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Comparison of 1D and 2D Theories of Thermoelastic Damping in Flexural Microresonators

Published online by Cambridge University Press:  01 February 2011

Sairam Prabhakar  and
Srikar Vengallatore
Sairam Prabhakar
Affiliation:
[email protected], McGill University, Mechanical Engineering, Montreal, H3A 2K6, Canada
Srikar Vengallatore
Affiliation:
[email protected], McGill University, Mechanical Engineering, Montreal, H3A 2K6, Canada
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Abstract

Thermoelastic damping (TED) represents the lower limit of material damping in flexural mode micro- and nanoresonators. Current predictive models of TED calculate damping due to thermoelastic temperature gradients along the beam thickness only. In this work, we develop a two dimensional (2D) model by considering temperature gradients along the thickness and the length of the beam. The Green's function approach is shown to be a robust means of solving the coupled heat conduction equation in one and two dimensions. In the 1D model, curvature information is lost and, hence, the effects of structural boundary conditions and mode shapes on TED are not captured. In contrast, the 2D model retains curvature information in the expression for TED and can account for beam end conditions and higher order modes. The differences between the 1D and 2D models are systematically explored over a range of beam aspect ratios, frequencies, boundary conditions, and flexural mode shapes.

Keywords

internal frictionmicroelectro-mechanical (MEMS)thermal stresses
Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 1052: Symposium DD – Microelectromechanical Systems–Materials and Devices , 2007 , 1052-DD06-22
Copyright
Copyright © Materials Research Society 2008

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References

[1] Roszhart, T. V., Tech. Dig. Solid-State Sens. Actuator Workshop, Hilton Head, 13–16 (1990).Google Scholar
[2] Zener, C., Phys. Rev., 52, 230–235 (1937).Google Scholar
[3] Lifshitz, R. and Roukes, M., Phys. Rev. B., 61, 5600–5609 (2000).Google Scholar
[4] Srikar, V. T. and Senturia, S. D., J. Microelectromech. Syst., 11, 499–504 (2002).Google Scholar
[5] De, S.K. and Aluru, N.R., Phys. Rev. B, 74, 144305 (2006).Google Scholar
[6] Chadwick, P., J. Mech. Phys. Solids., 10, 99–109 (1962).Google Scholar
[7] Alblas, J.B., J. Thermal. Stresses, 4, 333–355 (1981).Google Scholar
[8] Ozisik, M.N., Heat Conduction, 2nd ed. (John Wiley and Sons, New York, 1993) p. 214–257.Google Scholar
[9] Boley, B.A. and Weiner, J.H., Theory of Thermal Stresses, (Wiley, New York, 1960) p. 1–40.Google Scholar
[10] Nowick, A.S. and Berry, B.S., Anelastic Relaxation in Crystalline Solids, (Academic Press, New York, 1972)Google Scholar