Application of the Extended Kantorovich Method to the Vibrational Analysis of Electrically Actuated Microplates

This paper presents an extended Kantorovich approach to investigate the vibrational behavior of electrically actuated rectangular microplates. The model accounts for the electric force of the excitation and for the applied in plane loads. Starting from a one term Galerkin approximation and following the extended Kantorovich procedure, the partial differential equation governing the microplate vibration, is discretized to two ordinary differential equation with constant coefficients. These equations are then solved analytically and iteratively with a rapid convergence procedure for finding microplate natural frequencies and modeshapes. Results in some specific cases are validated against other theoretical results reported in the literature. It is shown that rapid convergence, high precision and independency of initial guess function make the EKM an effective and accurate design tool for design optimization.