A three-dimensional electromechanical model for geometric design and control of piezoelectric ring resonators with inner metallization

Abstract

The study of geometric influences on vibrational behavior offers a valuable pathway toward optimized design in MEMS. This work provides an extended polynomial method for analyzing how variations in the inner radius, and by extension the radial wall thickness, affect the vibration behavior of piezoelectric ring-shaped MEMS resonators with partial electrode coverage. The approach utilizes tailored Legendre polynomial expansions and applies window functions to accurately enforce boundary conditions over specific regions. This allows the model to capture wave propagation characteristics and the effects of metallization in the inner region with high fidelity. The method’s accuracy is verified through comparisons with previously published results. The analysis focuses on how the inner-to-outer radius ratio influences resonant frequencies (RFs), antiresonant frequencies (AFs), and dynamic electromechanical coupling coefficients (DEMCCs). A key observation is that the DEMCC associated with the third mode can exceed that of the fundamental mode and may increase by up to 3.34 times relative to equivalent solid disk counterparts, especially in structures with thin walls. Additional insights are provided through evaluations of dispersion characteristics, frequency parameters, admittance responses, and field distributions, offering valuable guidance for the design of optimized ring-shaped resonators in MEMS devices.