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Research Papers

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

[+] Author and Article Information
Yongpeng Tai

School of Mechanical Engineering,
Southeast University,
Jiangning, Nanjing 211189, China
e-mail: tai@seu.edu.cn

Pu Li

School of Mechanical Engineering,
Southeast University,
Jiangning, Nanjing 211189, China
e-mail: seulp@seu.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 24, 2013; final manuscript received February 10, 2014; published online April 1, 2014. Assoc. Editor: Paul C.-P. Chao.

J. Vib. Acoust 136(3), 031012 (Apr 01, 2014) (8 pages) Paper No: VIB-13-1258; doi: 10.1115/1.4026890 History: Received July 24, 2013; Revised February 10, 2014

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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References

Figures

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Fig. 1

Schematic diagram of a thin microplate

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Fig. 2

Schematic diagram of thin plates with coordinate systems. (a) The rectangular plate. (b) The circular plate.

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Fig. 3

Schematic diagram of a thin beam with its local coordinate system

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Fig. 4

Frequency dependence of the normalized entropy generation. (a) The modulus of the normalized entropy generation. (b) The phase of the normalized entropy generation.

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Fig. 5

Thermoelastic damping analyzed by three analytical methods, respectively. (a) Thermoelastic damping curves. (b) Percentage difference of the present model comparing to LR and Zener models.

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Fig. 6

Variation of thermoelastic damping and entropy generation with beam thickness. (a) Thermoelastic damping curves related to different L/b. (b) Entropy generation curves related to different L/b.

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Fig. 7

Variation of thermoelastic damping and entropy generation with beam thickness for constant beam length L = 200 μm. (a) Thermoelastic damping curves. (b) Entropy generation curve.

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Fig. 8

Variation of thermoelastic damping and entropy generation with beam length for constant beam thickness b = 10 μm. (a) Thermoelastic damping curves. (b) Entropy generation curve

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Fig. 9

Comparison between the measured and predicted thermoelastic damping for a set of clamped-clamped beam resonators in vacuum at 300 K

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Fig. 10

Variation of thermoelastic damping of a fully clamped rectangular microplate with thickness b at the first mode

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