IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v41y2009i4p2075-2080.html
   My bibliography  Save this article

Response of a stochastic Duffing–Van der Pol elastic impact oscillator

Author

Listed:
  • Wang, Liang
  • Xu, Wei
  • Li, Gaojie
  • Li, Dongxi

Abstract

The response of a Duffing–Van der Pol elastic impact system with one random parameter is investigated. The system is transformed to two high dimension deterministic systems according to Laguerre polynomial approximation, through which the response can be derived from deterministic numerical method. It is found that the behavior of the system changes from chaos to periodic through inverse period-doubling bifurcation when the spring stiffness of elastic impact force increases, and the idea that all the bifurcation points are advanced by random factor is presented. Numerical results show that the Laguerre polynomial approximation is an effective approach to solving the problems of elastic impact systems with random parameters.

Suggested Citation

  • Wang, Liang & Xu, Wei & Li, Gaojie & Li, Dongxi, 2009. "Response of a stochastic Duffing–Van der Pol elastic impact oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2075-2080.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:4:p:2075-2080
    DOI: 10.1016/j.chaos.2008.08.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077908003883
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2008.08.013?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. Lee, June-Yule & Yan, Jun-Juh, 2006. "Control of impact oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 136-142.
    2. de Souza, S.L.T. & Wiercigroch, M. & Caldas, I.L. & Balthazar, J.M., 2008. "Suppressing grazing chaos in impacting system by structural nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 864-869.
    3. de Souza, Silvio L.T. & Caldas, Iberê L. & Viana, Ricardo L., 2007. "Damping control law for a chaotic impact oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 745-750.
    4. Gendelman, Oleg V., 2006. "Modeling of inelastic impacts with the help of smooth-functions," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 522-526.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Liu, Li & Xu, Wei & Yue, Xiaole & Qiao, Yan, 2020. "Reliability of elastic impact system with Coulomb friction excited by Gaussian white noise," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    2. Feng, Jinqian & Liu, Junli, 2015. "Chaotic dynamics of the vibro-impact system under bounded noise perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 10-16.

    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. Guasch, Oriol & Van Hirtum, Annemie & Fernández, A. Inés & Arnela, Marc, 2022. "Controlling chaotic oscillations in a symmetric two-mass model of the vocal folds," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    2. Medeiros, E.S. & de Souza, S.L.T. & Medrano-T, R.O. & Caldas, I.L., 2011. "Replicate periodic windows in the parameter space of driven oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 44(11), pages 982-989.
    3. Li, Chao, 2019. "Stochastic response of a vibro-impact system with variable mass," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 151-160.
    4. Liu, Li & Xu, Wei & Yue, Xiaole & Qiao, Yan, 2020. "Reliability of elastic impact system with Coulomb friction excited by Gaussian white noise," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. Luo, Guanwei & Xie, Jianhua & Zhu, Xifeng & Zhang, Jiangang, 2008. "Periodic motions and bifurcations of a vibro-impact system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1340-1347.
    6. Firas Turki & Hassène Gritli & Safya Belghith, 2019. "Robust Position Control of a Two-Sided 1-DoF Impacting Mechanical Oscillator Subject to an External Persistent Disturbance by Means of a State-Feedback Controller," Complexity, Hindawi, vol. 2019, pages 1-14, December.

    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:41:y:2009:i:4:p:2075-2080. 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.