Surface Stress Effect on the Pull-In Instability of Hydrostatically and Electrostatically Actuated Rectangular Nanoplates With Various Edge Supports

Abstract

This paper is aimed to investigate the size-dependent pull-in behavior of hydrostatically and electrostatically actuated rectangular nanoplates including surface stress effects based on a modified continuum model. To this end, based on the Gurtin–Murdoch theory and Hamilton’s principle, the governing equation and corresponding boundary conditions of an actuated nanoplate are derived; the step-by-step linearization scheme and the differential quadrature (GDQ) method are used to discretize the governing equation and associated boundary conditions. The effects of the thickness of the nanoplate, surface elastic modulus and residual surface stress on the pull-in instability of the nanoplate are investigated. Plates made of two different materials including aluminum (Al) and silicon (Si) are selected to explain the variation of the pull-in voltage and pressure with respect to plate thickness.