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Thermoelastic dissipation of micro/nano beam resonators Open Access


Other title
Thermoelastic dissipation
Type of item
Degree grantor
University of Alberta
Author or creator
Tunvir, Kazi M S
Supervisor and department
Dr. Chongqing Ru (Mechanical Engineering)
Dr. Andrew Mioduchowski (Mechanical Engineering)
Examining committee member and department
Dr. Hao Zhang (Chemical and Materials Engineering)
Dr. Peter Schiavone (Mechanical Engineering)
Dr. Tian Tang (Mechanical Engineering)
Dr. Marcelo Epstein (Mechanical and Manufacturing Engineering)
Department of Mechanical Engineering

Date accepted
Graduation date
Doctor of Philosophy
Degree level
The work presented in this dissertation offers theoretical analysis of thermoelastic dissipation of micro/nano beam resonators operated with linear small-amplitude vibration or non-linear large-amplitude vibration under adiabatic or isothermal surface conditions. The aim is to find better design and better operating conditions for beam resonators of MEMS/NEMS for less thermoelastic dissipation. The beam resonators studied in this dissertation (which have not been studied in existing literature) include hollow tubular beams, solid beams of elliptical, triangular, or arbitrary rectangular cross-section, layered composite beams of circular and rectangular cross-sections, and stepped-beams of rectangular cross-section. For each case, detailed formulas are derived for quality factor (Q-factor) due to thermoelastic dissipation under adiabatic and isothermal surface conditions. In addition, thermoelastic dissipation in beam resonator of rectangular cross-section is analyzed for non-linear large-amplitude vibration under adiabatic or isothermal surface thermal condition with comparison to the results of small-amplitude linear vibration. The obtained results offer useful guiding ideas for design of beam resonators to achieve higher Q-factor with thermoelastic dissipation. For example, the present results show that, to achieve higher Q-factor, hollow tubular resonators with isothermal and adiabatic surface conditions are best to operate at low and high frequencies, respectively, as compared to beam resonators of solid circular or rectangular cross-section. Beam resonators of elliptical and triangular cross-sections are best to operate at high frequencies compared to solid rectangular cross-sections of same cross-sectional area and width irrespective of surface thermal conditions. In case of layered composite beams under either of the two surface thermal conditions, two-layered circular cross-sections is found better at high frequencies than three-layered rectangular cross-section of same material combination and layer sizes. Results for doubly-clamped stepped-beams show that a real beam resonator of rectangular cross-section with an undercut at a clamped end, known as a stepped-beam with single step having a change in cross-sectional size at the step in lateral direction only, provides higher Q-factor than a uniform beam of same thickness for all real lengths found in the literature. This dissertation also confirms that non-linear large-amplitude vibration is preferable over linear small-amplitude vibration for doubly-clamped beam resonators under adiabatic surface condition for which the Q-factor increases monotonically with amplitude of vibration, while the opposite is true under isothermal surface condition. The large-amplitude effect on thermoelastic dissipation becomes more significant for higher vibration frequencies than lower ones.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
Citation for previous publication
Tunvir, K., Ru, C.Q. and Mioduchowski, A. (2010). “Thermoelastic Dissipation of Hollow Micromechanical Resonators.” Physica E: Low-dimensional Systems and Nanostructures, 42 (9): 2341 – 52Tunvir, K., Ru, C.Q. and Mioduchowski, A. (2012). “Large-deflection Effect on Thermoelastic Dissipation of Microbeam Resonators.” Journal of Thermal Stresses 35(12): 1076-1094.Tunvir, K., Ru, C.Q. and Mioduchowski, A. (2012). “Effect of Cross-sectional Shape on Thermoelastic Dissipation of Micro/nano Elastic Beams.” International Journal of Mechanical Sciences, 62 (1): 77-88.Tunvir, K. (2012) “Thermoelastic Dissipation in Stepped-beam Resonators.” Microsystem Technologies (In press, published online). DOI: 10.1007/s00542-012-1676-9

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File title: Beam resonators have found broad application in a wide range of MEMS/NEMS as components of filters, oscillators and sensing application (Ekinci and Roukes 2005; Cimalla et al. 2007; Li and Hu 2011; Gil-Santos et al. 2009). They vibrate to generate...
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