Thermoelastic Damping in the Axisymmetric Vibration of Circular Microplate Resonators with Two-Dimensional Heat Conduction

Predicting thermoelastic damping (TED) is crucial in the design of high Q micromechanical resonators. Circular plates are common elements in the microresonators. In the past, some analytical models have been developed for TED in circular microplate resonators. However, to obtain a simple analytical expression, the previous models neglected the temperature gradient along the radial and circumferential directions, only the heat conduction through the thickness of the circular plate was considered. Thus the previous models cannot be used for general purpose design and optimization of microplate resonators. This paper presents a new analytical model for the TED in the circular microplates vibrating in the axisymmetric mode. Compared with the previous models, the present model considers two-dimensional heat conduction over thermoelastic temperature gradients along the thickness direction and the radial direction. The temperature field is represented by the product of the Bessel series along the radial direction and an unknown function along the thickness direction, which is determined in the solution procedure. The present model is validated by comparison with the previous model and the finite element method (FEM) model.