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Illustration of the homotopy perturbation method to the modified nonlinear single degree of freedom system

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  • Alim, Md. Abdul
  • Kawser, M. Abul

Abstract

Nonlinear Single degree of freedom (SDOF) systems are crucial for understanding the behavior of various real-world systems, designing and analyzing mechanical and dynamical systems. In this article we have modified the SDOF model by introducing the nonlinearity as well as damping with/without external force and applied the homotopy perturbation method (HPM) to explain its various phenomena. We have compared the analytical solutions obtained via the HPM to the provided numerical results by the fourth-order Runge-Kutta (RK4) method for verifying the precision and validity of the solutions. The presentation and explanation of the dynamic results can add a new dimension to the research field by influencing the importance of nonlinear SDOF systems.

Suggested Citation

  • Alim, Md. Abdul & Kawser, M. Abul, 2023. "Illustration of the homotopy perturbation method to the modified nonlinear single degree of freedom system," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    • Handle: RePEc:eee:chsofr:v:171:y:2023:i:c:s096007792300382x
    DOI: 10.1016/j.chaos.2023.113481
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    References listed on IDEAS

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    1. Biazar, J. & Ghazvini, H., 2009. "He’s homotopy perturbation method for solving systems of Volterra integral equations of the second kind," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 770-777.
    2. M. Abul Kawser & Md Abdul Alim & Marco Antonio Taneco Hern ndez, 2022. "Approximate Solutions of the Jet Engine Vibration Equation by the Homotopy Perturbation Method," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-7, December.
    3. Ji-Huan He & Man-Li Jiao & Chun-Hui He, 2022. "Homotopy Perturbation Method For Fractal Duffing Oscillator With Arbitrary Conditions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(09), pages 1-10, December.
    4. Wang, Meng & Tian, Bo & Zhou, Tian-Yu, 2021. "Darboux transformation, generalized Darboux transformation and vector breathers for a matrix Lakshmanan-Porsezian-Daniel equation in a Heisenberg ferromagnetic spin chain," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    5. He, Ji-Huan & Jiao, Man-Li & Gepreel, Khaled A. & Khan, Yasir, 2023. "Homotopy perturbation method for strongly nonlinear oscillators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 243-258.
    6. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
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    1. Huda J. Saeed & Ali Hasan Ali & Rayene Menzer & Ana Danca Poțclean & Himani Arora, 2023. "New Family of Multi-Step Iterative Methods Based on Homotopy Perturbation Technique for Solving Nonlinear Equations," Mathematics, MDPI, vol. 11(12), pages 1-13, June.

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