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Investigation of relation between singular points and number of limit cycles for a rotor–AMBs system

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  • Li, J.
  • Tian, Y.
  • Zhang, W.

Abstract

The relation between singular points and the number of limit cycles is investigated for a rotor-active magnetic bearings system with time-varying stiffness and single-degree-of-freedom. The averaged equation of the system is a perturbed polynomial Hamiltonian system of degree 5. The dynamic characteristics of the unperturbed system are first analyzed for a certain parameter group. The number of limit cycles and their configurations of the perturbed system under eight different parametric groups are obtained and the influence of eight control conditions on the number of limit cycles is studied. The results obtained here will play an important leading role in the study of the properties of nonlinear dynamics and control of the rotor-active magnetic bearings system with time-varying stiffness.

Suggested Citation

  • Li, J. & Tian, Y. & Zhang, W., 2009. "Investigation of relation between singular points and number of limit cycles for a rotor–AMBs system," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1627-1640.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:4:p:1627-1640
    DOI: 10.1016/j.chaos.2007.06.044
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    References listed on IDEAS

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    1. Zhang, Wei & Wang, Feng-Xia & Zu, Jean W., 2005. "Local bifurcations and codimension-3 degenerate bifurcations of a quintic nonlinear beam under parametric excitation," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 977-998.
    2. Wang, S. & Yu, P., 2006. "Existence of 121 limit cycles in a perturbed planar polynomial Hamiltonian vector field of degree 11," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 606-621.
    3. Zhang, W. & Yao, M.H. & Zhan, X.P., 2006. "Multi-pulse chaotic motions of a rotor-active magnetic bearing system with time-varying stiffness," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 175-186.
    4. Li, J. & Miao, S.F. & Zhang, W., 2007. "Analysis on bifurcations of multiple limit cycles for a parametrically and externally excited mechanical system," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 960-976.
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