Interaction of transverse pressure and in-plane internal stresses on bi-stability of electrostatically rectangular microplates

Abstract

Bi-stability behavior is commonly observed in an electrostatically actuated pressurised or initially curved microplates. Additionally, presence of in-plane internal stresses considerably changes the mechanical behaviour of the electrostatically actuated microplate. In this paper, the effects of in-plane internal stresses on bi-stability criteria of pressurised rectangular microplates are investigated. For this, the governing differential equation of motion of a rectangular plate is derived using Kirchhoffs plate theory including von Karmans nonlinearity, transverse pressure, axial in-plane internal stresses, and non-linear electrostatic actuation force. Further, Galerkins based reduced-order modelling technique is applied to solve the equation. The problem has been solved for two different sets of plate boundary conditions: simply supported and clamped. The analysis reveals that the presence of tensile or compressive in-plane internal stresses significantly changes the transverse pressure range for the occurrence of bi-stability on the voltage-deflection equilibrium path. Further, we have investigated the variation of Required threshold gap between microplate and substrate for bi-stability in presence of in-plane internal stresses. Results of this investigation can be used to design more efficient microplate based bi-stable N/MEMS devices.