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Multi-pulse orbits and chaotic dynamics in motion of parametrically excited viscoelastic moving belt

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  • Zhang, Wei
  • Yao, Minghui

Abstract

In this paper, the Shilnikov type multi-pulse orbits and chaotic dynamics of parametrically excited viscoelastic moving belt are studied in detail. Using Kelvin-type viscoelastic constitutive law, the equations of motion for viscoelastic moving belt with the external damping and parametric excitation are given. The four-dimensional averaged equation under the case of primary parametric resonance is obtained by directly using the method of multiple scales and Galerkin’s approach to the partial differential governing equation of viscoelastic moving belt. From the averaged equations obtained here, the theory of normal form is used to give the explicit expressions of normal form with a double zero and a pair of pure imaginary eigenvalues. Based on normal form, the energy-phrase method is employed to analyze the global bifurcations and chaotic dynamics in parametrically excited viscoelastic moving belt. The global bifurcation analysis indicates that there exist the heteroclinic bifurcations and the Silnikov type multi-pulse homoclinic orbits in the averaged equation. The results obtained above mean the existence of the chaos for the Smale horseshoe sense in parametrically excited viscoelastic moving belt. The chaotic motions of viscoelastic moving belts are also found by using numerical simulation. A new phenomenon on the multi-pulse jumping orbits is observed from three-dimensional phase space.

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  • 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.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:1:p:42-66
    DOI: 10.1016/j.chaos.2005.05.005
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Jin, Qiduo & Yuan, Fuh-Gwo & Ren, Yiru, 2023. "Auto-parametric resonance of flexible viscoelastic beams under interaction between longitudinal and transverse modes," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Yang, Shaopu & Shen, Yongjun, 2009. "Recent advances in dynamics and control of hysteretic nonlinear systems," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1808-1822.
    3. Chen, Li-Qun & Zhang, Wei & Zu, Jean W., 2009. "Nonlinear dynamics for transverse motion of axially moving strings," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 78-90.
    4. 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.

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