Theoretical modeling of a circular piezoelectric actuator for micro-systems

Based on the classical laminated plate theory and the piezoelectric plate and shell theory, this paper presents an analytical analysis of a circular piezoelectric actuator used in micro-systems. The actuator consists of four layers: piezoelectric ceramic, metal, electrodes and epoxy resin. Each layer has different dimensions, material properties and initial stress. For the simply supported boundary conditions, equations for the calculation of first-order resonance frequency and dynamic displacement of structure are derived by Rayleigh-Ritz method. A circular piezoelectric composite plate with elastic support is considered, and the results obtained from equations are consistent with the results from Finite Element simulation. The consistency of theoretical and simulation results validated the correctness and the validity of theoretical model. For various dimensions and material parameters, this analytical model can be used to predict the change of resonance frequency and dynamic displacement of the actuator. The analytical solution presented in this paper is significant for the optimization of piezoelectric actuator used in piezoelectric transducers.