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Analysis of the transient behavior in a two dof nonlinear system

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  • Ture Savadkoohi, Alireza
  • Manevitch, Leonid I.
  • Lamarque, Claude-Henri

Abstract

In this paper we analyze the behavior of a nonlinear system under impulse loadings. The system is composed of a master “linear” degree of freedom (dof) substructure which is attached to a slave “nonlinear” energy sink (NES) for the sake of the control. Melnikov integral is endowed in order to study the possibility of existence of chaos and transversal homoclinic orbits in the system. Then, the complexification method as an alternative to nonlinear normal modes is implemented to reveal the behavior of the system during the energy exchange between two oscillators. The non-smooth time transformation (NSTT) technique is implemented in order to enlighten the system behavior during its extremely nonlinear regime, meanwhile stable and unstable zones of the system during its quasi-linear regime are highlighted.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:6:p:450-463
    DOI: 10.1016/j.chaos.2011.03.007
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    References listed on IDEAS

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    1. 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.
    2. 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.
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