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Approximate Analytic Frequency of Strong Nonlinear Oscillator

Author

Listed:
  • Livija Cveticanin

    (Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovica 6, 21000 Novi Sad, Serbia)

  • Miodrag Zukovic

    (Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovica 6, 21000 Novi Sad, Serbia)

  • Dragan Cveticanin

    (Remming, List Ferenca 2, 21480 Srbobran, Serbia)

Abstract

In this paper, a new analytic expression for the frequency of vibration of a strong nonlinear polynomial-type oscillator is introduced. The method for frequency calculation is based on the transformation of the nonlinear oscillators into linear ones using the equality of their amplitudes and periods of vibration. The frequency of the linear oscillator is assumed to be the sum of frequencies corresponding to each nonlinearity in the original oscillator separately, i.e., the sum of frequencies of truly nonlinear oscillators. The obtained frequency is a complex function of amplitude, coefficient and order of nonlinearity. For simplification, the frequencies of the truly nonlinear oscillators are modified as power order functions of the exact frequency of the cubic oscillator which is linearly dependent on the amplitude of vibration. In this paper, the approximate frequency expression is developed for the harmonic any-order nonlinear oscillator and oscillators with the sum of polynomial nonlinearities. The accuracy of the obtained frequencies is tested on the examples of non-integer order nonlinear oscillators and also on a quadratic-cubic oscillator. The difference between the analytical and exact, numerically obtained results is negligible. The suggested approximate frequency expression has a simple algebraic form and is suitable for application by engineers and technicians.

Suggested Citation

  • Livija Cveticanin & Miodrag Zukovic & Dragan Cveticanin, 2024. "Approximate Analytic Frequency of Strong Nonlinear Oscillator," Mathematics, MDPI, vol. 12(19), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3040-:d:1488170
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    References listed on IDEAS

    as
    1. L. Cveticanin & T. Pogány, 2012. "Oscillator with a Sum of Noninteger-Order Nonlinearities," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-20, February.
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