Vibrational response of a piezoelectric MEMS resonator disc metallized with alternating electrical source

This paper present a study of vibrational behavior of a piezoelectric MEMS resonator disc partially metalized with electrical source in case of partial centralized metallization using Legendre polynomial method. Such method is based on solving coupled governing equation of motion and characteristic equations of piezoelectricity. The Formulation is simple to implement and consist of a decomposition of the mechanical and electrical displacement fields in a double series of Legendre polynomial basis. With a single calculation, the method is able to restitute the electro-optic behavior of the MEMS including resonance and anti resonance frequencies, electrical admittance, dispersion profiles and electromechanical coefficient for all orders.