Analytical solution for vibration characteristics of rotating graphene nanoplatelet-reinforced plates under rub-impact and thermal shock

Abstract

This article presents an analytical investigation on vibration characteristics of rotating graphene nanoplatelet (GPL)-reinforced plates subjected to rub-impact and thermal shock. The effective material properties are assumed to vary continuously and smoothly along the thickness direction of the plate and are determined via the Halpin–Tsai micromechanics model together with the rule of mixture. Considering the gyroscopic effect, the equations of motion are derived by adopting the Hamilton’s principle based on the Kirchhoff’s plate theory. Then, the Galerkin method and the small parameter perturbation method are utilized to obtain the free and forced vibration results for the rotating plate. A detailed parametric study is conducted to examine the effects of the GPL weight fraction, GPL distribution pattern, length-to-thickness ratio and length-to-width ratio of GPLs, and the rotating speed on free vibration characteristics of the nanocomposite plate. Attention is also given to the influences of the GPL weight fraction, thermal flow, and friction coefficient on forced vibration responses of the plate. The obtained results can play a role in the design of a rotating GPL-reinforced plate structure to achieve significantly improved mechanical performance.