@Article{sv.2022.014166,
AUTHOR = {Yusry O. El-Dib, Nasser S. Elgazery},
TITLE = {Damped Mathieu Equation with a Modulation Property of the Homotopy Perturbation Method},
JOURNAL = {Sound \& Vibration},
VOLUME = {56},
YEAR = {2022},
NUMBER = {1},
PAGES = {21--36},
URL = {http://www.techscience.com/sv/v56n1/46218},
ISSN = {2693-1443},
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.},
DOI = {10.32604/sv.2022.014166}
}