Nonlinear resonant behavior of thick multilayered nanoplates via nonlocal strain gradient elasticity theory

Abstract

In this study, the nonlinear forced vibration of simply supported multilayered nanoplates in the framework of the first-order shear deformation of Mindlin plate theory based on the nonlocal strain gradient elasticity theory is investigated. The nonlinear von Karman strain–displacement relation is employed. The interaction of van der Waals forces between adjacent layers of a multilayered nanoplate is considered. The harmonic balance method is used to analyze the nonlinear resonance behavior of a thick nanoplate. The primary resonance and the secondary resonance which consist of superhamonic and subharmonic resonance are investigated. As a main result, by increasing the thickness of a thick nanoplate, the subharmonic resonance disappears and the frequency response curves imply non-resonant behavior, responses with finite amplitudes and different shapes for different thicknesses of thick nanoplates. At the end, the natural frequencies of thick multilayered nanoplates are obtained, and the effect of variation of nonlocal parameter, strain gradient parameter, number of layers and thickness of the nanoplate on the frequency response curves and stable and unstable regions is investigated.