Vibrations of micro-beams actuated by an electric field via Parameter Expansion Method

This paper presents a new asymptotic procedure to predict the nonlinear vibrational behavior of micro-beams pre-deformed by an electric field. The nonlinear equation of motion includes both even and odd nonlinearities. A powerful analytical method called Parameter Expansion Method (PEM) is employed to obtain the approximated solution and frequency–amplitude relationship. It is demonstrated that the first two terms in series expansions are sufficient to produce an acceptable solution of mentioned system. The obtained results from numerical methods verify the soundness of the analytical procedure. Finally, the influences of basic parameters on pull-in instability and natural frequency are investigated.

► This article presents a new procedure to predict the micro-beams vibrating behavior.
► Parameter Expansion Method is used to obtain the exact solution of the problem.
► The nonlinear equation of motion has both even and odd nonlinearities.
► Nonlinear natural frequency as a function of amplitude are presented.
► Dynamic pull-in instability behavior of micro-beams are investigated.