Grain size and nanoscale effects on the nonlinear pull-in instability and vibrations of electrostatic actuators made of nanocrystalline material

Abstract

Presented herein is the study of grain size, grain surface energy and small scale effects on the nonlinear pull-in instability and free vibration of electrostatic nanoscale actuators made of nanocrystalline silicon (Nc-Si). A Mori–Tanaka micromechanical model is utilized to calculate the effective material properties of Nc-Si considering material structure inhomogeneity, grain size and grain surface energy. The small-scale effect is also taken into account using Mindlin’s strain gradient theory. Governing equations are derived in the discretized weak form using the variational differential quadrature method based on the third-order shear defamation beam theory in conjunction with the von Kármán hypothesis. The electrostatic actuation is modeled considering the fringing field effects based upon the parallel plate approximation. Moreover, the Casimir force effect is considered. The pseudo arc-length continuation technique is used to obtain the applied voltage-deflection curve of Nc-Si actuators. Then, a time-dependent small disturbance around the deflected configuration is assumed to solve the free vibration problem. By performing a numerical study, the influences of various factors such as length scale parameter, volume fraction of the inclusion phase, density ratio, average inclusion radius and Casimir force on the pull-in instability and free vibration of Nc-Si actuators are investigated.