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The method of multiple scales for forced oscillators with some real-power nonlinearities in the stiffness and damping force

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  • Kovacic, Ivana

Abstract

The steady-state response of forced damped nonlinear oscillators is considered, the restoring force of which has a non-negative real power-form nonlinear term and the linear term of which can be negative, zero or positive. The damping term is also assumed in a power form, thus covering polynomial and non-polynomial damping. The method of multiple scales with a new expansion parameter is presented in order to cover the cases when the nonlinearity is not necessarily small. Amplitude-frequency equations and approximate solutions for the steady-state response at the frequency of excitation are obtained and compared with numerical results, showing good agreement.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:10:p:891-901
    DOI: 10.1016/j.chaos.2011.07.006
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    1. 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.
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    Cited by:

    1. Huang, Dongmei & Xu, Wei & Shi, Lingling, 2016. "Response analysis and energy transmissibility of a vibration isolation system with real-power nonlinearities under a NMPPF controller," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 281-292.
    2. Huang, Dongmei & Li, Wei & Yang, Guidong & He, Meijuan, 2018. "Analysis of limit cycles and stochastic responses of a real-power vibration isolation system under delayed feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 125-134.

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