Analysis of Pull-In Parameters of a Microelectromechanical Beam With van der Waals Force Using Modified Couple Stress Theory

Abstract

This study investigates the pull-in parameters of a microcantilever beam influenced by electrostatic and van der Waals forces in microelectromechanical system (MEMS) devices. The classical continuum theory (CCMT) is inadequate because of the presence of nonpolar molecules, voids, and dielectric materials at the micro or nanoscale. Modified couple stress theory (MCST) is a nonclassical continuum technique used in microbeams for evolution of the length scale parameter (lm). Nonlinearity due to large-scale deflection and van der Waals force is highly significant at the microscale. The Galerkin method is used to solve the governing equation of microbeam model. The comparison of eigenfrequencies is conducted by numerical, finite element based method while varying the mass of microplate. The pull-in phenomena occurs when the actuating force is exceeds the mechanical force. The static pull-in parameters are determined using on CCMT and meshless local Petrov–Galerkin (MLPG) methods and verified through comsol software. The pull-in voltage (Vpi), displacement (wpi), and van der Waals parameter (Cpi) are in close match with numerical and analytical methods. The variation lm is influenced by damping constant, stiffness of microbeam under dynamic pull-in conditions.