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Bifurcations and chaos of the nonlinear viscoelastic plates subjected to subsonic flow and external loads

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  • An, Fengxian
  • Chen, Fangqi

Abstract

The subharmonic bifurcations and chaotic motions of the nonlinear viscoelastic plates subjected to subsonic flow and external loads are studied by means of Melnikov method. The critical conditions for the occurrence of chaotic motions are obtained. The chaotic features on the system parameters are discussed in detail. The conditions for subharmonic bifurcations are also obtained. For the system with no structural damping, chaotic motions can occur through infinite subharmonic bifurcations of odd orders. Furthermore, we confirm our theoretical predictions by numerical simulations. The theoretical results obtained here can help us to eliminate or suppress large nonlinear vibrations and chaotic motions of the nonlinear viscoelastic plates. Based on Melnikov method, complex dynamical behaviors of the nonlinear viscoelastic plates can be controlled by modifying the system parameters.

Suggested Citation

  • An, Fengxian & Chen, Fangqi, 2016. "Bifurcations and chaos of the nonlinear viscoelastic plates subjected to subsonic flow and external loads," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 78-85.
    • Handle: RePEc:eee:chsofr:v:91:y:2016:i:c:p:78-85
    DOI: 10.1016/j.chaos.2016.05.006
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    References listed on IDEAS

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    1. Ye, Min & Lu, Jing & Zhang, Wei & Ding, Qian, 2005. "Local and global nonlinear dynamics of a parametrically excited rectangular symmetric cross-ply laminated composite plate," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 195-213.
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    Cited by:

    1. Anague Tabejieu, L.M. & Nana Nbendjo, B.R. & Woafo, P., 2016. "On the dynamics of Rayleigh beams resting on fractional-order viscoelastic Pasternak foundations subjected to moving loads," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 39-47.
    2. Cao, Tianxiao & Hu, Yuda, 2024. "Dual-mode coupling resonance and dynamic stability of axially moving ferromagnetic thin plate strips in alternating magnetic field," Applied Mathematics and Computation, Elsevier, vol. 464(C).
    3. Azarboni, H. Ramezannejad & Ansari, R. & Nazarinezhad, A., 2018. "Chaotic dynamics and stability of functionally graded material doubly curved shallow shells," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 14-25.
    4. Cao, Tianxiao & Hu, Yuda, 2024. "Chaos prediction and bifurcation of soft ferromagnetic thin plates with motion in dual air-gap magnetic fields excited by armatures," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).

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