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Suppressing grazing chaos in impacting system by structural nonlinearity

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  • de Souza, S.L.T.
  • Wiercigroch, M.
  • Caldas, I.L.
  • Balthazar, J.M.

Abstract

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing.

Suggested Citation

  • de Souza, S.L.T. & Wiercigroch, M. & Caldas, I.L. & Balthazar, J.M., 2008. "Suppressing grazing chaos in impacting system by structural nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 864-869.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:3:p:864-869
    DOI: 10.1016/j.chaos.2007.01.022
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    References listed on IDEAS

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    1. Emans, Joseph & Wiercigroch, Marian & Krivtsov, Anton M., 2005. "Cumulative effect of structural nonlinearities: chaotic dynamics of cantilever beam system with impacts," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1661-1670.
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    Cited by:

    1. Wang, Liang & Xu, Wei & Li, Gaojie & Li, Dongxi, 2009. "Response of a stochastic Duffing–Van der Pol elastic impact oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2075-2080.
    2. Liu, Li & Xu, Wei & Yue, Xiaole & Qiao, Yan, 2020. "Reliability of elastic impact system with Coulomb friction excited by Gaussian white noise," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    3. Medeiros, E.S. & de Souza, S.L.T. & Medrano-T, R.O. & Caldas, I.L., 2011. "Replicate periodic windows in the parameter space of driven oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 44(11), pages 982-989.

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