An Analytical Model for Thermoelastic Damping in Microresonators Based on Entropy Generation

Abstract

This paper presents an analytical model for thermoelastic damping (TED) in micromechanical resonators, which is based on entropy generation, a thermodynamic parameter measuring the irreversibility in heat conduction. The analytical solution is derived from the entropy generation equation and provides an accurate estimation of thermoelastic damping in flexural resonators. This solution technique for estimation of thermoelastic damping is applied in beams and plates resonators. The derivation shows that the analytical expression for fully clamped and simply supported plates is similar to that for beams, but not the same as the latter due to different strain and stress fields. The present model is verified by comparing with Zener's approximation and the LR (Lifshitz and Roukes) method. The effect of structural dimensions on entropy generation corresponding to thermoelastic damping is investigated for beam resonators. The results of the present model are found to be in good agreement with the numerical and experimental results.