Primary and Secondary Resonance of Micro-resonators Based on Couple Stress Theory

Abstract

In this work, the influence of size effect on the primary and the secondary resonance of micro-resonators is investigated. The micro-resonator, which is considered in this study, is a clamped–clamped beam excited by AC and DC electrostatic voltage. The DC voltage is applied to prevent doubling of excitation frequency and tune the range of system’s working frequency. We computed the beam’s motion equation using Euler–Bernoulli theory for wide beams considering couple stress theory and geometrical nonlinearity. For micro-resonators with high quality factor and small amplitude of harmonic excitation, we captured frequency response curves using shooting method, then we used multiple time scale method for its validation. Due to the limitation of the multiple time scale perturbation method for the computation of frequency responses in large amplitude harmonic excitation, the shooting method has been used, regardless of how big the harmonic excitation amplitude or how small the micro-resonator’s quality factor is. Another contribution of this paper is the analysis of the influence of size effect on the system’s hardening and softening as well as its effect on reduction of pull-in band. This work presents that considering the size effect will result in reduction or elimination of pull-in band and also the nonlinear behavior of the system will be inclined to become linear in primary resonance.