Mathematical Modelling of Electrostatically Actuated Cantilever Beams

Abstract

Abstract This study presents a mathematical model for an electrostatically actuated cantilever beam using COMSOL Multiphysics and Wolfram Mathematica. The model is used to investigate the pull-in voltage phenomenon, which refers to the voltage required to pull the beam to touch the bottom electrode. The cantilever beam is modeled as a micro-electromechanical system (MEMS) structure and is electrostatically actuated by applying a voltage between the beam and the bottom electrode. The model takes into account the electrostatic forces and the mechanical deflection of the beam. Parametric analysis is performed using COMSOL Multiphysics and then Wolfram Mathematica tool is used to validate the results obtained from the simulations. The mathematical model is developed using Galerkin's method. This study provides insights into the design and optimization of MEMS devices for various applications such as sensors and actuators.