High-Order Energy Balance Method to Nonlinear Oscillators


Creative Commons License

Durmaz S., Kaya M. O.

JOURNAL OF APPLIED MATHEMATICS, vol.2012, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2012
  • Publication Date: 2012
  • Doi Number: 10.1155/2012/518684
  • Journal Name: JOURNAL OF APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Istanbul Technical University Affiliated: Yes

Abstract

Energy balance method (EBM) is extended for high-order nonlinear oscillators. To illustrate the effectiveness of the method, a cubic-quintic Duffing oscillator was chosen. The maximum relative errors of the frequencies of the oscillator read 1.25% and 0.6% for the first- and second-order approximation, respectively. The third-order approximation has an accuracy as high as 0.008%. Excellent agreement of the approximated frequencies and periodic solutions with the exact ones is demonstrated for several values of parameters of the oscillator.