IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v174y2023ics0960077923007816.html
   My bibliography  Save this article

Auto-parametric resonance of flexible viscoelastic beams under interaction between longitudinal and transverse modes

Author

Listed:
  • Jin, Qiduo
  • Yuan, Fuh-Gwo
  • Ren, Yiru

Abstract

For a system encompassing subsystems, dynamic modal interaction may experience unanticipated vibrations among subsystems that are excited indirectly. This paper focuses attention to a nonlinear auto-parametric resonance phenomenon of a flexible beam introduced via modal coupling of longitudinal forced resonance and transverse parametric resonance under longitudinal pulsatile excitation. The coupled resonance equations are first modeled based on the Euler-Bernoulli beam theory by incorporating nonlinear curvature, von Kármán's nonlinear strain-displacement relationship and the flexible beam model characterizing nonlinear inertia and displacement interaction. The Galerkin truncation-incremental harmonic balance method (IHBM) is then introduced to obtain both the stability boundary and amplitude-frequency bifurcation maps. Through the corresponding relationship between stability boundary and bifurcation diagram, the energy exchange between two modes is identified as well as the instability region and bifurcation topology can be tuned. It is found that the modal interaction greatly widens the instability region with at most two resonance bands of lateral resonance. By tuning structural and foundation damping, resonance can be controlled to occur only in one frequency band of the pair as desired. This research provides guidance to design broadband energy harvesting or vibration suppression equipment with tunable working frequency band for using the strategy of auto-parametric resonance.

Suggested Citation

  • Jin, Qiduo & Yuan, Fuh-Gwo & Ren, Yiru, 2023. "Auto-parametric resonance of flexible viscoelastic beams under interaction between longitudinal and transverse modes," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923007816
    DOI: 10.1016/j.chaos.2023.113880
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923007816
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113880?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. Cabanas, Ana M. & Rivas, Ronald & Pérez, Laura M. & Vélez, Javier A. & Díaz, Pablo & Clerc, Marcel G. & Pleiner, Harald & Laroze, David & Malomed, Boris A., 2021. "A quasi-periodic route to chaos in a parametrically driven nonlinear medium," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    2. Zhang, Wei & Yao, Minghui, 2006. "Multi-pulse orbits and chaotic dynamics in motion of parametrically excited viscoelastic moving belt," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 42-66.
    3. Gzal, M. & Kislovsky, V. & Hasan, M.A. & Starosvetsky, Y., 2023. "Analysis of the response of damped and parametrically driven, strongly anharmonic Klein-Gordon chain - Part 1: Phase locked traveling breathers," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    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. Chen, Li-Qun & Zhang, Wei & Zu, Jean W., 2009. "Nonlinear dynamics for transverse motion of axially moving strings," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 78-90.
    2. Yang, Shaopu & Shen, Yongjun, 2009. "Recent advances in dynamics and control of hysteretic nonlinear systems," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1808-1822.
    3. Ali, Muhammad Aown & Chaudhary, Naveed Ishtiaq & Khan, Taimoor Ali & Mao, Wei-Lung & Lin, Chien-Chou & Raja, Muhammad Asif Zahoor, 2024. "Design of key term separated identification model for fractional input nonlinear output error systems: Auxiliary model based Runge Kutta optimization algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    4. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Alquhayz, Hani & Abdalla, Manal Z.M. & Alhagyan, Mohammed & Gargouri, Ameni & Shoaib, Muhammad, 2023. "Design of intelligent hybrid NAR-GRNN paradigm for fractional order VDP chaotic system in cardiac pacemaker with relaxation oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    5. Luo, Bin & Xiao, Yang & Chen, Zhigang & Zhu, Kejun & Lu, Hanjing, 2024. "Emergence of chaos in an electroactive artificial muscle PVC gel under state-varying electromechanical parameters," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    6. Gzal, Majdi & Kislovsky, Victor & Starosvetsky, Yuli, 2024. "Emergence of relaxation beat-waves in genuinely nonlinear Klein-Gordon chain with bi-harmonic parametric excitation," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    7. 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.
    8. Xie, Mengxue & Hu, Yuda, 2025. "Bifurcation and chaos in axially moving ferromagnetic thin plates with imperfections under magnetic field and line load," Chaos, Solitons & Fractals, Elsevier, vol. 190(C).
    9. Reyes, L.I. & Pérez, L.M. & Pedraja-Rejas, L. & Díaz, P. & Mendoza, J. & Bragard, J. & Clerc, M.G. & Laroze, D., 2024. "Characterization of Faraday patterns and spatiotemporal chaos in parametrically driven dissipative systems," Chaos, Solitons & Fractals, Elsevier, vol. 186(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:chsofr:v:174:y:2023:i:c:s0960077923007816. 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.