A mathematical control for the pseudo-pull-in stability arising in a micro-electromechanical system

Abstract

A micro-electromechanical system’s reliability depends strongly upon its periodic motion; however, the pull-in instability might arise when the applied voltage is high enough. No criterion is available to judge the reliability condition in a simple but effective way. This paper tackles this challenge mathematically. The sufficient conditions for the periodic motion and the pull-in instability of a micro-electromechanical system with a current-carrying conductor are established, respectively. There is an uncertain area, where the system behaves firstly periodic motion, and after a certain number of cycles, the pull-in instability occurs. This new phenomenon is called as a pseudo-pull-in stability (pseudo-periodic motion); its main factors affecting the pseudo-periodic motion are elucidated.