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Nonlinear free vibration of functionally graded graphene nanoplatelet-reinforced composite rectangular plates using the full layerwise finite element method

Tayebi M. S., Jedari Salami S., Tavakolian M.

Archives of Mechanics

2024

Vol. 76, nr 3

225--252

This investigation is the first effort to study the nonlinear free vibration response of functionally graded (FG) graphene nanoplatelet (GPL)-reinforced composite rectangular plates using the full layerwise (LW) finite element method. The innovation of this article, which has not been investigated thus far, is a nonlinear vibration analysis with equivalent precision to three-dimensional (3D) elasticity while benefiting from decreased computational cost, ease of mesh adjustment, and faster achievement of the element stiffness matrix due to preserving the 2D structure. The modified Halpin–Tsai model and the rule of mixtures are employed to specify the effective material properties for composite plates with three different arrangements of GPLs. After confirming the results and formulation, an exhaustive parametric study is executed to examine how various characteristics of GPLs and the plate affect the nonlinear-to-linear frequency (NTL) ratio of the FG GPL-reinforced composite plate. The noteworthy finding is that inserting a small percentage of GPLs in pure epoxy changes its NTL ratio significantly. The effect of the GPL dimension on the NTL ratio is insignificant when the thickness-to-length ratio of GPLs is smaller than 10-3.