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Dynamics of linear oscillator coupled to strongly nonlinear attachment with multiple states of equilibrium

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  • Gendelman, O.V.
  • Lamarque, C.H.

Abstract

Energy transfer in 2 DOF systems comprised of linear oscillator with unit mass and strongly nonlinear oscillator with multiple states of equilibrium and relatively small mass is investigated by analytic and numerical methods. We demonstrate that the process of energy transfer is governed by structure of damped nonlinear normal modes of the system. Various dynamical regimes dependent on the system parameters are revealed and conditions for efficient energy pumping to the strongly nonlinear attachment are formulated. Possibility of transient chaotic response is investigated.

Suggested Citation

  • Gendelman, O.V. & Lamarque, C.H., 2005. "Dynamics of linear oscillator coupled to strongly nonlinear attachment with multiple states of equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 24(2), pages 501-509.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:2:p:501-509
    DOI: 10.1016/j.chaos.2004.09.088
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    Cited by:

    1. Ture Savadkoohi, Alireza & Manevitch, Leonid I. & Lamarque, Claude-Henri, 2011. "Analysis of the transient behavior in a two dof nonlinear system," Chaos, Solitons & Fractals, Elsevier, vol. 44(6), pages 450-463.
    2. Manevitch, L.I. & Gourdon, E. & Lamarque, C.H., 2007. "Parameters optimization for energy pumping in strongly nonhomogeneous 2 dof system," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 900-911.
    3. El-Bassiouny, A.F., 2009. "On methods for continuous systems with quadratic, cubic and quantic nonlinearities," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1308-1316.

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