Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-27T09:12:19.015Z Has data issue: false hasContentIssue false
  • English
  • Français

Vibrational Behavior of an Electrically Actuated Micro-Beam with Thermoelastic Damping

Published online by Cambridge University Press:  17 March 2014

A. Karami mohammadi  and
N. Ale Ali
A. Karami mohammadi*
Affiliation:
Department of Mechanical Engineering, Shahrood University of Technology, Iran
N. Ale Ali
Affiliation:
Department of Mechanical Engineering, Shahrood University of Technology, Iran
*
akaramim@yahoo.com
Get access

Abstract

In this paper, a resonator is modeled as a microbeam under the effect of thermoelastic damping and actuated electrically. Two models, small and large deformation models, are represented by considering linear and nonlinear Euler-Bernoulli beam theory. These models are compared against voltage, and the difference between these models is shown and discussed. In the large deformation model, the microbeam deflected due to applied DC voltage, and vibration of microbeam occurs around this static deflection. The vibration equation is linearized around static deflection and by applying harmonic vibration, equation for mode shape and frequency is obtained. The complex frequency is calculated by numerical method and then used for obtaining the Q-factor of thermoelastic damping. The stretching effect and thermoelastic damping is validated with the literature. The result shows that for the high values of voltage, the large deformation model is more accurate. The behavior of thermoelastic damping is also investigated against the geometrical and material properties.

