IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v194y2022icp552-562.html
   My bibliography  Save this article

The damping Helmholtz–Rayleigh–Duffing oscillator with the non-perturbative approach

Author

Listed:
  • El-Dib, Yusry O.

Abstract

The present study suggests a very simple, effective new method to study the damping quadratic–cubic nonlinear oscillation in physical phenomena such as fluid, solid-state physics, optics, plasma physics, dispersion, and convection systems with no perturbation. The damping nonlinear oscillation is converted to its equivalent linear oscillation. The exact solution of the corresponding linear oscillation is verified by the first-order homotopy perturbation method which shows an exact agreement. Stability conditions are imposed from the frequency formula. The accuracy of the proposed approach has shown that the approximate analytical solutions are in excellent agreement with the corresponding exact solutions.

Suggested Citation

  • El-Dib, Yusry O., 2022. "The damping Helmholtz–Rayleigh–Duffing oscillator with the non-perturbative approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 552-562.
    • Handle: RePEc:eee:matcom:v:194:y:2022:i:c:p:552-562
    DOI: 10.1016/j.matcom.2021.12.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475421004481
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2021.12.014?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. El-Dib, Yusry O., 2021. "Homotopy perturbation method with rank upgrading technique for the superior nonlinear oscillation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 555-565.
    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. Wei, Mengke & Han, Xiujing, 2024. "Fast–slow dynamics related to sharp transition behaviors in the Rayleigh oscillator with two slow square wave excitations," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. El-Dib, Yusry O. & Elgazery, Nasser S., 2022. "A novel pattern in a class of fractal models with the non-perturbative approach," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Sivashankar, M. & Sabarinathan, S. & Nisar, Kottakkaran Sooppy & Ravichandran, C. & Kumar, B.V. Senthil, 2023. "Some properties and stability of Helmholtz model involved with nonlinear fractional difference equations and its relevance with quadcopter," Chaos, Solitons & Fractals, Elsevier, vol. 168(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.

      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:matcom:v:194:y:2022:i:c:p:552-562. 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: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

      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.