IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v123y2019icp14-23.html
   My bibliography  Save this article

Stability and bifurcation analysis of single-degree-of-freedom linear vibro-impact system with fractional-order derivative

Author

Listed:
  • Niu, Jiangchuan
  • Liu, Ruyu
  • Shen, Yongjun
  • Yang, Shaopu

Abstract

The stability and bifurcation of the single-degree-of-freedom linear vibro-impact system with fractional-order derivative are investigated, where the one-sided impact model under external harmonic excitation is considered. The approximate analytical solutions of the transient and steady state of the vibro-impact system are obtained by the averaging method, and the general solution of the system is obtained by the superposition method. The approximate analytical solution and numerical solution of the system are compared, and they are in good agreement with each other, which proves the accuracy of the approximate solution. Based on the approximate analytical solution, the stability of periodic motion of the vibro-impact system is studied by changing it to the fixed point on the mapping plane with the help of Poincaré mapping. With the change of the fractional order, the frequency and amplitude of the external excitation, the bifurcation behaviors of the system are analyzed in detail. As the results show, saddle-node bifurcation, grazing bifurcation, period-doubling bifurcation and chaotic motion are found in the system.

Suggested Citation

  • Niu, Jiangchuan & Liu, Ruyu & Shen, Yongjun & Yang, Shaopu, 2019. "Stability and bifurcation analysis of single-degree-of-freedom linear vibro-impact system with fractional-order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 14-23.
    • Handle: RePEc:eee:chsofr:v:123:y:2019:i:c:p:14-23
    DOI: 10.1016/j.chaos.2019.03.035
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077919300967
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.03.035?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. Shen, Yongjun & Yang, Shaopu & Sui, Chuanyi, 2014. "Analysis on limit cycle of fractional-order van der Pol oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 67(C), pages 94-102.
    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. Xie, Jiaquan & Zhao, Fuqiang & He, Dongping & Shi, Wei, 2022. "Bifurcation and resonance of fractional cubic nonlinear system," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. Lyu, Xiaohong & Zhu, Xifeng & Gao, Quanfu & Luo, Guanwei, 2020. "Two-parameter bifurcations of an impact system under different damping conditions," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).

    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. Azhdari, Meysam & Binazadeh, Tahereh, 2022. "A novel adaptive SMC strategy for sustained oscillations in nonlinear sandwich systems based on stable limit cycle approach," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Hakimi, A.R. & Azhdari, M. & Binazadeh, T., 2021. "Limit cycle oscillator in nonlinear systems with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    3. Li, Zengshan & Chen, Diyi & Ma, Mengmeng & Zhang, Xinguang & Wu, Yonghong, 2017. "Feigenbaum's constants in reverse bifurcation of fractional-order Rössler system," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 116-123.
    4. Guo, Feng & Wang, Xue-yuan & Qin, Ming-wei & Luo, Xiang-dong & Wang, Jian-wei, 2021. "Resonance phenomenon for a nonlinear system with fractional derivative subject to multiplicative and additive noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 562(C).
    5. Dai, Hongzhe & Zheng, Zhibao & Wang, Wei, 2017. "On generalized fractional vibration equation," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 48-51.
    6. Yang, Yongge & Xu, Wei & Gu, Xudong & Sun, Yahui, 2015. "Stochastic response of a class of self-excited systems with Caputo-type fractional derivative driven by Gaussian white noise," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 190-204.
    7. Xu, Beibei & Chen, Diyi & Zhang, Hao & Wang, Feifei, 2015. "Modeling and stability analysis of a fractional-order Francis hydro-turbine governing system," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 50-61.
    8. Amar Debbouche & Juan J. Nieto & Delfim F. M. Torres, 2017. "Optimal Solutions to Relaxation in Multiple Control Problems of Sobolev Type with Nonlocal Nonlinear Fractional Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 7-31, July.

    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:123:y:2019:i:c:p:14-23. 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.