Wave Propagation Characteristics in A MEMS Piezoelectric Annular Plate: A Semi-analytical Study

Abstract

Our paper focuses on wave propagation in a circular annular piezoelectric plate with hexagonal elastic symmetry used in Micro-Electromechanical Systems (MEMS). The objective is to examine the properties of two piezoelectric materials: PZT-5A, a soft ceramic used in ultrasonic sensors, and PZT-4, a strong ceramic used in ultrasonic actuators. We developed the Legendre orthogonal polynomial method to obtain semi-analytical solutions for the governing equations. One strength of our method is that it can analyze the global structure using a single formalism calculation. The analysis takes into consideration the alternating current excitation and directly includes the boundary conditions into the vibration equations. As a result, we found that the limit value of voltage \({V}_{0}\) across the electrodes equals \(160 V\) that can be applied to determine the maximum von Mises stress without exceeding the yield stress value of \(31.2\text{ MPa}\) for the PZT4. The electromechanical coupling coefficient shows that the fundamental mode is the most piezoactive mode in the structure. Furthermore, we present the natural frequencies, electrical input impedance, field profiles, and dispersion curves. To validate the efficiency and accuracy of our approach, we compared our results with those obtained using voltage excitation and analytical data. Ultimately, we achieved a good agreement between them.