Advertisement

Nonlinear Dynamics

, Volume 77, Issue 1–2, pp 87–98 | Cite as

Effects of the van der Waals force, squeeze-film damping, and contact bounce on the dynamics of electrostatic microcantilevers before and after pull-in

  • Mansour Abtahi
  • Gholamreza Vossoughi
  • Ali Meghdari
Original Paper

Abstract

The operational range of microcantilever beams under electrostatic force can be extended beyond pull-in in the presence of an intermediate dielectric layer. In this paper, a systematic method for deriving dynamic equation of microcantilevers under electrostatic force is presented. This model covers the behavior of the microcantilevers before and after the pull-in including the effects of van der Waals force, squeeze-film damping, and contact bounce. First, a polynomial approximate shape function with a time-dependent variable for each configuration is defined. Using Hamilton’s principle, dynamic equations of microcantilever in all configurations have been derived. Comparison between modeling results and previous experimental data that have been used for validation of the model shows a good agreement.

Keywords

Microcantilever beams Electrostatic force Dynamic modeling Floating Pinned and flat configurations 

References

  1. 1.
    Ostasevicius, V., Dauksevicius, R.: Microsystems dynamics. In: Tzafestas, S.G. (ed.) International Series on Intelligent Systems, Control, and Automation: Science and Engineering, vol. 44, pp. 3–4. Springer, Lithuania (2011)Google Scholar
  2. 2.
    Lishchynska, M., Cordero, N., Slattery, O., O’Mahony, C.: Modelling electrostatic behaviour of microcantilevers incorporating residual stress gradient and non-ideal anchors. J. Micromech. Microeng. 15, 10–14 (2005)CrossRefGoogle Scholar
  3. 3.
    Agarwal, N., Aluru, N.R.: Stochastic analysis of electrostatic MEMS subjected to parameter variations. J. Microelectromech. Syst. 18, 1454–1468 (2009)CrossRefGoogle Scholar
  4. 4.
    Chaterjee, S., Pohit, G.: A large deflection model for the pull-in analysis of electrostatically actuated microcantilever beams. J. Sound Vib. 322, 969–986 (2009)CrossRefGoogle Scholar
  5. 5.
    Nayfeh, A.H., Younis, M.I., Abdel-Rahman, E.M.: Dynamic pull-in phenomenon in MEMS resonators. Nonlinear Dyn. 48, 153–163 (2007)CrossRefMATHGoogle Scholar
  6. 6.
    Hu, Y.C., Chang, C.M., Huang, S.C.: Some design considerations on the electrostatically actuated microstructures. Sens. Actuators A. 112, 155–161 (2004)CrossRefGoogle Scholar
  7. 7.
    De, S.K., Aluru, N.R.: Full-Lagrangian schemes for dynamic analysis of electrostatic MEMS. J. Microelectromech. Syst. 13, 737–758 (2004)CrossRefGoogle Scholar
  8. 8.
    Muldavin, J.B., Rebeiz, G.M.: High-isolation CPW MEMS shunt switches. 1. Modeling. IEEE Trans. Microwave Theory Technol. 48, 1045–1052 (2000)CrossRefGoogle Scholar
  9. 9.
    Newman, H.S.: RF MEMS switches and applications. In: Proceedings of the IEEE 02CH37320, 40th Annual International Reliability Physics Symposium, Dallas, TX, pp. 111–115 (2002)Google Scholar
  10. 10.
    Mahameed, R., Rebeiz, G.M.: Electrostatic RF MEMS Tunable Capacitors with Analog Tunability and Low Temperature Sensitivity. In: Proceedings of the IEEE MTT-S Int. Microwave Symp. Dig., Anaheim, CA, pp. 1254–1257 (2010)Google Scholar
  11. 11.
    Ionis, G.V., Dec, A., Suyama, K.: A zipper-action differential micro-mechanical tunable capacitor. In: Proc. MEMS Conf., Berkeley, pp. 24–26 (2001)Google Scholar
  12. 12.
    Fourn, E., Pothier, A., Champeaux, C., Tristant, P., Catherinot, A., Blondy, P., Tanné, G., Rius, E., Person, C., Huret, F.: MEMS switchable interdigital coplanar filter. IEEE Trans. Microwave Theory Tech. 51, 320–324 (2003)CrossRefGoogle Scholar
  13. 13.
