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Thermoelastic damping is a critical issue for designing very high quality factor microresonators. This paper derives the entropy generation, associated with the irreversibility in heat conduction, that is used for ring resonators in in-plane vibration and presents an analytical model of thermoelastic damping according to heat increments calculated by entropy theory. We consider the heat flow only in radial thickness of the ring and obtain a complex temperature field that is out of phase with the mechanical stress. The thermoelastic dissipation is calculated in the perspective of heat increments that appear due to entropy generation. The analytical model is validated by comparing with an LR (Lifshitz and Roukes) model, finite-element method and measurement. The accuracy of the present model is found to be very high for different ambient temperatures and structures. The effects of structure dimensions and vibration frequencies on entropy generation and thermoelastic damping is investigated for ring resonators under in-plane vibration.

Entropy Generation and Thermoelastic Damping in the In-plane Vibration of Microring Resonators