paper Dynamics of periodic solution to a electrostatic Micro-Electro-Mechanical system

A canonical mass-spring model of electrostatically actuated Micro-Electro-Mechanical System (MEMS) is studied. We investigate the existence and bifurcations of the periodic solution by means of the continuation theorem of Manasevich and Mawhin with techniques of a priori estimate and bifurcation theory. The main results answer the open problem proposed by P. Torres in the known literature. It also reveals that the system undergoes saddle node and period doubling bifurcation leading to the multiplicity of periodic solution. Moreover, bistability of periodic solution generated by the combination of these bifurcations is detected for the first time, which provides some new insight into the so called pull-in instability in the system. At last, periodic orbits with different stability and corresponding time series are given to illustrate the results.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This study investigates a canonical mass-spring model of electrostatically actuated Micro-Electro-Mechanical System (MEMS). The existence and bifurcations of periodic solutions are explored using the continuation theorem of Manasevich and Mawhin with techniques of a priori estimate and bifurcation theory. The main results provide answers to an open problem proposed by P. Torres and reveal saddle node and period doubling bifurcations in the system, resulting in the multiplicity of periodic solutions. Additionally, the study discovers bistability of periodic solutions, generated by the combination of these bifurcations, shedding light on the pull-in instability in the system. Finally, periodic orbits with different stability and corresponding time series are presented to illustrate the findings.