NONLINEAR FREE VIBRATION ANALYSIS OF AN EMBEDDED DOUBLE LAYER GRAPHENE SHEET IN POLYMER MEDIUM

Abstract

This paper investigates the nonlinear free vibration of a double layer graphene sheet (DLGS) embedded in a polymer matrix aroused by the nonlinear van der Waals (vdW) interactions based on the classic Kirchhoff plate theory. Harmonic balance method is used to predict the nonlinear relation between deflection amplitudes and resonant frequencies of the DLGS. The embedded DLGS presents a hardening nonlinearity in both in-phase vibration (IPV) and anti-phase vibration (APV) modes. The surrounding polymer medium is found to have significant effect on the resonant frequency, especially for the IPV mode. For example, the variation of the resonant frequencies of an embedded DLGS is less dependent on the graphene aspect ratio and mode numbers as compared with a free-standing one. Uni-axial and bi-axial in-plane load effects upon the vibrational behavior of DLGS are also investigated. It is concluded that due to the influence of the nonlinear interlayer and interfacial vdW forces on the DLGS, prediction on both linear and nonlinear resonant frequencies for the embedded DLGS is quite different from that for a free-standing one. This study is expected to be useful for understanding the nonlinear mechanical behavior of graphenes with their potential applications in nanocomposites.