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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

Lifshitz, R., and Roukes, M. L., 2000, “Thermoelastic Damping in Micro- and Nanomechanical Systems,” Phys. Rev. B, 61(8), pp. 5600–5609. [CrossRef]
De, S. K., and Aluru, N. R., 2006, “Theory of Thermoelastic Damping in Electrostatically Actuated Microstructures,” Phys. Rev. B, 74(14), p. 144305. [CrossRef]
Chandorkar, S. A., Candler, R. N., Duwel, A., Melamud, R., Agarwal, M., Goodson, K. E., and Kenny, T. W., 2009, “Multimode Thermoelastic Dissipation,” J. Appl. Phys., 105(4), p. 043505. [CrossRef]
Zener, C., 1937, “Internal Friction in Solids. I. Theory of Internal Friction in Reeds,” Phys. Rev., 52(3), pp. 230–235. [CrossRef]
Zener, C., 1938, “Internal Friction in Solids. II. General Theory of Thermoelastic Internal Friction,” Phys. Rev., 53(1), pp. 90–99. [CrossRef]
Bishop, J. E., and Kinra, V. K., 1997, “Elastothermodynamic Damping in Laminated Composites,” Int. J. Solids Struct., 34(9), pp. 1075–1092. [CrossRef]
Kinra, V. K., and Milligan, K. B., 1994, “A 2nd-Law Analysis of Thermoelastic Damping,” ASME J. Appl. Mech., 61(1), pp. 71–76. [CrossRef]
Prabhakar, S., and Vengallatore, S., 2008, “Theory of Thermoelastic Damping in Micromechanical Resonators With Two-Dimensional Heat Conduction,” J. Microelectromech. Syst., 17(2), pp. 494–502. [CrossRef]
Wong, S. J., Fox, C. H. J., Mcwilliam, S., Fell, C. P., and Eley, R., 2004, “A Preliminary Investigation of Thermo-Elastic Damping in Silicon Rings,” J. Micromech. Microeng., 14(9), pp. S108–S113. [CrossRef]
Wong, S. J., Fox, C. H. J., and Mcwilliam, S., 2006, “Thermoelastic Damping of the In-Plane Vibration of Thin Silicon Rings,” J. Sound Vib., 293(1–2), pp. 266–285. [CrossRef]
Vengallatore, S., 2005, “Analysis of Thermoelastic Damping in Laminated Composite Micromechanical Beam Resonators,” J. Micromech. Microeng., 15(12), pp. 2398–2404. [CrossRef]
Prabhakar, S., and Vengallatore, S., 2007, “Thermoelastic Damping in Bilayered Micromechanical Beam Resonators,” J. Micromech. Microeng., 17(3), pp. 532–538. [CrossRef]
Prabhakar, S., and Vengallatore, S., 2009, “Thermoelastic Damping in Hollow and Slotted Microresonators,” J. Microelectromech. Syst., 18(3), pp. 725–735. [CrossRef]
Sharma, J. N., and Grover, D., 2011, “Thermoelastic Vibrations in Micro-/Nano-Scale Beam Resonators With Voids,” J. Sound Vib., 330(12), pp. 2964–2977. [CrossRef]
Kim, S. B., and Kim, J. H., 2011, “Quality Factors for the Nano-Mechanical Tubes With Thermoelastic Damping and Initial Stress,” J. Sound Vib., 330(7), pp. 1393–1402. [CrossRef]
Evoy, S., Olkhovets, A., Sekaric, L., Parpia, J. M., Craighead, H. G., and Carr, D. W., 2000, “Temperature-Dependent Internal Friction in Silicon Nanoelectromechanical Systems,” Appl. Phys. Lett., 77(15), pp. 2397–2399. [CrossRef]
Nayfeh, A. H., and Younis, M. I., 2004, “Modeling and Simulations of Thermoelastic Damping in Microplates,” J. Micromech. Microeng., 14(12), pp. 1711–1717. [CrossRef]
Hao, Z., 2008, “Thermoelastic Damping in the Contour-Mode Vibrations of Micro- and Nano-Electromechanical Circular Thin-Plate Resonators,” J. Sound Vib., 313(1–2), pp. 77–96. [CrossRef]
Li, P., Fang, Y., and Hu, R., 2012, “Thermoelastic Damping in Rectangular and Circular Microplate Resonators,” J. Sound Vib., 331(3), pp. 721–733. [CrossRef]
Hao, Z. L., Xu, Y., and Durgam, S. K., 2009, “A Thermal-Energy Method for Calculating Thermoelastic Damping in Micromechanical Resonators,” J. Sound Vib., 322(4–5), pp. 870–882. [CrossRef]
Tai, Y. P., Li, P., and Zuo, W. L., 2012, “An Entropy Based Analytical Model for Thermoelastic Damping in Micromechanical Resonators,” Adv. Manuf. Technol. Syst., 159, pp. 46–50. [CrossRef]
Boley, B. A., and Weiner, J. H., 1960, Theory of Thermal Stresses, Wiley, New York.
Roszhart, T. V., 1990, “The Effect of Thermoelastic Internal Friction on the Q of Micromachined Silicon Resonators,” 4th Techical Digest, IEEE Solid-State Sensor and Actuator Workshop, Hilton Head Island, SC, June 4–7, pp. 13–16. [CrossRef]
Pourkamali, S., Hashimura, A., Abdolvand, R., Ho, G. K., Erbil, A., and Ayazi, F., 2003, “High-Q Single Crystal Silicon HARPSS Capacitive Beam Resonators With Self-Aligned Sub-100-nm Transduction Gaps,” J. Microelectromech. Syst., 12(4), pp. 487–496. [CrossRef]

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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