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Active control with delay of horseshoes chaos using piezoelectric absorber on a buckled beam under parametric excitation

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  • Nana Nbendjo, B.R.
  • Woafo, P.

Abstract

We consider the control of an undamped buckled beam, subjected to parametric excitations. Control with delay is applied to suppress chaotic vibrations. Using the Melnikov function approach, we obtain the threshold condition for the inhibition of Smale horseshoes chaos. Emphasis is laid on the effect of time delay.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:1:p:73-79
    DOI: 10.1016/j.chaos.2005.10.070
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    References listed on IDEAS

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    1. Zhang, Wei, 2005. "Chaotic motion and its control for nonlinear nonplanar oscillations of a parametrically excited cantilever beam," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 731-745.
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    Cited by:

    1. Wu, Wenjuan & Chen, Zengqiang & Yuan, Zhuzhi, 2009. "The evolution of a novel four-dimensional autonomous system: Among 3-torus, limit cycle, 2-torus, chaos and hyperchaos," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2340-2356.
    2. Hamdi, Mustapha & Belhaq, Mohamed, 2009. "Self-excited vibration control for axially fast excited beam by a time delay state feedback," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 521-532.
    3. 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.
    4. Sah, Simohamed & Belhaq, Mohamed, 2008. "Effect of vertical high-frequency parametric excitation on self-excited motion in a delayed van der Pol oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1489-1496.

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