IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i6p937-d1610415.html
   My bibliography  Save this article

Vibration of the Liénard Oscillator with Quadratic Damping and Constant Excitation

Author

Listed:
  • Livija Cveticanin

    (Faculty of Technical Sciences, University of Novi Sad, 21000 Novi Sad, Serbia)

  • Nicolae Herisanu

    (Department of Mechanics and Strength of Materials, University Politehnica Timisoara, 300222 Timisoara, Romania)

  • Gamal Mohamed Ismail

    (Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia
    Department of Mathematics, Faculty of Science, Sohag University, Sohag 82534, Egypt)

  • Miodrag Zukovic

    (Faculty of Technical Sciences, University of Novi Sad, 21000 Novi Sad, Serbia)

Abstract

In this paper, the Liénard oscillator with nonlinear deflection, quadratic damping, and constant excitation is considered. In general, there is no analytic solution for the Liénard equation. However, for certain parameter values, the exact analytic solution exists and has the form of the Ateb function. In addition, for the oscillator with weakly perturbed parameters, the approximate analytic solution is obtained. For the considered Liénard equation, independently of parameter values, the first integral is found. The main advantage of the first integral is that after simple analysis and without solving the equation of motion, it gives important data about oscillation: the dependence of vibration on initial conditions and on the variation of the constant of excitation. In addition, by integration of the first integral, the period of vibration follows. The results of the research on the Liénard equation are applied for optimization of the properties of a sieve in the process industry. For the sieve with mass variation, dependent on the displacement function, the influence of excitation force on the system vibration is analyzed, and the optimal value is suggested.

Suggested Citation

  • Livija Cveticanin & Nicolae Herisanu & Gamal Mohamed Ismail & Miodrag Zukovic, 2025. "Vibration of the Liénard Oscillator with Quadratic Damping and Constant Excitation," Mathematics, MDPI, vol. 13(6), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:6:p:937-:d:1610415
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/6/937/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/6/937/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Livija Cveticanin & Nicolae Herisanu & Ivona Ninkov & Mladen Jovanovic, 2022. "New Closed-Form Solution for Quadratic Damped and Forced Nonlinear Oscillator with Position-Dependent Mass: Application in Grafted Skin Modeling," Mathematics, MDPI, vol. 10(15), pages 1-15, July.
    2. L. Cveticanin & T. Pogány, 2012. "Oscillator with a Sum of Noninteger-Order Nonlinearities," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-20, February.
    3. L. Cveticanin & T. Pogány, 2012. "Oscillator with a Sum of Noninteger‐Order Nonlinearities," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    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. Andriy Andrukhiv & Mariia Sokil & Bohdan Sokil & Solomiia Fedushko & Yuriy Syerov & Vincent Karovic & Tetiana Klynina, 2021. "Influence of Impulse Disturbances on Oscillations of Nonlinearly Elastic Bodies," Mathematics, MDPI, vol. 9(8), pages 1-13, April.
    2. Livija Cveticanin, 2023. "Exact Closed-Form Solution for the Oscillator with a New Type of Mixed Nonlinear Restitution Force," Mathematics, MDPI, vol. 11(3), pages 1-11, January.
    3. Livija Cveticanin & Miodrag Zukovic & Dragan Cveticanin, 2024. "Approximate Analytic Frequency of Strong Nonlinear Oscillator," Mathematics, MDPI, vol. 12(19), pages 1-17, September.

    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:jmathe:v:13:y:2025:i:6:p:937-:d:1610415. 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.