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Forced oscillators with non-linear spring: A simple analytical approach

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  • Wang, S.
  • Wiercigroch, M.

Abstract

An analytical method of finding the amplitude frequency and phase frequency characteristics of a forced oscillator with non-linear restoring force is proposed. The non-linear restoring force is simply fitted by a linear one with varying stiffness. The analytical expression of amplitude frequency characteristics predicts the jump or bifurcation points; and keeps highly consistent with the numerical results. This method can be used to both smooth and piecewise linear restoring force.

Suggested Citation

  • Wang, S. & Wiercigroch, M., 2009. "Forced oscillators with non-linear spring: A simple analytical approach," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1784-1790.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:4:p:1784-1790
    DOI: 10.1016/j.chaos.2008.07.048
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    References listed on IDEAS

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    1. He, Ji-Huan, 2007. "Variational approach for nonlinear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1430-1439.
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    Cited by:

    1. Kovacic, Ivana, 2011. "The method of multiple scales for forced oscillators with some real-power nonlinearities in the stiffness and damping force," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 891-901.

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