300m 400m
-8m
-4m
0
4m
8m
[s]
[m]
Time [s]
Fig. 4.  Vibration responses of laminated epoxy composites with and without nano Al
2
O
3
:
a) C1, b) C1WN, c) C2, d) C2WN, e) Q1, f) Q1WN, g) Q2, and h) Q2WN

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)5-6, 224-234
231 The Dynamic Behaviour of Symmetrical Laminated Nano-composite Containing Equal Numbers of Glass and Carbon Fibre Layers  
damping ratio of C1 by 24.2 %, and the damping ratio 
of C2WN is lower than the damping ratio of C1WN 
by 8 %. Its behaviour is due to the fact that the ratio 
of the maximum peak amplitude to the minimum peak 
amplitude is higher for C1 and C1WN than that for 
C2 and C2WN, respectively as shown in Fig. 4. The 
reverse situation for quasi group, where the damping 
ratio for Q2 is higher than damping ratio of Q1 by 5.62 
% and the damping ratio for Q2WN is higher than the 
damping ratio of Q1WN by 6.64 % is due to the fact 
that the ratio of the maximum peak amplitude to the 
minimum peak amplitude is higher for Q2 and Q2WN 
than Q1 and Q1WN, respectively, as shown in Fig. 4. 
The stacking sequence and angle of orientation have 
a major effect on the value of the bending modulus, 
natural frequency, and damping ratio. For structural 
material system, it is necessary to make a balance 
between these properties alongside its strength. The 
configuration Q2 and Q2WN [G0/G90/C45/C-45]
s
 is 
specialized by increasing flexural modulus, natural 
frequency, and damping ratio simultaneously, in 
comparison with Q1 and Q1WN [G0/C90/C45/G-45]
s
, 
respectively, as shown in Tables 4 and 5.
 3  NUMERICAL WORKS
Ansys workbench simulation package was used to find 
the first six natural frequencies and its mode shape 
and compare it with the analytical and experimental 
one by using the steps shown in Fig. 7.
Fig. 7.  Steps of modelling laminates in ANSYS
Firstly, the mechanical properties for each lamina 
must be entered to the engineering data. Then the 
arrangement of fibres in the laminated composite was 
energy dissipation by friction (heat) [2] and [3]. Despite 
the amplitude of the dynamic response for C2, C2WN, 
Q2, and Q2WN being lower than the amplitude for 
C1, C1WN, Q1 and Q1WN, respectively, as shown in 
Fig. 4, but the damping ratio of C2 is lower than the 
Table 5.  The experimental free vibration results (natural frequency 
& damping ratio)
Laminates Natural frequency [Hz] Damping ratio [%]
C1 22.75 0.629
C1WN 22.25 0.707
C2 23.5 0.477
C2WN 23 0.651
Q1 19 0.487
Q1WN 18.5 0.647
Q2 20.25 0.516
Q2WN 19.5 0.693
Fig. 5.  Natural frequencies of all laminates with  
and without nano Al
2
O
3
Fig. 6.  Damping ratios of all laminates with  
and without nano Al
2
O
3

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)5-6, 224-234
232 Mohammed; A.A.K. – Hassan, G.I. – Khdir, Y.K.
3
rd
, 5
th
, and 6
th 
modes existed in C2 laminate, while 
for 4
th
 mode, the maximum natural frequency existed 
in Q2, where in the laminates C2 and Q2 stacking 
sequence of G/G/C/C/C/C/G/G was utilized.
Finally, it is found that the analytical, 
experimental, and numerical natural frequencies are 
very close to each other, as shown in Fig. 9.
Table 6.  The first six natural frequencies and its mode shapes for all laminates
No Mode shape
Natural frequency [Hz]
C1 C1WN C2 C2WN Q1 Q1WN Q2 Q2WN
1 23.185 22.752 23.8 23.313 19.821 19.452 20.59 20.138
2
 
145.16 142.45 148.98 145.94 124.08 121.77 128.9 126.07
3
 
263.89 258.42 265.8 260.2 218.92 214.86 231.4 225.78
4
 
309.84 303.71 309.75 303.59 320.66 313.71 326 318.95
5
 
405.87 398.29 416.45 407.94 347.04 340.58 360.5 352.71
6
 
793.69 778.86 808.91 791.91 679.17 666.55 705.7 690.54
Fig. 8.  Numerical natural frequency for all laminated composites
defined by using Ansys Composite PrepPost ACP (Pre) 
to create FEM models for different stacking sequences 
of laminates and finally the model analysis was used 
to evaluate until the first six natural frequencies with 
their mode’s shapes are given, as shown in Table 6. 
It is obvious from Table 6 and Fig. 8 that all modes 
are bending modes, except mode 4 is torsional mode. 
Moreover, the maximum natural frequency for 1
st
, 2
nd
, 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)5-6, 224-234
233 The Dynamic Behaviour of Symmetrical Laminated Nano-composite Containing Equal Numbers of Glass and Carbon Fibre Layers  
Fig. 9.  Natural frequencies comparison in analytical, experimental, 
and numerical methods
4  CONCLUSIONS
Structural components need to have high strength and 
stiffness along with high damping capacity. In this 
paper, the following conclusions can be made.
1. The maximum natural frequency for the cross- 
and quasi-laminate group was obtained for C2 
and Q2 laminates.
2. The relationship between the natural frequency 
and damping ratio is inversely proportional.
3. Both flexural modulus and damping ratio were 
increased with addition of 2 % nano-Al
2
O
3
, while 
the natural frequency was decreased.
4. The maximum damping ratio for the cross- and 
quasi laminate group was obtained for C1W and 
Q2W laminates, respectively.
5. The new aspect of this work is in the Q2 and 
Q2W configurations, which is appropriate to 
use in industry for structural element parts with 
higher bending modulus, natural frequency, and 
damping ratio properties.
6. The analytical, experimental, and numerical 
(ANSYS) natural frequencies are very close to 
each other.
5  NOMENCLATURES
D
ij
   flexural stiffness matrix, [Pa·m
3
]
[Q
ij
] reduced stiffness matrix, [Pa]
h  laminate thickness, [mm]
D
11
*
  first element in the flexural compliance
  matrix [1/(Pa·m
3
)] 
E
b
  flexural modulus, [GPa]
wn  fundamental natural frequency, [Hz]
l  beam length, [m]
I
yy
  moment of inertia, [m
4
]
ρ  density, [kg/m
3
]
A  cross sectional area, [m
2
]
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