Structural Engineering and Mechanics

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Nonlinear response of a resonant viscoelastic microbeam under an electrical actuation

  • Zamanian, M. (Mechanical & Aerospace Engineering Department, Tarbiat Modares University) ;
  • Khadem, S.E. (Mechanical & Aerospace Engineering Department, Tarbiat Modares University) ;
  • Mahmoodi, S.N. (Center for Vehicle Systems & Safety, Department of Mechanical Engineering, Virginia Tech)
  • Received : 2007.11.07
  • Accepted : 2010.02.01
  • Published : 2010.07.10
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Abstract

In this paper, using perturbation and Galerkin method, the response of a resonant viscoelastic microbeam to an electric actuation is obtained. The microbeam is under axial load and electrical load. It is assumed that midplane is stretched, when the beam is deflected. The equation of motion is derived using the Newton's second law. The viscoelastic model is taken to be the Kelvin-Voigt model. In the first section, the static deflection is obtained using the Galerkin method. Exact linear symmetric mode shape of a straight beam and its deflection function under constant transverse load are used as admissible functions. So, an analytical expression that describes the static deflection at all points is obtained. Comparing the result with previous research show that using deflection function as admissible function decreases the computation errors and previous calculations volume. In the second section, the response of a microbeam resonator system under primary and secondary resonance excitation has been obtained by analytical multiple scale perturbation method combined with the Galerkin method. It is shown, that a small amount of viscoelastic damping has an important effect and causes to decrease the maximum amplitude of response, and to shift the resonance frequency. Also, it shown, that an increase of the DC voltage, ratio of the air gap to the microbeam thickness, tensile axial load, would increase the effect of viscoelastic damping, and an increase of the compressive axial load would decrease the effect of viscoelastic damping.

Keywords

References

  1. Abdel-Rahman, E.M., Younis, M.I. and Nayfeh, A.H. (2002), "Characterization of the mechanical behavior of an electrically actuated microbeam", J. Micromech. Microeng, 12, 759-766. https://doi.org/10.1088/0960-1317/12/6/306
  2. Abdel-Rahman, E.M., Younis, M.I. and Nayfeh, A.H. (2003), "Secondary resonances of electrically actuated resonant microsensors", J. Micromech. Microeng, 13, 491-501. https://doi.org/10.1088/0960-1317/13/3/320
  3. Choi, B. and Lovell, E.G. (1997), "Improved analysis of microbeams under mechanical and electrostatic loads", J. Micromech. Microeng, 7, 24-29. https://doi.org/10.1088/0960-1317/7/1/005
  4. Dufour, I., Lochon, F., Heinrich, S.M. and Josse, F. (2007), "Effect of coating viscoelasticity on quality factor and limit of detection of microcantilever chemical sensors", IEEE Sens. J., 7, 230-236. https://doi.org/10.1109/JSEN.2006.888600
  5. Fu, Y.M. and Zhang, J. (2009), "Nonlinear static and dynamic responses of an electrically actuated viscoelastic microbeam", Acta Mech. Sinica, 25, 211-218. https://doi.org/10.1007/s10409-008-0216-4
  6. Fu, Y.M. and Zhang, J. (2009), "Active control of the nonlinear static and dynamic responses for piezoelectric viscoelastic microplates", Smart Mater. Struct., 18, 095037. https://doi.org/10.1088/0964-1726/18/9/095037
  7. Fu, Y.M., Zhang, J. and Bi, R.G. (2009), "Analysis of the nonlinear dynamic stability for an electrically actuated viscoelastic microbeam", Microsyst. Technol., 15, 763-769. https://doi.org/10.1007/s00542-009-0791-8
  8. Ijntema, D.J. and Tilmans, H.A. (1992), "Static and dynamic aspects of an air-gap capacitor", Sensor. Actuat. APhys., 35, 121-128. https://doi.org/10.1016/0924-4247(92)80150-2
  9. Mahmoodi, S.N., Khadem, S.E. and Jalili, N. (2006), "Theoretical development and closed-form solution of nonlinear vibrations of a directly excited nanotube-reinforced composite cantilevered beam", Arch. Appl. Mech., 75, 153-163. https://doi.org/10.1007/s00419-005-0426-1
  10. Najar, F., Choura, S., Borgi, S.E., Abdel-Rahman, E.M. and Nayfeh, A.H. (2005), "Modeling and design of variable-geometryelectrostatic microactuators", J. Micromech. Microeng, 15, 419-429. https://doi.org/10.1088/0960-1317/15/3/001
  11. Nayfeh, A.H. and Pai, P.F. (2004), Linear and Nonlinear Structural Mechanics, John Wiley & Sons, New York.
  12. Nayfeh, A.H. and Younis, M.I. (2005), "Dynamics of MEMS resonators under superharmonic and subharmonic excitations", J. Micromech. Microeng, 15, 1840-1847. https://doi.org/10.1088/0960-1317/15/10/008
  13. Rochus, V., Rixen, D.J. and Golinval, J.C. (2005), "Electrostatic coupling of MEMS structures: transient simulations and dynamic pull-in", Nonlinear Anal., 63, e1619-e1633. https://doi.org/10.1016/j.na.2005.01.055
  14. Tilmans, H.A. and Legtenberg, R. (1994), "Electrostatically driven vacuum-encapsulated polysilicon resonators Part II: Theory and performance", Sensor. Actuat. A-Phys., 45, 67-84. https://doi.org/10.1016/0924-4247(94)00813-2
  15. Uncuer, M., Marinkovic, B. and Koser, H. (2007), "Simulation of clamped-free and clamped- clamped microbeams dynamics for nonlinear mechanical switch applications", Proceedings of the COMSOL Conference, Boston.
  16. Wenzel, M.J., Josse, F. and Heinrich, S.M. (2009), "Deflection of a viscoelastic cantilever under a uniform surface stress: Applications to static-mode microcantilever sensors undergoing adsorption", J. Appl. Phys., 105, 064903. https://doi.org/10.1063/1.3086626
  17. Younis, M.I., Abdel-Rahman, E.M. and Nayfeh, A.H. (2003), "A reduced-order model for electrically actuated microbeam-based MEMS", J. Microelectomech. S., 12, 672-680. https://doi.org/10.1109/JMEMS.2003.818069
  18. Younis, M.I. and Nayfeh, A.H. (2003), "A Study of the nonlinear response of a resonant microbeam to an electric actuation", Nonlinear Dyn., 31, 91-117. https://doi.org/10.1023/A:1022103118330
  19. Zamanian, M., Khadem, S.E. and Mahmoodi, S.N. (2008), "The effect of a piezoelectric layer on the mechanical behavior of an electrostatic actuated microbeam", Smart Mater. Struct., 17, 065024. https://doi.org/10.1088/0964-1726/17/6/065024
  20. Zamanian, M., Khadem, S.E. and Mahmoodi, S.N. (2009), "Analysis of non-linear vibrations of a microresonator under piezoelectric and electrostatic actuations", Proc. IMechE Part C: J. Mech. Eng. Sci., 223, 329-344. https://doi.org/10.1243/09544062JMES1147
  21. Zamanian, M. and Khadem, S.E. (2010), "Nonlinear vibration of an electrically actuated microresonator tuned by combined DC piezoelectric and electric actuations", Smart Mater. Struct., 19, 015012. https://doi.org/10.1088/0964-1726/19/1/015012
  22. Zhang, W. and Meng, G. (2005), "Nonlinear dynamical system of micro-cantilever under combined parametric and forcing excitations in MEMS", Sensor. Actuat. A-Phys., 119, 291-299. https://doi.org/10.1016/j.sna.2004.09.025

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