Stability analysis of a capacitive micro-resonator with embedded pre-strained SMA wires

Abstract

This paper presents a study on the effects of the SMA wires’ characteristics on tuning the stability of a capacitive micro-resonator. In the proposed model, pre-strained SMA wires have been embedded in a double clamped resonant microbeam which is actuated electrostatically. The governing equations of the system have been introduced and then an eigen-value problem has been adopted to investigate stability. Galerkin-based numerical methods have been used to solve the governing equation of motion for obtaining the motion trajectories of the beam. The effects of the number of SMA wires, their diameter, pre-strain and temperature on the pull-in instability and frequency response of the resonator have been shown. Critical values of recovery stress and SMA temperature for avoiding instability, with and without applying DC voltage have been obtained. The results have shown that by changing each of the SMA parameters, one can reach a needed magnitude of recovery stress as well as transmitted longitudinal force to the host beam, and consequently control and tune the stability and resonance frequency of the micro-resonator.