Closed Form Solutions for the Statical Behavior of Micromirrors Under Capillary Forces

In this paper, the static behavior of micromirrors under the effect of capillary forces is studied. First the equation governing the static behavior of micromirrors is obtained using both Newton method and minimum potential energy principle. Then energy method is employed to investigate the static instability of micromirrors equilibrium points. It is proved that when there exist two equilibrium points, the smaller one is stable and the larger one is unstable. Furthermore a design equation is suggested for the successful fabrication process of micromirrors in the stable operatives range. Then the statical behavior of micromirrors is investigated numerically and analytically using the Homotopy Perturbation Method (HPM). It is observed that with increasing the instability number defined in the paper, the rotation angle of the micromirror is increased and suddenly the pull-in occurs. The analytical results well follow the numerical ones and so the presented analytical method can be used for a fast and accurate design tool for micromirrors fabrication.