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Resonance of a nonlinear forced system with two-frequency parametric and self-excitations

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  • Abdelhafez, H.M.

Abstract

The resonance of a single-degree-of-freedom forced nonlinear system with two-frequency parametric and self-excitations is investigated. In particular, the case in which the parametric excitation terms and the excitation force with close frequencies is examined. The method of multiple scales is used to determine the equations of modulation of amplitude and phase. The behaviour of steady-state responses and their stability are studied. The effects of damping, and magnitudes of self-excitation, parametric excitation and the excitation force are analyzed. The theoretical results are verified by numerical integration results of the governing equation and the modulation equations.

Suggested Citation

  • Abdelhafez, H.M., 2004. "Resonance of a nonlinear forced system with two-frequency parametric and self-excitations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 66(1), pages 69-83.
    • Handle: RePEc:eee:matcom:v:66:y:2004:i:1:p:69-83
    DOI: 10.1016/j.matcom.2004.03.002
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    References listed on IDEAS

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    1. Abdelhafez, H.M., 2002. "Resonance of multiple frequency excitated systems with quadratic, cubic and quartic non-linearity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 61(1), pages 17-34.
    2. El-Bassiouny, A.F. & Abdelhafez, H.M., 2001. "Prediction of bifurcations for external and parametric excited one-degree-of-freedom system with quadratic, cubic and quartic non-linearities," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 57(1), pages 61-80.
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