Perturbation analysis of an electrostatic Micro-Electro-Mechanical System (MEMS) subjected to external and non-linear parametric excitations

  • Authors

    • Abd-Elrehim Elnaggar Department of Mathematics, Faculty of Science, Benha University, Egypt.
    • Atef El-Bassiouny Department of Mathematics, Faculty of Science, Benha University, Egypt.
    • Gamal Mosa Department of Mathematics, Faculty of Science, Benha University, Egypt.
    2014-06-22
    https://doi.org/10.14419/ijbas.v3i3.2772

  • Electrostatic micro-electro-mechanical system (MEMS) is a special branch with a wide range of applications in sensing and actuating devices in MEMS. In this paper the perturbation analysis of the electrostatically actuated MEMS resonant sensors  which represented by a modified Duffing - Van der Pol equation subjected to weakly non-linear parametric and external excitations is studied by using a perturbation technique (multiple time scales). Harmonic resonance and subharmonic resonances of order (1/2 and 1/3) are investigated. For each resonances we obtain the modulation equations in the amplitude and phase, steady state solutions, frequency-response equations and stability conditions are determined.  Effects of different parameters on the system behavior are investigated numerically. Results are presented graphically and discussion is provided.

    Keywords: MEMS, Weakly non-linear dynamical systems, Micro-cantilever, Parametric and Forcing excitations.

