A coupled two degree of freedom pull-in model for micromirrors under capillary force

The current paper presents a two degree of freedom model for the problem of micromirrors under capillary force. The principal of minimum potential energy is employed for finding the equilibrium equations governing the deflection and the rotation of the micromirror. Then, using the implicit function theorem, a coupled bending-torsion model is presented for pull-in characteristics of micromirrors under capillary force and the concept of instability mode is introduced. It is observed that with increasing ratio of bending and torsion stiffness, the dominant instability mode changes from bending mode to the torsion mode. In order to verify the accuracy of the coupled model, static behavior of a group of micromirrors is investigated both analytically using the presented model and numerically using the commercial finite element software ANSYS. It is observed that results of the coupled model match well with the results of finite element simulations, but they both deviate considerably from the results of the pure torsion model. The presented coupled model can be used for safe and stable design of micromirrors under capillary force.