IDEAS home Printed from https://ideas.repec.org/a/gam/jjopen/v6y2023i1p10-151d1084073.html
   My bibliography  Save this article

Approximate Solutions for Undamped Nonlinear Oscillations Using He’s Formulation

Author

Listed:
  • Stylianos Vasileios Kontomaris

    (Faculty of Engineering and Architecture, Metropolitan College, 15125 Athens, Greece
    BioNanoTec Ltd., 2404 Nicosia, Cyprus)

  • Georgios Chliveros

    (Faculty of Engineering and Architecture, Metropolitan College, 15125 Athens, Greece)

  • Anna Malamou

    (Radar Systems and Remote Sensing Lab, School of Electrical & Computer Engineering, National Technical University of Athens, 15780 Athens, Greece)

Abstract

Solving nonlinear oscillations is a challenging task due to the mathematical complexity of the related differential equations. In many cases, determining the oscillation’s period requires the solution of complicated integrals using numerical methods. To avoid the complexity, there are many empirical equations in the literature that can be used instead of rigorous mathematical analysis to provide an acceptable approximation. In this paper, a recently developed method, He’s formulation, is applied to find the period in many different cases of nonlinear oscillators. The cases are those of the Duffing equation, the Helmholtz nonlinear oscillator, the simple pendulum and the case of a vertical oscillation under the influence of a nonlinear elastic force. The results of the method are accurate; thus, He’s formulation is a strong tool for solving nonlinear oscillations.

Suggested Citation

  • Stylianos Vasileios Kontomaris & Georgios Chliveros & Anna Malamou, 2023. "Approximate Solutions for Undamped Nonlinear Oscillations Using He’s Formulation," J, MDPI, vol. 6(1), pages 1-12, February.
    • Handle: RePEc:gam:jjopen:v:6:y:2023:i:1:p:10-151:d:1084073
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2571-8800/6/1/10/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2571-8800/6/1/10/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. L. Cveticanin & U. Kozmidis Luburic & Gy. Mester, 2018. "Periodic Motion in an Excited and Damped Cubic Nonlinear Oscillator," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-6, June.
    2. Cveticanin, L., 2003. "Analytic solution of the system of two coupled differential equations with the fifth-order non-linearity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 317(1), pages 83-94.
    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. Weaam Alhejaili & Alvaro H. Salas & Samir A. El-Tantawy, 2023. "Ansatz and Averaging Methods for Modeling the (Un)Conserved Complex Duffing Oscillators," Mathematics, MDPI, vol. 11(9), pages 1-12, April.
    2. Weaam Alhejaili & Alvaro H. Salas & Samir A. El-Tantawy, 2022. "Analytical and Numerical Study on Forced and Damped Complex Duffing Oscillators," Mathematics, MDPI, vol. 10(23), pages 1-13, November.

    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:gam:jjopen:v:6:y:2023:i:1:p:10-151:d:1084073. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.