Effects of geometric nonlinearity on the pull-in instability of circular microplates based on modified strain gradient theory

Abstract

Presented in this study is an analytical investigation on the size-dependent nonlinear vibration and pull-in instability of circular microplates subjected to the electrostatic, Casimir, and hydrostatic forces. Based on the modified strain gradient theory in conjunction with the Kirchhoff thin plate theory and von Kármán’s nonlinear kinematic relations, the governing equations were derived using the variational principle. The Galerkin technique (GT) and Homotopy analysis method (HAM) are employed to present the analytical solution considering the clamped boundary condition. Different comparative studies are presented to show the accuracy of the model. As the main novelty of this study, the effects of the geometric nonlinearity on the strain gradient dynamic pull-in instability of circular microplates are presented through a wide range of analytical results. It is observed that by increasing the gap distance, the impacts of nonlinear strains on pull-in behavior become more remarkable. © 2020 IOP Publishing Ltd Printed in the UK