The Vibrational Motion of a Dynamical System Using Homotopy Perturbation Technique
The Vibrational Motion of a Dynamical System Using Homotopy Perturbation Technique作者机构：Mathematics Department Faculty of Science Tanta University Tanta Egypt Department of Physics and Engineering Mathematics Faculty of Engineering Tanta University Tanta Egypt Kafrelsheikh Higher Institute of Engineering and Technology Kafrelsheikh Egypt
出 版 物：《Applied Mathematics》 (应用数学（英文）)
年 卷 期：2020年第11卷第11期
页 面：1081-1099页
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Homotopy Technique Nonlinear Vibration Lagrange’s Equation Stability
摘 要：This paper outlines the vibrational motion of a nonlinear system with a spring of linear stiffness. Homotopy perturbation technique (HPT) is used to obtain the asymptotic solution of the governing equation of motion. The numerical solution of this equation is obtained using the fourth order Runge-Kutta method (RKM). The comparison between both solutions reveals high consistency between them which confirms that, the accuracy of the obtained solution using aforementioned perturbation technique. The time history of the attained solution is represented through some plots to reveal the good effect of the different parameters of the considered system on the motion at any instant. The conditions of the stability of the attained solution are presented and discussed.
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