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Damped Mathieu Equation with a Modulation Property of the Homotopy Perturbation Method

Yusry O. El-Dib, Nasser S. Elgazery*

Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt

* Corresponding Author: Nasser S. Elgazery. Email: email

(This article belongs to the Special Issue: Analytical Methods for Nonlinear Vibration & Active Control in Nano/Micro Devices and Systems)

Sound & Vibration 2022, 56(1), 21-36. https://doi.org/10.32604/sv.2022.014166

Abstract

In this article, the main objective is to employ the homotopy perturbation method (HPM) as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients. As a simple example, the nonlinear damping Mathieu equation has been investigated. In this investigation, two nonlinear solvability conditions are imposed. One of them was imposed in the first-order homotopy perturbation and used to study the stability behavior at resonance and non-resonance cases. The next level of the perturbation approaches another solvability condition and is applied to obtain the unknowns become clear in the solution for the first-order solvability condition. The approach assumed here is so significant for solving many parametric nonlinear equations that arise within the engineering and nonlinear science.

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APA Style
El-Dib, Y.O., Elgazery, N.S. (2022). Damped mathieu equation with a modulation property of the homotopy perturbation method. Sound & Vibration, 56(1), 21-36. https://doi.org/10.32604/sv.2022.014166
Vancouver Style
El-Dib YO, Elgazery NS. Damped mathieu equation with a modulation property of the homotopy perturbation method. Sound Vib . 2022;56(1):21-36 https://doi.org/10.32604/sv.2022.014166
IEEE Style
Y.O. El-Dib and N.S. Elgazery, “Damped Mathieu Equation with a Modulation Property of the Homotopy Perturbation Method,” Sound Vib. , vol. 56, no. 1, pp. 21-36, 2022. https://doi.org/10.32604/sv.2022.014166

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cc Copyright © 2022 The Author(s). Published by Tech Science Press.
This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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