Coupling Effects Between Torsion and Bending in Torsional Micromirrors Under Capillary Forces

Abstract

In the current paper, a general theoretical model for the problem of micromirrors under the effect of capillary forces is presented. The presented model considers the coupling effect between torsion and bending of the torsion beams supporting the micromirror. First, the energy method, the principal of minimum potential energy is utilized for finding the equations governing the micromirror rotation and its deflection. Then using the implicit functions theorem, the equations governing the pull-in angle and pull-in displacement of the micromirror is derived. The results, shows that ignoring the bending effect in micromirrors under the effect of capillary forces, can cause a significant (up to several hundred percents) underestimation of the pull-in angle. It is observed that with increasing the ratio of the bending stiffness to the torsion stiffness, the dominant instability mode changes from bending mode to the torsion mode. It is shown that when the bending stiffness of the system is relatively low, the equilibrium point of a one degree of freedom torsion model considerably deviates from that of coupled model. The presented model in this paper can be used for safe and stable design of micromirrors under capillary force.