Approximate analytical solutions to nonlinear oscillations via semi-analytical method

Ismail, Gamal M.; Kamel, Alwaleed; Alsarrani, Abdulaziz

doi:10.1016/j.aej.2024.04.040

Alexandria Engineering Journal

2024

DOI: 10.1016/j.aej.2024.04.040

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Approximate analytical solutions to nonlinear oscillations via semi-analytical method

Gamal M. Ismail,

Alwaleed Kamel,

Abdulaziz Alsarrani

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2024

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Approximate Analytic Frequency of Strong Nonlinear Oscillator

Cveticanin,

Zukovic,

Cveticanin

2024

Mathematics

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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.

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Approximate Analytic Frequency of Strong Nonlinear Oscillator

Cveticanin,

Zukovic,

Cveticanin

2024

Mathematics

View full text Add to dashboard Cite

show abstract

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Approximate analytical solutions to nonlinear oscillations via semi-analytical method

Cited by 1 publication

References 26 publications

Approximate Analytic Frequency of Strong Nonlinear Oscillator

Approximate Analytic Frequency of Strong Nonlinear Oscillator

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