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.
  • 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.

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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.