TY  - EJOU
AU  - El-Dib, Yusry O. 
AU  - Elgazery, Nasser S. 

TI  - Damped Mathieu Equation with a Modulation Property of the Homotopy Perturbation Method
T2  - Sound \& Vibration

PY  - 2022
VL  - 56
IS  - 1
SN  - 2693-1443

AB  - 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.
KW  - Damped Mathieu Equation; parametric nonlinear oscillator; resonance instability; homotopy perturbation method (HPM)

DO  - 10.32604/sv.2022.014166