Analytical modeling of bending effect on the torsional response of electrostatically actuated micromirrors

This paper presents analytical solutions for the nonlinear problem of electrostatically actuated torsional micromirrors considering the bending of the torsional beams. First the energy method is used for finding the equilibrium equations. Then the explicit function theorem is utilized for finding the equations governing the instability mode of the mirror. These equations are then solved using Homotopy Perturbation Method (HPM) for the especial case of α = 0 where α   is a small nondimensional geometrical parameter defining the starting point of the underneath electrodes. Then straight forward perturbation method is applied for finding the pull-in angle and pull-in displacement of the micromirror for the general case of α≠0α≠0. The presented results which were in excellent agreement with numerical simulations show that neglecting the bending effect in electrostatic torsion micro actuators can lead to several hundred percent of overestimation of the stability limits of the device. In order to study the voltage-angle and voltage-displacement behavior of the micromirror, equilibrium equations are solved using HPM. Presented results are in good agreement with numerical simulations and also with experimental findings.