IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v122y2019icp179-188.html
   My bibliography  Save this article

Probabilistic response analysis for a class of nonlinear vibro-impact oscillator with bilateral constraints under colored noise excitation

Author

Listed:
  • Liu, Di
  • Li, Junlin
  • Meng, Yu

Abstract

In this paper, a new stochastic method combining the stochastic averaging of quasi-conservative and energy loss is developed to analyze the probabilistic response of a class of nonlinear vibro-impact oscillator with bilateral barriers driven by colored noise. According to the relationships between the total energy and the potential energy of impact positions of the nonlinear system, the energy loss of every movement period of the unperturbed nonlinear vibro-impact system with given total energy is analyzed in detail. Based on this analysis, an averaged Ito^ stochastic differential equation is derived through the stochastic method which combining a nonlinear transformation and the stochastic averaging of quasi-conservative, in which the averaged Ito^ equation has the typical characteristics of piecewise smooth. Next, the stationary probability density function (SPDF) is obtained by solving the averaged drift and diffusion terms of the corresponding piecewise smooth Fokker-Planck equation for the averaged Ito^ equation with the Fourier series expansion. Finally, an example is given to validate the effectiveness of the proposed method. The effects of four physical quantities of the stochastic vibro-impact system: the positions of impact, restitution coefficient, noise intensity and correlation time of the colored noise, on the probabilistic response are discussed by the SPDFs in detail, and the results are verified through the Monte Carlo simulation.

Suggested Citation

  • Liu, Di & Li, Junlin & Meng, Yu, 2019. "Probabilistic response analysis for a class of nonlinear vibro-impact oscillator with bilateral constraints under colored noise excitation," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 179-188.
    • Handle: RePEc:eee:chsofr:v:122:y:2019:i:c:p:179-188
    DOI: 10.1016/j.chaos.2019.03.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077918305472
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.03.024?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. Liu, Kaihe & Jin, Yanfei, 2013. "Stochastic resonance in periodic potentials driven by colored noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5283-5288.
    2. 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.
    3. Yang, Guidong & Xu, Wei & Gu, Xudong & Huang, Dongmei, 2016. "Response analysis for a vibroimpact Duffing system with bilateral barriers under external and parametric Gaussian white noises," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 125-135.
    4. Liu, Di & Xu, Yong & Li, Junlin, 2017. "Probabilistic response analysis of nonlinear vibration energy harvesting system driven by Gaussian colored noise," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 806-812.
    5. Li, Chao & Xu, Wei & Feng, Jinqian & Wang, Liang, 2013. "Response probability density functions of Duffing–Van der Pol vibro-impact system under correlated Gaussian white noise excitations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1269-1279.
    6. Zhao, Xiangrong & Xu, Wei & Gu, Xudong & Yang, Yongge, 2015. "Stochastic stationary responses of a viscoelastic system with impacts under additive Gaussian white noise excitation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 431(C), pages 128-139.
    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. Guo, Shu-Ling & Yang, Yong-Ge & Sun, Ya-Hui, 2021. "Stochastic response of an energy harvesting system with viscoelastic element under Gaussian white noise excitation," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    2. 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.
    3. Jin, Yanfei & Wang, Heqiang, 2020. "Noise-induced dynamics in a Josephson junction driven by trichotomous noises," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    4. Dongmei Huang & Shengxi Zhou & Zhichun Yang, 2019. "Resonance Mechanism of Nonlinear Vibrational Multistable Energy Harvesters under Narrow-Band Stochastic Parametric Excitations," Complexity, Hindawi, vol. 2019, pages 1-20, December.
    5. Navarro-López, Eva M. & Licéaga-Castro, Eduardo, 2009. "Non-desired transitions and sliding-mode control of a multi-DOF mechanical system with stick-slip oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2035-2044.
    6. Zhao, Xiangrong & Xu, Wei & Gu, Xudong & Yang, Yongge, 2015. "Stochastic stationary responses of a viscoelastic system with impacts under additive Gaussian white noise excitation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 431(C), pages 128-139.
    7. Yue, Xiaole & Yu, Bei & Li, Yongge & Xu, Yong, 2022. "Dynamic response and bifurcation for Rayleigh-Liénard oscillator under multiplicative colored noise," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    8. Yang, Tao & Cao, Qingjie, 2020. "Dynamics and high-efficiency of a novel multi-stable energy harvesting system," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    9. Deng, Hang & Ye, Jimin & Huang, Dongmei, 2023. "Design and analysis of a galloping energy harvester with V-shape spring structure under Gaussian white noise," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    10. Feng, Jing & Xu, Wei & Xu, Yong & Wang, Xiaolong, 2018. "Phase transition and alternation in a model of perceptual bistability in the presence of Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 367-378.
    11. 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).
    12. Fezeu, G.J. & Fokou, I.S. Mokem & Buckjohn, C. Nono Dueyou & Siewe Siewe, M. & Tchawoua, C., 2020. "Resistance induced P-bifurcation and Ghost-Stochastic resonance of a hybrid energy harvester under colored noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    13. Bi, Haohao & Lei, Youming & Han, Yanyan, 2019. "Stochastic resonance across bifurcations in an asymmetric system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1296-1312.
    14. Yang, Guidong & Xu, Wei & Gu, Xudong & Huang, Dongmei, 2016. "Response analysis for a vibroimpact Duffing system with bilateral barriers under external and parametric Gaussian white noises," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 125-135.
    15. Wu, Juan & Xu, Yong & Ma, Shaojuan, 2019. "Realizing the transformation of logic gates in a genetic toggle system under Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 171-179.

    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:122:y:2019:i:c:p:179-188. 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.