Improvement to the averaging method using the Jacobian elliptic function

T. Okabe, T. Kondou

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


The averaging method was improved by using the Jacobian elliptic sine (sn), cosine (cn) and delta (dn) functions as generating solutions in order to obtain a highly accurate periodic solution for a strongly nonlinear dynamical system. The proposed method can be applied to a relatively general nonlinear system based on the single degree-of-freedom Duffing equation. Two methods of stability analysis were applied and evaluated for the approximate solutions obtained by the proposed method. The approximate solutions obtained by the proposed method for practical examples were compared to the solutions obtained by the shooting method. The results confirmed that the proposed method provides a more accurate solution and more accurate stability analysis results than those obtained by the conventional averaging method that uses trigonometric functions as the generating solution.

Original languageEnglish
Pages (from-to)339-364
Number of pages26
JournalJournal of Sound and Vibration
Issue number1-2
Publication statusPublished - Feb 6 2009

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Acoustics and Ultrasonics


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