Keywords

MicrobeamresonatorThermoelastic dampingElectrostatic actuation
Type
Research Article
Information
Journal of Mechanics , Volume 30 , Issue 3 , June 2014 , pp. 219 - 227
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Nayfeh, A. H. and Younis, M. I., “A New Approach to the Modeling and Simulation of Flexible Micro-structures Under the Effect of Squeeze-Film Damping,” Journal of Micromechanics and Microengineering, 14, p. 170 (2004).CrossRefGoogle Scholar
2.Nayfeh, A. H. and Younis, M. I., “Modeling and Simulations of Thermoelastic Damping in Microplates,” Journal of Micromechanics and Microengi-neering, 14, p. 1711 (2004).CrossRefGoogle Scholar
3.Sun, Y. and Saka, M., “Thermoelastic Damping in Micro-Scale Circular Plate Resonators,” Journal of Sound and Vibration, 329, pp. 328–337, (2009).CrossRefGoogle Scholar
4.Zener., C., “Internal Friction in Solids I. Theory of Internal Friction In Reeds,” Physical Review, 52, p. 230 (1937).CrossRefGoogle Scholar
5.Zener, C., “Internal Friction in Solids II. General Theory of Thermoelastic Internal Friction,” Physical Review, 53, p. 90 (1937).CrossRefGoogle Scholar
6.Alblas, J. B., “A Note on the Theory of Thermoelastic Damping,” Journal of Thermal Stresses, 4, pp. 333–355 (1981).CrossRefGoogle Scholar
7.Lifshitz, R. and Roukes, M. L., “Thermoelastic Damping in Micro- and Nanomechanical Systems,” Physical Review B, B61, p. 5600 (2000).CrossRefGoogle Scholar
8.Sudipto, K. De and Aluru, N. R., “Theory of Thermoelastic Damping in Electrostatically Actuated Microstructures,” Physical Review B, B74, p. 144305 (2006).Google Scholar
9.Prabhakar, S. and Vengallatore, S., “Theory of Thermoelastic Damping in Micromechanical Resonators with Two-Dimensional Heat Conduction,” Journal of Microelectromechanical Systems, 17, pp. 494–502 (2008).CrossRefGoogle Scholar
10.Yi, Y. B. and Matin, M. A., “Eigenvalue Solution of Thermoelastic Damping in Beam Resonators Using a Finite Element Analysis,” Journal of Vibration and Acoustics, 129, pp. 478–483 (2007).CrossRefGoogle Scholar
11.Serra, E. and Bonaldi, M., “A Finite Element Formulation for Thermoelastic Damping Analysis,” International Journal for Numerical Methods in Engineering, 78, pp. 671–691 (2009).CrossRefGoogle Scholar
12.Choi, J., Cho, M. and Rhim, J. “Efficient Prediction of the Quality Factors of Micromechanical Resonators,” Journal of Sound and Vibration, 329, pp. 84–95 (2010).CrossRefGoogle Scholar
13.Guo, F. L. and Rogerson, G. A., “Thermoelastic Coupling Effect on a Micro-Machined Beam Resonator,” Mechanics Research Communications, 30, pp. 513–518 (2003).CrossRefGoogle Scholar
14.Batra, R. C., Porfiri, M. and Spinello, D., “Review of Modeling Electrostatically Actuated Microelec-tromechanical Systems,” Smart Materials and Structures, 12, p. 759 (2007).Google Scholar
15.Abdel-Rahman, E. M., Younis, M. I. and Nayfeh, A. H., “Characterization of the Mechanical Behavior of an Electrically Actuated Microbeam,” Journal of Micromechanics and Microengineering, 16, pp. R23–R31 (2002).Google Scholar
16.Nayfeh, A. H. and Younis, M. I., “Dynamics of MEMS Resonators Under Superharmonic and Sub-harmonic Excitations,” Journal of Micromechanics and Microengineering, 15, p. 1810 (2005).CrossRefGoogle Scholar
17.Younis, M. I. and Nayfeh, A. H., “A Study of the Nonlinear Response of a Resonant Microbeam to an Electric Actuation,” Nonlinear Dynamics, 31, pp. 91–117 (2003).CrossRefGoogle Scholar
18.Younis, M. I., Abdel-Rahman, E. M. and Nayfeh, A. H., “A Reduced-Order Model for Electrically Actuated Microbeam-Based,” MEMS Journal of Micro-mechanics Systems, 12, pp. 672–680 (2003).CrossRefGoogle Scholar
19.Abdel-Rahman, E. M. and Nayfeh, A. H., “Secondary Resonances of Electrically Actuated Resonant Microsensors,” Journal of Micromechanics and Microengineering, 13, p. 4917 (2003).CrossRefGoogle Scholar
20.Nayfeh, A. H. and Younis, M. I., “Dynamics of MEMS Resonators Under Superharmonic and Sub-harmonic Excitations,” Journal of Micromechanics and Microengineering, 15, p. 1840 (2005).CrossRefGoogle Scholar
21.Najar, F., Choura, S., Abdel-Rahman, E. M., El-Borgi, S. and Nayfeh, A. H., “Dynamic Analysis of Variable-Geometry Electrostatic Microactuators,” Journal of Micromechanics and Microengineering, 16, p. 2449 (2006).CrossRefGoogle Scholar
22.Zhao, X., Abdel-Rahman, E. M. and Nayfeh, A. H., “A Reduced-Order Model for Electrically Actuated Microplates,” Journal of Micromechanics and Microengineering, 14, p. 900 (2004).CrossRefGoogle Scholar
23.Vogl, G. W. and Nayfeh, A. H., “A Reduced-Order Model for Electrically Actuated Clamped Circular Plates,” Journal of Micromechanics and Microengineering, 15, p. 684 (2005).CrossRefGoogle Scholar
24.Ouakad, H. M., and Younis, M. I., “The Dynamic Behavior of MEMS Arch Resonators Actuated Electrically,” International Journal of Non-Linear Mechanics, 45, pp. 704–713 (2010).CrossRefGoogle Scholar
25.Batra, R. C., Porfiri, M. and Spinello, D., “Electromechanical Model of Electrically Actuated Narrow Microbeams,” Journal of Microelectromech, 15, pp. 1175–1189 (2006).CrossRefGoogle Scholar
26.Fargas Marqu`es, A., Costa Castell´o, R. and Shkel, A. M., “Modelling the Electrostatic Actuation of MEMS: State of the Art 2005,” Technical Report, IOC-DT-P-2005-18, p. 66 (2005).Google Scholar
27.Nayfeh, A. H. and Pai, P. F., Linear and Nonlinear Structural Mechanics, Wiley-Interscience, Hoboken, New Jersey, p. 763 (2004).CrossRefGoogle Scholar
28.Süli, E. and Mayers, D. F., An Introduction to Numerical Analysis, Cambridge University Press, England, pp. 361–380 (2003).CrossRefGoogle Scholar