PSI - Issue 45
Oscar Zi Shao Ong et al. / Procedia Structural Integrity 45 (2023) 140–147 O.Z.S. Ong et al. / Structural Integrity Procedia 00 (2019) 000 – 000
142
3
,
11 E z
1 m CNT E E V z E CNT
(4)
m
V z V z E E V z V z G G 2 22 CNT m CNT m 3 CNT m CNT m 12
,
22 E z
(5)
,
12 G z
(6)
22 E z E z 11
v z v z 21 12
,
(7)
where is the CNT efficiency parameter, which is dependent on the volume fraction of CNT. For * 1 2 0.11, 0.149, 0.934 CNT V , * 1 2 0.14, 0.150, 0.941 CNT V , * 1 2 0.17, 0.149, 1.381 CNT V , and 2 3 (Zhong et al. 2018). The linear non-zero stresses of a FG CNT reinforced Kirchhoff plate are (Fu et al. 2016)
2
2
E
E
3
3
1
2
,
z
v
z
11
11
21
xx
2
2
1
1
12 21 v v x
v v
y
x
y
12 21
(8)
2
2
2
E
E
3
3
3
2
1
1
2
,
2
2
,
z
v
z
G
z
22
11
21
12
yy
xy
2
2
1
1
12 v v y 21
v v
x
y
x y x
y
x
12 21
where ε 1 , ε 2 and ε 3 are the axial, lateral and transverse displacements, respectively. The kinetic energy of the mass imperfection is then formulated
2
2
2
1 2
3 t t t 1 2
x x y y dA .
A
K
M
(9)
0
0
mass
Utilising the Hamilton method, the equation of motions (axial, lateral and transverse) are obtained,
3
2
2
1 2 2 t
3
3
3
2 y
1 x
2 2
2
3
I
I
A
B
A
B
1
2
1
1
2
2
2
2
2
x
x t
x
y
(10)
2 3
2 1
1
2
2
2
2
) x x y y ( (
)
0,
D
D
M
1
2
0
0
2
y
y
x
x y
t
3
2
2 2 2 t
1
3
3
1
2
2
2 2
2
2
I
I
D
D
1
2
1
2
2
x
y
x
x y
y t
(11)
2
2
2 2 2 t
3
3
2 y
1 x
2
2
2
) x x y y ( (
) 0
,
M
C
B
C
B
0
0
1
1
2
2
2
2
y
y
x 1
3 2 2 t
4
4
3
3
2
1
3
3
1
2
I
I
I
1
2
3
2
2
2 2 2 x t
2 2 2 y t
x t
y t
3 2
2
2
3
3
2 y
1 x
x y
3
2
4
2
) x x y ( (
)
A
B
A
B
M
y
(12)
2
2
3
3
0
0
2
2
2
2
x
y
t
2
2
2
2
3
3
2
1 x
1
2
2
2
2
2
4
0,
C
B
3 C B
D
D
2
2
3
3
2
3
2
2
2
y
x y
y
x
x y
y
x
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