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.

本文介绍了SMA导线特性对调整电容式微谐振器稳定性的影响。在提出的模型中，预应变的SMA导线已嵌入到双钳位的共振微束中，该束由静电驱动。介绍了系统的控制方程，然后采用特征值问题研究稳定性。基于Galerkin的数值方法已被用来求解运动的控制方程，以获得光束的运动轨迹。已经显示了SMA导线的数量，其直径，预应变和温度对谐振器的拉入不稳定性和频率响应的影响。已获得在施加和不施加直流电压的情况下避免不稳定性的恢复应力和SMA温度的临界值。