ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Approximate Analytical Solutions of A Nonlinear Oscillator Equation Modeling A Constrained Mechanical System

Journal of Applied Nonlinear Dynamics 6(1) (2017) 17--26 | DOI:10.5890/JAND.2017.03.002

Serge Bruno Yamgoué$^{1}$; Bonaventure Nana$^{1}$; François Beceau Pelap$^{2}$

$^{1}$ Department of Physics, Higher Teacher Training College Bambili, The University of Bamenda, P.O. Box 39 Bamenda, CAMEROON

$^{2}$ Laboratoire de Mécanique et de Mod´elisation des Systèmes Physiques (L2MSP), Département de Physique, Université de Dschang, BP 69 Dschang, CAMEROUN

Abstract

In this paper, we consider a class of nonlinear oscillators whose equations of motion are in the form of that of a cubic Duffing oscillator extended by a term which is a quadratic monomial in the velocity and whose coefficient is a rational function of the position. We apply a combination of harmonic balance and Newton method to seek analytical approximations to the periodic solutions to the equation. The analysis can be applied directly to the equation in its "natural" rational form or after reducing it to the same denominator and considering only the numerator. The advantages and drawback of these two usages of the method are also discussed.

Acknowledgments

We express our gratitude to the anonymous reviewers for drawing our attention to several relevant bibliographical papers used in this work.

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