Bifurcation analysis of torsional micromirror actuated by electrostatic forces

In this paper, static and dynamic behavior of an electro statically actuated torsional micro actuator is studied. The micro actuator is composed of a micro mirror and two torsional beams, which are excited with two electrodes. Unlike the traditional micro actuators, the electrostatic force exerted to both side of micro mirror, so the model is exposed to a DC voltage applied from the ground electrodes. The static governing equation of the torsional micro actuator 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 micro actuator 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 increasing the applied voltage leads the structure to an unstable condition by undergoing to saddle node and pitchfork bifurcations when the voltages ratio is zero and one, respectively.