Bifurcation analysis of torsional micromirror actuated by electrostatic forces

Abstract

In this paper, static and dynamic behavior of an electrostatically actuated torsional micro-actuator is studied. The microactuator is composed of a micromirror and two torsional beams, which are excited with two electrodes. Unlike in the traditional microactuators, the electrostatic force is exerted to both sides of micromirror, so the model is exposed to a DC voltage applied from the ground electrodes. The static governing equation of the torsional microactuator is derived and the relation between rotation angle and the driving voltage is determined. Local and global bifurcation analysis is performed, considering torsional characteristics of the micro-beams. By solving static deflection equation, the fixed points of the actuator are obtained. Critical values of the applied voltage leading to qualitative changes in the microactuator behavior through a saddle-node or pitchfork bifurcations for different spatial condition are obtained. Furthermore, the effects of different gap and electrode sizes as well as beam lengths on the dynamic behavior are investigated. It is shown that an increase of the applied voltage leads the structure to an unstable condition by undergoing saddle-node and pitchfork bifurcations when the voltages ratio is zero and one, respectively.