Linear and nonlinear free vibrations of electrostatically actuated micro-/nanomechanical resonators

Abstract

This paper is concerned with linear and nonlinear free vibrations of an axially stressed clamped---clamped micro-/nanobeam actuated by one-sided electrode configuration. Galerkin procedure and a proper shape function are used to establish a dynamic reduced-order model, where the integral of the electromechanical forcing term is obtained in an explicit and closed form. This model makes the analysis of dynamic behaviors convenient for the micro-/nanobeam. For linear free vibration, the fundamental natural frequency formulas of the system are validated by comparing with published experiment data while the Newton method coupled with the harmonic balance method is developed to obtain analytical approximate period and periodic solution for the nonlinear system. These approximate solutions have explicit expressions and they can readily be used to derive the effects of various physical parameters on dynamic behavior of micro-/nanobeams. Exact solution in an integral form is also presented. For small as well as large amplitudes of nonlinear vibration, the new analytical approximate solutions show excellent agreement with respect to the numerically integrated solutions obtained from the integral-form exact solutions.