IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v38y2008i4p1152-1167.html
   My bibliography  Save this article

Transient and steady nonlinear responses for a rotor-active magnetic bearings system with time-varying stiffness

Author

Listed:
  • Zhang, Wei
  • Zu, Jean W.

Abstract

In this paper, we investigate transient and steady nonlinear dynamics in rotor-active magnetic bearings (AMBs) system with 8-pole legs and the time-varying stiffness. The model of parametrically excited two-degree-of-freedom nonlinear system with the quadratic and cubic nonlinearities is established to explore the periodic and quasiperiodic motions as well as the bifurcations and chaotic dynamics of the system. The method of multiple scales is used to obtain the averaged equations in the case of primary parameter resonance and 1/2 subharmonic resonance. Numerical approach is applied to the averaged equations to find the periodic, quasiperiodic solutions and local bifurcations. It is found that there exist 2-period, 3-period, 4-period, 5-period, multi-period and quasiperiodic solutions in the rotor-AMBs system with 8-pole legs and the time-varying stiffness. The catastrophic phenomena for the amplitude of transient nonlinear oscillations are first observed in the rotor-AMBs system with 8-pole legs and the time-varying stiffness. The procedures of motion from the transient state chaotic motion to the steady state periodic and quasiperiodic motions are also found. The results obtained here show that there exists the ability of auto-controlling transient state chaos to the steady state periodic and quasiperiodic motions in the rotor-AMBs system with 8-pole legs and the time-varying stiffness.

Suggested Citation

  • Zhang, Wei & Zu, Jean W., 2008. "Transient and steady nonlinear responses for a rotor-active magnetic bearings system with time-varying stiffness," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1152-1167.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:4:p:1152-1167
    DOI: 10.1016/j.chaos.2007.02.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007790700080X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.02.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zhang, W. & Zu, J.W. & Wang, F.X., 2008. "Global bifurcations and chaos for a rotor-active magnetic bearing system with time-varying stiffness," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 586-608.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Inayat-Hussain, Jawaid I., 2009. "Geometric coupling effects on the bifurcations of a flexible rotor response in active magnetic bearings," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2664-2671.
    2. Cao, D.X. & Zhang, W., 2008. "Global bifurcations and chaotic dynamics for a string-beam coupled system," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 858-875.
    3. Li, Tzuu-Hseng S. & Kuo, Chao-Lin & Guo, Nai Ren, 2007. "Design of an EP-based fuzzy sliding-mode control for a magnetic ball suspension system," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1523-1531.
    4. Jing Wang & Shaojuan Ma & Peng Hao & Hehui Yuan, 2019. "Hopf Bifurcation and Control of Magnetic Bearing System with Uncertain Parameter," Complexity, Hindawi, vol. 2019, pages 1-12, December.
    5. Wang, Xia & Chen, Fangqi, 2012. "Global dynamics of two coupled parametrically excited van der Pol oscillators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(9), pages 1551-1571.
    6. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:38:y:2008:i:4:p:1152-1167. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.