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

141

2

1. Introduction Carbon nanotubes (CNTs), uncovered by Iijima (2002) in 1991, created by a cylinder formed by rolling a graphene sheet with caps at each end (Dresselhaus, Dresselhaus, and Saito 1995), have superior material properties, including high strength, thermal and electrical conductivity (Dresselhaus et al. 2000; Guo et al. 2005; Chae et al. 2007; Chae et al. 2009), which make them excellent candidates for reinforcement of macrostructures, such as plates, shells, and beams. CNT reinforced macrostructures are widely used in mechanical, automobile, and medical industries, which led to a wide range of research into the dynamics of the CNT reinforced structures (Liew, Pan, and Zhang 2020). A number of studies specifically on the dynamics of CNT reinforced plates, were reported in recent years. Fu et al. (2016) investigated the nonlinear dynamics of a functionally graded (FG) CNT reinforced plate with an elastic layer using the classical plate theory and the two-step perturbation technique. The boundaries of principle unstable regions of the simply supported system moved up as the elastic layer stiffness increases. García-Macías et al. (2016) initiated the research in vibrations of FG CNT reinforced skew plates. Zhang (2017) extended the research to examine the dynamics of FG CNT reinforced skew plates, considering the shear effects, using the element-free IMLS method, where the effects of altering the CNT pattern and angle of the skew plate were studied. However very limited studies are reported on a FG CNT reinforced plate with mass imperfections. To address these research gaps and contribute to what is yet to be known, this research aims to investigate and analyse the dynamics of a FG CNT reinforced plate with mass imperfections via developments to mathematical models of the macrostructure. The pattern of UD, FG-O and FG-X, and simply supported boundary conditions for the Kirchhoff plate are considered in this study approach. Specific objectives were to help better design CNT reinforced plates, effects of plate aspect ratio and thickness, functionally graded pattern, and, magnitude and position of mass imperfections which are studied in details and presented here. 2. CNT reinforced plate formulation As shown in Fig. 1, the FG CNT reinforced plate with length ( x axis), a , width ( y axis), b , and thickness ( z axis), h , alongside a mass imperfection with a magnitude, M , located at ( x 0 , y 0 ), has the boundary conditions of simply supported on four of the edges. The matrix volume fraction   m V and CNT volume fraction   CNT V follow the formula below:     1 . m CNT V z V z   (1) where the CNT distribution along the thickness of the plate follows the functions detailed below (Daikh et al. 2022):

UD:

  V z V  CNT

*

,

CNT

FG-O:

2        2 1 z h 

 

*

,

CNT V z

V

(2)

CNT

FG-X:

2        2 z h

 

*

.

CNT V z

V

CNT

This is followed by the material properties of the FG CNT reinforced plate (density,  , Young’s modulus, E , shear modulus, G , Poisson’s ratio, v ) based on the rule of mixture, considering the anisotropic properties of CNT (Shen 2009) are       , CNT CNT m m z V z V z      (3)