An Analytical Model for Thermoelastic Damping of Micro-Ring Gyroscopes

Predicting thermoelastic damping is essential in the design of the next generation of layered composite microresonators. We present an analytical model for thermoelastic damping in circular microplates using the framework developed by Bishop and Kinra. The thermoelastic damping spectrum will exhibit two distinct peaks when the thermal conductivity of the substrate is much greater or less than that of the film. Increment of the thickness of a layer with the bigger Zener’s modulus will increase the peak damping.

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

Entropy ◽

10.3390/e21070631 ◽

2019 ◽

Vol 21 (7) ◽

pp. 631 ◽

Cited By ~ 1

Author(s):

Yongpeng Tai ◽

Pu Li ◽

Yan Zheng ◽

Jie Tian

Keyword(s):

Analytical Model ◽

Entropy Generation ◽

Critical Issue ◽

Ring Resonators ◽

Thermoelastic Damping ◽

Ambient Temperatures ◽

Plane Vibration ◽

Radial Thickness ◽

Complex Temperature ◽

Very High

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.

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

Journal of Vibration and Acoustics ◽

10.1115/1.4026890 ◽

2014 ◽

Vol 136 (3) ◽

Cited By ~ 6

Author(s):

Yongpeng Tai ◽

Pu Li

Keyword(s):

Analytical Model ◽

Entropy Generation ◽

Present Model ◽

Stress Fields ◽

Accurate Estimation ◽

Solution Technique ◽

Thermoelastic Damping ◽

Micromechanical Resonators ◽

Parameter Measuring ◽

Good Agreement

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.

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An Entropy Based Analytical Model for Thermoelastic Damping in Micromechanical Resonators

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.159.46 ◽

2012 ◽

Vol 159 ◽

pp. 46-50 ◽

Cited By ~ 2

Author(s):

Yong Peng Tai ◽

Pu Li ◽

Wan Li Zuo

Keyword(s):

Quality Factor ◽

Analytical Model ◽

Entropy Generation ◽

Accurate Estimation ◽

Thermoelastic Damping ◽

Small Vibration ◽

Micromechanical Resonators ◽

Thin Beam ◽

Parameter Measuring ◽

Linear Thermoelasticity

In this paper, we present 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 temperature field of thin beam with small vibration is obtained by solving governing equations of linear thermoelasticity. The analytical solution is derived from the entropy generation equation. This method of entropy generation can provide an accurate estimation of the quality factor in flexural resonators. The results are compared with Zener’s approximation and LR (Lifshitz and Roukes) method. It is shown that the analytical model described in this paper is valid to estimate the quality factor due to thermoelastic damping.

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