Stability Analysis in Parametrically Excited Electrostatic Torsional Micro-actuators

This paper addresses the static and dynamic stabilities of a parametrically excited torsional micro-actuator. The system is composed of a rectangular micro-mirror symmetrically suspended between two electrodes and acted upon by a steady (dc ) while simultaneously superimposed to an (ac ) voltage. First, the stability of the system subjected to a quasi-statically applied (dc ) voltage is investigated, where the pull-in instability, equilibrium positions, and bifurcation points of the system are determined. Then by superimposing an (ac) voltage and extracting a Mathieu type governing equation the effects of (ac ) component on the stability of the system is investigated. By varying excitation parameters (steady (dc) voltage and time-dependent amplitude of (ac ) excitation), transition curves and the stability margins of the micro-mirror are demonstrated. Theoretically obtained margins are checked by means of numerical simulations. The results show that superimposing the harmonic (ac ) component could have a stabilizing effect and allow an increase of the steady (dc ) component beyond the pull-in value. The obtained results could be used in design of micro-actuators.