Abstract
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.
Highlights
Microrings are a common resonator of MEMS, which are widely applied to MEMS sensors and actuators [1,2,3,4]
First the thermoelastic damping model of this paper for ring resonators is validated by comparing with the experimental data and other theories results
This paper studied the entropy generation of a ring resonator vibrating under in-plane modes and presents an analytical model of thermoelastic damping based on entropy theory
Summary
Microrings are a common resonator of MEMS (a microelectromechanical system), which are widely applied to MEMS sensors and actuators [1,2,3,4]. Compared to Zener theory, the present model uses a complex temperature field to calculate the entropy generation and heat increments instead of using a modal superposition temperature field to calculate mechanical work loss in which the first thermal mode is usually dominant and reserved. The analytical model in this paper is different from the model of Wong et al [9] calculated by mechanical energy loss based on the LR theory but is different from the Zener theory It can be an alternative method with high accuracy to predict TED in ring resonators and provide verification from the perspective of entropy generation for other methods. This solution technology can improve the computational efficiency by avoiding the complex frequency [26]
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