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The damping Helmholtz–Rayleigh–Duffing oscillator with the non-perturbative approach

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  • El-Dib, Yusry O.

Abstract

The present study suggests a very simple, effective new method to study the damping quadratic–cubic nonlinear oscillation in physical phenomena such as fluid, solid-state physics, optics, plasma physics, dispersion, and convection systems with no perturbation. The damping nonlinear oscillation is converted to its equivalent linear oscillation. The exact solution of the corresponding linear oscillation is verified by the first-order homotopy perturbation method which shows an exact agreement. Stability conditions are imposed from the frequency formula. The accuracy of the proposed approach has shown that the approximate analytical solutions are in excellent agreement with the corresponding exact solutions.

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  • El-Dib, Yusry O., 2022. "The damping Helmholtz–Rayleigh–Duffing oscillator with the non-perturbative approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 552-562.
    • Handle: RePEc:eee:matcom:v:194:y:2022:i:c:p:552-562
    DOI: 10.1016/j.matcom.2021.12.014
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    References listed on IDEAS

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    1. El-Dib, Yusry O., 2021. "Homotopy perturbation method with rank upgrading technique for the superior nonlinear oscillation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 555-565.
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    Cited by:

    1. El-Dib, Yusry O. & Elgazery, Nasser S., 2022. "A novel pattern in a class of fractal models with the non-perturbative approach," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Wei, Mengke & Han, Xiujing, 2024. "Fast–slow dynamics related to sharp transition behaviors in the Rayleigh oscillator with two slow square wave excitations," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    3. Sivashankar, M. & Sabarinathan, S. & Nisar, Kottakkaran Sooppy & Ravichandran, C. & Kumar, B.V. Senthil, 2023. "Some properties and stability of Helmholtz model involved with nonlinear fractional difference equations and its relevance with quadcopter," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

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