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Nonlinear dynamical analysis of axially moving viscoelastic strings

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  • Zhang, Neng-Hui
  • Chen, Li-Qun

Abstract

In this paper, nonlinear dynamical behaviors of axially moving viscoelastic strings are investigated. The one-term and the two-term Galerkin truncations using translating string eigenfunctions are respectively employed to reduce the partial-differential equation that governs the transverse motions of the string to a set of ordinary differential equations. The bifurcation diagrams are presented in the case that the amplitude of the periodic perturbation, or the dynamic viscosity is respectively varied while other parameters are fixed. The dynamical behaviors are numerically identified based on the Poincare maps. Numerical results show that regular and chaotic motions occur in the transverse vibration of the axially moving viscoelastic strings.

Suggested Citation

  • Zhang, Neng-Hui & Chen, Li-Qun, 2005. "Nonlinear dynamical analysis of axially moving viscoelastic strings," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 1065-1074.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:4:p:1065-1074
    DOI: 10.1016/j.chaos.2004.09.113
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    Cited by:

    1. Zhang, Wei & Yao, Minghui, 2006. "Multi-pulse orbits and chaotic dynamics in motion of parametrically excited viscoelastic moving belt," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 42-66.
    2. Ghayesh, Mergen H. & Amabili, Marco & Farokhi, Hamed, 2013. "Two-dimensional nonlinear dynamics of an axially moving viscoelastic beam with time-dependent axial speed," Chaos, Solitons & Fractals, Elsevier, vol. 52(C), pages 8-29.
    3. Cao, D.X. & Zhang, W., 2008. "Global bifurcations and chaotic dynamics for a string-beam coupled system," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 858-875.
    4. Ha, Jih-Lian & Chang, Jer-Rong & Fung, Rong-Fong, 2007. "Nonlinear dynamic behavior of a moving viscoelastic string undergoing three-dimensional vibration," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1117-1134.

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