Modeling of Thermoelastic Damping in Bulk-Mode Vibrations of Micromechanical Ring Resonator Using Energy Method

In this paper, thermoelastic damping in bulk-mode vibrations of the micromechanical ring resonator is modeled using the energy method. Assuming that the thermoelastic coupling is very weak, the resonance frequencies and elastic displacements are first calculated using two-dimensional plane stress equations. An analytical expression for thermoelastic quality factor is then derived based on uncoupled linear thermoelasticity under adiabatic conditions.The validity of the derived expressions is demonstrated by comparing the analytical results with simulation results of modal and harmonic analysis using ANSYS software. Results show that the relative error of the analytical results decreases with increasing the ratio of the outer-to-inner ring radius. Moreover, the effects of resonance frequency and ring geometry on thermoelastic quality factor in various mode shapes of bulk-mode vibrations are discussed. The present analysis is applied as an appropriate tool to design bulk-mode ring resonators with high quality factor.