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, cilt.61, sa.3, ss.578-585, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 61 Sayı: 3
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1016/j.camwa.2010.12.003
  • Dergi Adı: COMPUTERS & MATHEMATICS WITH APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.578-585
  • Anahtar Kelimeler: 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
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

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.