  • References

    1. W.C. Chuang, H.L. Lee, P.Z. Chang and Y.C. Hu, Review on the Modeling of Electrostatic MEMS, Sensors, 10 (6)(2010) 6149-6171.
    2. S. Pamidighantam, R. Puers, K. Baert, and A.C. Tilmans, Pull-in voltage analysis of electrostatically actuated beamstructures with fixed-fixed and fixed-free end conditions, J. Micromech. Microeng,12 (2002) 454-464.
    3. T. Sasayama, S. Suzuki, S. Tsuchitani, A. Koide, M. Suzuki, N. Ichikawa and T. Nakazawa, Highly reliable silicon micromachined physical sensors in mass production, Sensors and Actuators A,54 (1996) 714-717.
    4. M.H. Bao, H. Yang, H. Yin and S.Q. Shen, Effects of electrostatic forces generated by the driving signal on capacitive sensing devices, Sensors and Actuators A,24 (2000) 213219.
    5. S. Lee, R. Ramadoss, M. Buck, V.M. Bright, K.C. Gupta and Y.C. Lee, Reliability testing of °flexible printed circuitbased RF MEMS capacitive switches, Microelectronics Reliability,44 (2004) 245250.
    6. B. MoCarthy, G.G. Adams, N.E. McGruer and D. Potter, A dynamical model, including contact bounce of an electrostatically actuated microswitch, J Microelectromech Syst,11 (2002) 276-283.
    7. M. Mehregany, P. Nagarkar, S.D. Senturia and J.H. Lang, Operation of microfabricated harmonic and ordinary side-drive motors, Proc. 3rd. IEEE MEMS Workshop, Napa Valley, CA, (1990) 1-8.
    8. L.S. Tavrow, S.F. Bart and J.H. Lang, Operational characteristics of microfabricated electric motors,Sensors and Actuators A, 35 (1992) 33-44.
    9. E.S. Hung S.D. Senturia, Extending the travel range of analog-tuned electrostatic actuators, J. Microelectromech Syst,8 (4) (1999) 497-505.
    10. P. Osterberg, Electrostatically actuated microelectromechanical test structures for material property measurement, PhD thesis, MIT (1995).
    11. M.I. Younis , E.M. Abdel-Rahman and A.H. Nayfeh, Static and dynamic behavior of an electrically excited resonant microbeam, Proceedings of the 43rd AIAA structures, structural dynamics, and materials conference. Denver,CO, (2002) AIAA Paper 2002/1305.
    12. E.M. Abdel-Rahman, M.I. Younis and A.H. Nayfeh, A nonlinear reduced-order model for electrostatic MEMS, Proceedings of the 19th biennial conference in mechanical vibration and noise (VIB). Chicago, IL , (2003) Paper DETC2003/VIB-48517.
    13. J.A. Walraven, Future challenges for MEMS failure analysis, Proceedings of ITC international test conference, 33 (4) (2003) 850-5.
    14. E.M. Abdel-Rahman, M.I. Younis and A.H. Nayfeh, Characterization of the mechanical behavior of an electrically actuated microbeam, J. Micromech Microeng, 12 (2002) 766-95.
    15. H.A. Tilmans and R. Legtenberg, Electrostatically driven vacuum-encapsulated polysilicon resonators, Part II: theory and performance, Sensors Actuators A, 45 (1994) 67-84.
    16. M.I. Younis, E.M. Abdel-Rahman and A.H. Nayfeh, Dynamic simulations of a novel RF MEMS switch, Proceedings 7th Int. Conf. Modeling and Simulation of Microsystems: NanoTech, Boston, MA, (2004) 287-290.
    17. L. Lin, C.T.-C. Nguyen, R.T. Howe and A.P. Pisano, Microelectromechanical filters for signal processing, Proceedings IEEE MEMS, Travemunde, Germany, (1992) 226-231.
    18. Z. Jin and Y. Wang, Electrostatic resonator with second superharmonic resonance, Sens. Actuators A, 64 (1998) 273-279.
    19. M.I. Younis and A.H. Nayfeh, A study of the nonlinear response of a resonant microbeam to electric actuation, Nonlinear Dyn., 31 (2003) 91-117.
    20. E.M. Abdel-Rahman and A.H. Nayfeh, Secondary resonances of electrically actuated resonant microsensors, Journal of Micromechanics and Microengineering, 13 (2003) 491-501.
    21. A.H. Nayfeh and M.I. Younis, Dynamics of MEMS resonators under superharmonic and subharmonic excitations, J. of Micromechanics and Microengineering, 15 (2005) 1840-1847.
    22. W.M. Zhang and G. Meng, Nonlinear Dynamic Analysis of Electrostatically Actuated Resonant MEMS Sensors Under Parametric Excitation. IEEE sensors journal, 7 (2007) 370-380.
    23. W.M. Zhang, G. Meng and K.X. Wei, Dynamics of nonlinear coupled electrostatic micromechanical resonators under two frequency parametric and external excitations, Shock and Vibration, 17 (2010) 759-770.
    24. A.M. Elnaggar, Existence and Determination of Superharmonic Synchronizations as Solution,of a Quasi-Linear Physical System, Indian. J.Pure. Appl. Math., 16 (1985) 139-142.
    25. A.M. Elnaggar, A.F. El-Bassiouny and K.M. Khalil, Saddle-node bifurcation control for an odd non-linearity problem, Global J. of Pure and Applied Mathematics, 7 (2011) 213-229.
    26. A.M. Elnaggar, A.F. El-Bassiouny and G.A. Mosa, Harmonic and sub-harmonic resonance of MEMS subjected to a weakly non-linear parametric and external excitations, International Journal of Applied Mathematical Research (IJAMR), North America, 2 (2) (2013) 252-263.
    27. A.M. Elnaggar and K.M. Khalil, Control of the nonlinear oscillator bifurcation under a superharmonic resonance. Journal of Applied Mechanics and Technical Physics, 54 (1) (2013) 34-43.
    28. R.C. Batra, M. Por¯ri and D. Spinello, Vibrations of narrow micro beams predeformed by an electric field, Journal of Sound and Vibration, 309 (3) (2008) 600-612.
    29. N. Kacem, S. Hentz, D. Pinto, B. Reig and V. Nguyen, Nonlinear dynamics of nanomechanical beam resonators: improving the performance of NEMS- based sensor, Nanotechnology,20 (27) (2009) 275501.
    30. N. Kacem, S. Hentz, H. Fontaine, V. Nguyen, P. Robert, B. Legrand and L. Buchaillot, From MEMS to NEMS: modelling and characterization of the non linear dynamics of resonators, a way to enhance the dynamic range, NSTI Nanotech, 3 (2008) 619-622
    31. N. Kacem, S. Baguet, S. Hentz and R. Dufour, Computational and quasi-analytical models for non-linear vibrations of resonant MEMS and NEMS sensors, International Journal of Non-Linear Mechanics, 46 (3) (2011) 532-542.
    32. J.F. Rhoads, S.W. Shaw and K.L. Turner, Non-linear dynamics and its applications in micro- and nanoresonators, J. Dyn. Syst. Meas. Control, 132 (2010) 034001 (1-034001.14).
    33. K.L. Turner, P.G. Hartwell, F.M. Bertsch and N.C. Macdonald, Parametric resonance in a microelectromechanical torsional oscillator, Proceedings of ASME International Mechanical Engineering Congress and Exposition, Proceedings of the Microelectromechanical Systems (MEMS), Anaheim, CA, USA, (1998) 335-340.
    34. J.B. Starr, Squeeze-film damping in solid-state accelerometers, Proceedings IEEE Solid State Sensor and Actuator Workshop, Hilton Head Island, SC, (1990) 44-47.
    35. A.H. Nayfeh, Introduction to Perturbation Techniques, Wiley-Interscience, New York (1981).

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    Elnaggar, A.-E., El-Bassiouny, A., & Mosa, G. (2014). Perturbation analysis of an electrostatic Micro-Electro-Mechanical System (MEMS) subjected to external and non-linear parametric excitations. International Journal of Basic and Applied Sciences, 3(3), 209-223. https://doi.org/10.14419/ijbas.v3i3.2772