An Entropy Based Analytical Model for Thermoelastic Damping in Micromechanical Resonators

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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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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Evaluation of thermoelastic damping in micromechanical resonators with axial pretension: An analytical model accounting for two-dimensional thermal conduction

Journal of Thermal Stresses ◽

10.1080/01495739.2019.1623141 ◽

2019 ◽

Vol 42 (9) ◽

pp. 1192-1205 ◽

Cited By ~ 1

Author(s):

Siyu Chen ◽

Jie Song ◽

Fenglin Guo

Keyword(s):

Analytical Model ◽

Thermal Conduction ◽

Two Dimensional ◽

Thermoelastic Damping ◽

Micromechanical Resonators

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Microcrystalline diamond micromechanical resonators with quality factor limited by thermoelastic damping

Applied Physics Letters ◽

10.1063/1.4793234 ◽

2013 ◽

Vol 102 (7) ◽

pp. 071901 ◽

Cited By ~ 20

Author(s):

Hadi Najar ◽

Amir Heidari ◽

Mei-Lin Chan ◽

Hseuh-An Yang ◽

Liwei Lin ◽

...

Keyword(s):

Quality Factor ◽

Thermoelastic Damping ◽

Micromechanical Resonators

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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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High quality factor nanocrystalline diamond micromechanical resonators limited by thermoelastic damping

Applied Physics Letters ◽

10.1063/1.4871803 ◽

2014 ◽

Vol 104 (15) ◽

pp. 151903 ◽

Cited By ~ 25

Author(s):

Hadi Najar ◽

Mei-Lin Chan ◽

Hsueh-An Yang ◽

Liwei Lin ◽

David G. Cahill ◽

...

Keyword(s):

Quality Factor ◽

Nanocrystalline Diamond ◽

High Quality Factor ◽

Thermoelastic Damping ◽

High Quality ◽

Micromechanical Resonators

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A Numerical Method for Predicting Thermoelastic Damping in Micromechanical Resonators

2008 Second International Conference on Integration and Commercialization of Micro and Nanosystems ◽

10.1115/micronano2008-70036 ◽

2008 ◽

Author(s):

Yang Xu ◽

Zhili Hao

Keyword(s):

Numerical Method ◽

Thermal Field ◽

Elastic Field ◽

Complex Frequency ◽

Thermoelastic Damping ◽

Structural Geometry ◽

Micromechanical Resonators ◽

Beam Resonator ◽

Modeling Software ◽

Parameter Measuring

This paper presents a numerical method for predicting thermoelastic damping (TED) in micromechanical resonators with any arbitrary structural geometry. In this numerical method, TED is interpreted as the generation of thermal energy per cycle of vibration from the viewpoint of thermal field. Consequently, TED is mathematically expressed in terms of entropy — a parameter measuring the irreversibility in heat conduction, and then numerically calculated in ANSYS/Multiphysics. The validity of this numerical method has been verified using the well-known solution to TED in a beam resonator and experimental data in the literature. Compared to the commonly used interpretation of TED in the elastic field-complex frequency, this numerical method does not involve complex values and thus offers the advantages of simplicity and compatibility with finite element modeling software.

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