Approximate solutions for nonlinear oscillation of a mass attached to a stretched elastic wire


Durmaz S., Altay Demirbağ S., Kaya M. O.

COMPUTERS & MATHEMATICS WITH APPLICATIONS, vol.61, no.3, pp.578-585, 2011 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 61 Issue: 3
  • Publication Date: 2011
  • Doi Number: 10.1016/j.camwa.2010.12.003
  • Journal Name: COMPUTERS & MATHEMATICS WITH APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.578-585
  • Keywords: Nonlinear oscillator, He's max-min approach, He's frequency-amplitude method, Parameter-expansion method, HOMOTOPY-PERTURBATION METHOD, VARIATIONAL ITERATION METHOD, FREQUENCY-AMPLITUDE FORMULATION, HIGHER-ORDER APPROXIMATIONS, PARAMETER-EXPANSION METHOD, MAX-MIN APPROACH, MUSICAL SCALES, EQUATIONS, FORCE, DISCONTINUITIES

Abstract

In this paper, the approximate solutions of the mathematical model of a mass attached to a stretched elastic wire are presented. At the beginning of the study, the equation of motion is derived in a detailed way. He's max-min approach, He's frequency-amplitude method and the parameter-expansion method are implemented to solve the established model. The numerical results are further compared with the approximate analytical solutions for both a small and large amplitude of oscillations, and a very good agreement is observed. The relative errors are computed to illustrate the strength of agreement between the numerical and approximate analytical results. (C) 2010 Elsevier Ltd. All rights reserved.