Stability and Bifurcation Analysis of an Asymmetrically Electrostatically Actuated Microbeam

Abstract

This paper deals with the study of bifurcational behavior of a capacitive microbeam actuated by asymmetrically located electrodes in the upper and lower sides of the microbeam. A distributed and a modified two degree of freedom (DOF) mass–spring model have been implemented for the analysis of the microbeam behavior. Fixed or equilibrium points of the microbeam have been obtained and have been shown that with variation of the applied voltage as a control parameter the number of equilibrium points is changed. The stability of the fixed points has been investigated by Jacobian matrix of system in the two DOF mass–spring model. Pullin or critical values of the applied voltage leading to qualitative changes in the microbeam behavior have been obtained and has been shown that the proposed model has a tendency to a static instability by undergoing a pitchfork bifurcation whereas classic capacitive microbeams cease to have stability by undergoing to a saddle node bifurcation.