Harmonic and sub-harmonic resonance of MEMS subjected to a weakly non-linear parametric and external excitations

  • Authors

    • Gamal Ahmed Mosa assistant lecturer
    • A. M. El-naggar Professor of applied mathematics
    • A. F. Elbassiouny Professor of applied mathematics
    2013-04-02
    https://doi.org/10.14419/ijamr.v2i2.620
  • This paper presents a simplified mathematical model for the purpose of studying the resonant responses of a nonlinear dynamical system, (micro - electro – mechanical systems (MEMS)), which represented by a Van-der Pol equation subjected to a weakly non-linear parametric and forcing excitations. Using Multiple scales method, the Van-der Pol equation is transformed to a system of second order differential equation up to first order of small parameter " . Three types of resonances are studied (harmonic resonance and subharmonic resonances of even order (one - half and one - fourth )). The modulation equations for each resonances, steady state solutions, frequency-response equations, stability analysis are determined. Numerical analysis for frequency-response equations and stability conditions are carried out. Results are presented graphically by group of  figures. Finally discussion for these figures are given.

    Author Biographies

    • Gamal Ahmed Mosa, assistant lecturer

      Department of math. , faculty of science, Benha university, Egypt.

      B. O. 13518

    • A. M. El-naggar, Professor of applied mathematics

      Department of math. , faculty of science, Benha university, Egypt.

      B. O. 13518

    • A. F. Elbassiouny, Professor of applied mathematics

      Department of math. , faculty of science, Benha university, Egypt.

      B. O. 13518

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  • How to Cite

    Mosa, G. A., El-naggar, A. M., & Elbassiouny, A. F. (2013). Harmonic and sub-harmonic resonance of MEMS subjected to a weakly non-linear parametric and external excitations. International Journal of Applied Mathematical Research, 2(2), 252-263. https://doi.org/10.14419/ijamr.v2i2.620