IDEAS home Printed from https://ideas.repec.org/a/hin/jnlmpe/8875589.html
   My bibliography  Save this article

An Exact Solution to the Quadratic Damping Strong Nonlinearity Duffing Oscillator

Author

Listed:
  • Alvaro H. Salas
  • S. A. El-Tantawy
  • Noufe H. Aljahdaly

Abstract

The nonlinear equations of motion such as the Duffing oscillator equation and its family are seldom addressed in intermediate instruction in classical dynamics; this one is problematic because it cannot be solved in terms of elementary functions before. Thus, in this work, the stability analysis of quadratic damping higher-order nonlinearity Duffing oscillator is investigated. Hereinafter, some new analytical solutions to the undamped higher-order nonlinearity Duffing oscillator in the form of Weierstrass elliptic function are obtained. Posteriorly, a novel exact analytical solution to the quadratic damping higher-order nonlinearity Duffing equation under a certain condition (not arbitrary initial conditions) and in the form of Weierstrass elliptic function is derived in detail for the first time. Furthermore, the obtained solutions are camped to the Runge–Kutta fourth-order (RK4) numerical solution.

Suggested Citation

  • Alvaro H. Salas & S. A. El-Tantawy & Noufe H. Aljahdaly, 2021. "An Exact Solution to the Quadratic Damping Strong Nonlinearity Duffing Oscillator," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-8, January.
    • Handle: RePEc:hin:jnlmpe:8875589
    DOI: 10.1155/2021/8875589
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/MPE/2021/8875589.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/MPE/2021/8875589.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2021/8875589?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ali, Irfan & Masood, W. & Rizvi, H. & Alrowaily, Albandari W. & Ismaeel, Sherif M.E. & El-Tantawy, S.A., 2023. "Archipelagos, islands, necklaces, and other exotic structures in external force-driven chaotic dusty plasmas," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Noufe H. Aljahdaly & S. A. El-Tantawy, 2021. "On the Multistage Differential Transformation Method for Analyzing Damping Duffing Oscillator and Its Applications to Plasma Physics," Mathematics, MDPI, vol. 9(4), pages 1-12, February.
    3. Çayan, Seda & Özhan, B. Burak & Sezer, Mehmet, 2022. "A Taylor-Splitting Collocation approach and applications to linear and nonlinear engineering models," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

    More about this item

    Statistics

    Access and download statistics

    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:hin:jnlmpe:8875589. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    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.