Study on high performance averaging method for systems based on duffing equation with strong nonlinearity (in cases that the Jacobian elliptic sine and delta functions are used)

Tadashi Okabe, Takahiro Kondou, Shinji Hamao

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The improved averaging method suggested in our previous report is developed in order to obtain a highly accurate periodic solution for a strongly nonlinear system. In this reports, the Jacobian elliptic sine and delta functions are applied as generating solutions for harmonically excited Duffing-type equations with softening spring and snap through spring, respectively. Two types of stability criterion for approximate solutions obtained by the present method are also discussed. The present method is applied to the systems with some kind of nonlinear spring. By comparing with the very accurate numerical solutions obtained by applying the shooting method, it is confirmed that the present method gives more accurate solution and more accurate results for stability of the solution than those obtained by the traditional averaging method using the trigonometric function as a generating solution.

Original languageEnglish
Pages (from-to)312-319
Number of pages8
JournalNippon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C
Volume69
Issue number2
Publication statusPublished - Feb 1 2003

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Delta functions
Stability criteria
Nonlinear systems

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering

Cite this

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