Applied Mathematics

Volume 11, Issue 11 (November 2020)

ISSN Print: 2152-7385   ISSN Online: 2152-7393

Google-based Impact Factor: 0.83  Citations  

The Vibrational Motion of a Dynamical System Using Homotopy Perturbation Technique

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DOI: 10.4236/am.2020.1111073    97 Downloads   206 Views  

ABSTRACT

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.

Cite this paper

Amer, T. , Galal, A. and Elnaggar, S. (2020) The Vibrational Motion of a Dynamical System Using Homotopy Perturbation Technique. Applied Mathematics, 11, 1081-1099. doi: 10.4236/am.2020.1111073.

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