A predict-correct numerical integration scheme for solving nonlinear dynamic equations

Fan Jianping, Huang Tao, Tang Chak-yin, Wang Cheng

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)

Abstract

A new numerical integration scheme incorporating a predict-correct algorithm for solving the nonlinear dynamic systems was proposed in this paper. A nonlinear dynamic system governed by the equation {A figure is presented} = F(v, t) was transformed into the form as {A figure is presented} = Hv + f(v, t). The nonlinear part f (v, t) was then expanded by Taylor series and only the first-order term retained in the polynomial. Utilizing the theory of linear differential equation and the precise time-integration method, an exact solution for linearizing equation was obtained. In order to find the solution of the original system, a third-order interpolation polynomial of v was used and an equivalent nonlinear ordinary differential equation was regenerated. With a predicted solution as an initial value and an iteration scheme, a corrected result was achieved. Since the error caused by linearization could be eliminated in the correction process, the accuracy of calculation was improved greatly. Three engineering scenarios were used to assess the accuracy and reliability of the proposed method and the results were satisfactory.
Original languageEnglish
Pages (from-to)289-296
Number of pages8
JournalActa Mechanica Solida Sinica
Volume19
Issue number4
DOIs
Publication statusPublished - 1 Dec 2006

Keywords

  • bifurcation
  • direct integration method
  • internal resonance
  • jumping phenomenon
  • nonlinear dynamics
  • saturation phenomenon

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering

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