Thermoelastic damping in rectangular microplate resonators with three-dimensional heat conduction

Abstract

Accurate determination of thermoelastic damping (TED) can be regarded as a crucial component in the design and optimization of microplate resonators with high quality factors. Three types of rectangular plates are often used in microresonators, which are the fully clamped plate, the cantilever plate and the fixed-fixed plate (the clamped-free-clamped-free plate) respectively. The three microplates usually operate in the fundamental mode. In this paper, a primary frame work of computing the TED in the rectangular microplates with three-dimensional (3-D) heat conduction is first presented. Then by utilizing the Rayleigh's method, three analytical models are derived in detail for the TED in the three types of rectangular plates mentioned previously. Compared with the previous one-dimensional (1-D) model, the effect of thermal boundary conditions at clamped edges on TED was considered in this work. The simulated results of the present models have shown a much closer agreement with the FEM results than those of the previous 1-D model for all plates. The convergence rates of the present models are carefully investigated. The comparison of temperature field distribution obtained from the previous 1-D model and the present model is also presented.