IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v321y2018icp780-793.html
   My bibliography  Save this article

Analysis of a quintic system with fractional damping in the presence of vibrational resonance

Author

Listed:
  • Yan, Zhi
  • Wang, Wei
  • Liu, Xianbin

Abstract

In the present paper, the phenomenon of the vibrational resonance in a quantic oscillator that possesses a fractional order damping and is driven by both the low and the high frequency periodic signals is investigated, and the approximate theoretical expression of the response amplitude at the low-frequency is obtained by utilizing the method of direct partition of motions. Based on the definition of the Caputo fractional derivative, an algorithm for simulating the system is introduced, and the new method is shown to have higher precision and better feasibility than the method based on the Grünwald –Letnikov expansion. Due to the order of the fractional derivative, various new resonance phenomena are found for the system with single-well, double-well, and triple-well potential, respectively. Moreover, the value of fractional order can be treated as a bifurcation parameter, through which, it is found that the slowly-varying system can be transmitted from a bistability system to a monostabillity one, or from tristability to bistability, and finally to monostabillity. Unlike the cases of the integer-order system, the critical resonance amplitude of the high-frequency signal in the fractional system does depend on the damping strength and can be significantly affected by the fractional-order damping. The numerical results given by the new method is found to be in good agreement with the analytical predictions.

Suggested Citation

  • Yan, Zhi & Wang, Wei & Liu, Xianbin, 2018. "Analysis of a quintic system with fractional damping in the presence of vibrational resonance," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 780-793.
  • Handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:780-793
    DOI: 10.1016/j.amc.2017.11.028
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630031730810X
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2017.11.028?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. 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.
    2. Ghayesh, Mergen H. & Amabili, Marco & Farokhi, Hamed, 2013. "Two-dimensional nonlinear dynamics of an axially moving viscoelastic beam with time-dependent axial speed," Chaos, Solitons & Fractals, Elsevier, vol. 52(C), pages 8-29.
    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. Li Jiang & Tao Wang & Qing-Xue Huang, 2023. "Resonance Analysis of Horizontal Nonlinear Vibrations of Roll Systems for Cold Rolling Mills under Double-Frequency Excitations," Mathematics, MDPI, vol. 11(7), pages 1-15, March.

    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. Li Jiang & Tao Wang & Qing-Xue Huang, 2023. "Resonance Analysis of Horizontal Nonlinear Vibrations of Roll Systems for Cold Rolling Mills under Double-Frequency Excitations," Mathematics, MDPI, vol. 11(7), pages 1-15, March.
    2. Ning, Xin & Ma, Yanyan & Li, Shuai & Zhang, Jingmin & Li, Yifei, 2018. "Response of non-linear oscillator driven by fractional derivative term under Gaussian white noise," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 102-107.
    3. Farokhi, Hamed & Ghayesh, Mergen H. & Amabili, Marco, 2013. "In-plane and out-of-plane nonlinear dynamics of an axially moving beam," Chaos, Solitons & Fractals, Elsevier, vol. 54(C), pages 101-121.
    4. Liu, Q.X. & Liu, J.K. & Chen, Y.M., 2017. "An analytical criterion for jump phenomena in fractional Duffing oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 216-219.
    5. Sun, Zhongkui & Dang, Puni & Xu, Wei, 2019. "Detecting and measuring stochastic resonance in fractional-order systems via statistical complexity," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 34-40.
    6. 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).
    7. Dai, Hongzhe & Zheng, Zhibao & Wang, Wei, 2017. "On generalized fractional vibration equation," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 48-51.
    8. Jin, Chen & Sun, Zhongkui & Xu, Wei, 2022. "Stochastic bifurcations and its regulation in a Rijke tube model," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).

    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:apmaco:v:321:y:2018:i:c:p:780-793. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.