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On the dynamics of Rayleigh beams resting on fractional-order viscoelastic Pasternak foundations subjected to moving loads

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  • Anague Tabejieu, L.M.
  • Nana Nbendjo, B.R.
  • Woafo, P.

Abstract

The standard averaging method is used to provide an analytical explanation on the effects of spacing loads, load velocity, order of the fractional viscoelastic property of shear layer material on the amplitude of the beam. The geometric nonlinearity is taken into account in the model. The analysis shows that, when the moving loads are uniformly distributed upon all the length of the structure, it vibrates the least possible. Moreover, as the order of the derivative increases, the resonant amplitude of the beam vibration decreases. In other hand, by means of Melnikov technique, a necessary condition for onset of horseshoes chaos resulting from heteroclinic bifurcation is derived analytically. We point out the critical weight of moving loads and order of the fractional derivative above which the system becomes unstable.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:93:y:2016:i:c:p:39-47
    DOI: 10.1016/j.chaos.2016.10.001
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    References listed on IDEAS

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    1. Kingni, S.T. & Nana, B. & Mbouna Ngueuteu, G.S. & Woafo, P. & Danckaert, J., 2015. "Bursting oscillations in a 3D system with asymmetrically distributed equilibria: Mechanism, electronic implementation and fractional derivation effect," Chaos, Solitons & Fractals, Elsevier, vol. 71(C), pages 29-40.
    2. 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.
    3. Nana Nbendjo, B.R. & Woafo, P., 2007. "Active control with delay of horseshoes chaos using piezoelectric absorber on a buckled beam under parametric excitation," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 73-79.
    4. 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.
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    Cited by:

    1. Miwadinou, C.H. & Monwanou, A.V. & Hinvi, L.A. & Chabi Orou, J.B., 2018. "Effect of amplitude modulated signal on chaotic motions in a mixed Rayleigh–Liénard oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 89-101.
    2. Anague Tabejieu, L.M. & Nana Nbendjo, B.R. & Filatrella, G., 2019. "Effect of the fractional foundation on the response of beam structure submitted to moving and wind loads," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 178-188.
    3. 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).

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