    Ketterl, T., Weller, T., Fries, D.: A micromachined tunable CPW resonator. In: Proc. IEEE MTT-S Int. Microwave Symp. Digest, Phoenix, AZ, vol. 1, pp. 345–348 (2001)Google Scholar
  14. 14.
    Gilbert, J.R., Legtenberg, R., Senturia, S.D.: 3D coupled electromechanics for MEMS: applications of CoSolve-EM. In: Proc. Int. Conf. on MEMS, Amsterdam, The Netherlands, pp. 122–127 (1995)Google Scholar
  15. 15.
    Gilbert, J.R., Ananthasuresh, G.K., Senturia, S.D.: 3D modeling of contact problems and hysteresis in coupled electro-mechanics. In: Proc. 9th Int. Workshop on Microelectromechanical Systems, San Diego, CA, pp. 127–132 (1996)Google Scholar
  16. 16.
    Lam, T., Darling, R.B.: Physical modeling of MEMS cantilever beams and the measurement of stiction force. In: Proc. Model. Simul. Microsyst., pp. 418–421 (2001)Google Scholar
  17. 17.
    Knapp, J.A., de Boer, M.P.: Mechanics of microcantilever beams subject to combined electrostatic and adhesive forces. J. Microelectromech. Syst. 11, 754–764 (2002)CrossRefGoogle Scholar
  18. 18.
    Yin, Z., Ya-pu, Z.: Static study of cantilever beam stiction under electrostatic force influence. Acta Mech. Solida Sinica. 17, 104–112 (2004)Google Scholar
  19. 19.
    Basu, S., Prabhakar, A., Bhattacharya, E.: Estimation of stiction force from electrical and optical measurements on cantilever beams. J. Microelectromech. Syst. 16, 1254–1262 (2007)CrossRefGoogle Scholar
  20. 20.
    Gorthi, S., Mohanty, A., Chatterjee, A.: Cantilever beam electrostatic MEMS actuators beyond pull-in. J. Micromech. Microeng. 16, 1800–1810 (2006) Google Scholar
  21. 21.
    Vyasarayani, C.P., Abdel-Rahman, E.M., McPhee, J.: Modeling of contact and stiction in electrostatic microcantilever actuators. J. Nanotechnol. Eng. Med. 3, 011003.1–011003.8 (2012)Google Scholar
  22. 22.
    Abtahi, M., Vossoughi, G.R., Meghdari, A.: Full operational range dynamic modeling of microcantilever beams under electrostatic force. J. Microelectromech. Syst. 22, 1190–1198 (2013)CrossRefGoogle Scholar
  23. 23.
    Delrio, F.W., De Boer, M.P., Knapp, J.A., Reedy Jr, E.D., Clews, P.J., Dunn, M.L.: The role of van der Waals forces in adhesion of micromachined surfaces. Nat. Mater. 4, 629–634 (2005)CrossRefGoogle Scholar
  24. 24.
    Nayfeh, A.H., Younis, M.I.: A new approach to the modeling and simulation of flexible microstructures under the effect of squeeze-film damping. J. Micromech. Microeng. 14, 170–181 (2003)Google Scholar
  25. 25.
    Moghimi Zand, M., Ahmadian, M.T.: Characterization of coupled-domain multi-layer microplates in pull-in phenomenon, vibrations and dynamics. Int. J. Mech. Sci. 49, 1226–1237 (2007)Google Scholar
  26. 26.
    LaRose, R.P., Murphy, K.D.: Impact dynamics of MEMS switches. Nonlinear Dyn. 60, 327–339 (2010)CrossRefMATHGoogle Scholar
  27. 27.
    Allen, M.S., Massad, J.E., Field Jr, R.V.: Input and design optimization under uncertainty to minimize the impact velocity of an electrostatically actuated MEMS switch. J. Vib. Acoust. 130, 021009.1–021009.9 (2008)CrossRefGoogle Scholar
  28. 28.
    Pandey, A.K., Pratap, R.: Effect of flexural modes on squeeze film damping in MEMS cantilever resonators. J. Micromech. Microeng. 17, 2475–2484 (2007)CrossRefGoogle Scholar
  29. 29.
    Osterberg, P.: Electrostatically Actuated Microelectromechanical Test Structures for Material Property Measurement. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA (1995)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Mansour Abtahi
    • 1
  • Gholamreza Vossoughi
    • 1
  • Ali Meghdari
    • 1
  1. 1.Center of Excellence in Design, Robotics & Automation (CEDRA), Department of Mechanical EngineeringSharif University of TechnologyTehranIran

Personalised recommendations