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Design, analysis and horseshoes chaos control on tension leg platform system with fractional nonlinear viscoelastic tendon force under regular sea wave excitation

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  • Ngounou, A.M.
  • Mba Feulefack, S.C.
  • Anague Tabejieu, L.M.
  • Nana Nbendjo, B.R.

Abstract

In this paper, the dynamic response of a Tension Leg Platform (TLP) system with fractional nonlinear viscoelastic tendon force under regular sea wave is investigated. Analytical and numerical methods are employed to analyse the effect of the fractional viscoelastic parameter, the tendon viscosity coefficient and the number of tendons on the amplitude of the system. It is found that, when the tendon viscosity coefficient and the number of tendons increase, the amplitude of vibration decreases. We also show that, increase of the fractional order derivative also contributes to decrease the unstable range of amplitude. Nevertheless, beyond a certain value of the fractional parameter, we rather observe an increase in amplitude. In other hand, Melnikov technique is used to derive the analytical criterion for the appearance of the heteroclinic chaos in the system. Analytical prediction is tested against numerical simulations based on the basin of attraction. It is found that, the appearance of horseshoes chaos depend of the fractional viscoelastic parameter, the tendon viscosity coefficient and the number of tendons.

Suggested Citation

  • Ngounou, A.M. & Mba Feulefack, S.C. & Anague Tabejieu, L.M. & Nana Nbendjo, B.R., 2022. "Design, analysis and horseshoes chaos control on tension leg platform system with fractional nonlinear viscoelastic tendon force under regular sea wave excitation," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s096007792200162x
    DOI: 10.1016/j.chaos.2022.111952
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    References listed on IDEAS

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    1. Lokenath Debnath, 2003. "Recent applications of fractional calculus to science and engineering," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-30, January.
    2. 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.
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