An exact analytical solution for coupled vibration analysis of a piezoelectric resonator

Piezoelectric resonators are widely used as the active components in devices such as sensors, actuators, communication filters, and micro/nano-electro-mechanical systems (MEMS / NEMS). Due to the piezoelectric effect, Poisson’s ratio, and its finite dimension, the thickness and lateral vibration modes in a piezoelectric resonator are inevitably coupled. In this paper, an exact analytical model for coupled vibration analysis of a piezoceramic disk is developed based on a new superstition method. The free vibrations are decomposed into thickness and lateral directions in a new form of Fourier-Bessel series and then they are superimposed to satisfy the boundary conditions. To verify the validity of the analytical model proposed here, numerical simulations are performed using COMSOL Multiphysics. An excellent agreement is observed. This analytical model can be applied to the design and optimization of piezoelectric devices.