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Self-excited vibration control for axially fast excited beam by a time delay state feedback

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  • Hamdi, Mustapha
  • Belhaq, Mohamed

Abstract

This work examines the control of self-excited vibration of a simply-supported beam subjected to an axially high-frequency excitation. The investigation of the resonant cases are not considered in this paper. The control is implemented via a corrective position feedback with time delay. The objective of this control is to eliminate the undesirable self-excited vibrations with an appropriate choice of parameters. The issue of stability is also addressed in this paper. Using the technique of direct partition of motion, the dynamic of discretized equations is separated into slow and fast components. The multiple scales method is then performed on the slow dynamic to obtain a slow flow for the amplitude and phase. Analysis of this slow flow provides analytical approximations locating regions in parameters space where undesirable self-excited vibration can be eliminated. A numerical study of these regions is performed on the original discretized system and compared to the analytical prediction showing a good agreement.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:2:p:521-532
    DOI: 10.1016/j.chaos.2008.02.023
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    References listed on IDEAS

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    1. Bourkha, Rachid & Belhaq, Mohamed, 2007. "Effect of fast harmonic excitation on a self-excited motion in Van der Pol oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 621-627.
    2. 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.
    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. 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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