ANALYTICAL MODELING OF SQUEEZE FILM DAMPING IN MICROMIRRORS

In the current paper, Extended Kantorovich Method (EKM) has been utilized to analytically solve the problem of squeezed film damping in micromirrors. A one term Galerkin approximation is used and following the extended Kantorovich procedure, the solution of the Reynolds equation which governs the squeezed film damping in micromirrors is reduced to solution of two uncoupled ordinary differential equation which can be solved iteratively with a rapid convergence for finding the pressure distribution underneath the micromirror. It is shown that the EKM results are independent of the initial guess function. It is also shown that since EKM is highly convergent, practically one iterate is sufficient for obtaining a precise response. Furthermore using the presented closed form solutions for the squeezed film damping torque, it is proved that when the tilting angle of the mirror is small, the damping is linear viscous one. Results of this paper can be used for accurate dynamical simulation of micromirrors under the effect of squeezed film damping.