Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/9620
Title: A predict-correct numerical integration scheme for solving nonlinear dynamic equations
Authors: Fan, J
Huang, T
Tang, CY 
Wang, C
Keywords: Bifurcation
Direct integration method
Internal resonance
Jumping phenomenon
Nonlinear dynamics
Saturation phenomenon
Issue Date: 2006
Publisher: Huazhong University of Science and Technology
Source: Acta mechanica solida sinica, 2006, v. 19, no. 4, p. 289-296 How to cite?
Journal: Acta mechanica solida Sinica 
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.
URI: http://hdl.handle.net/10397/9620
ISSN: 0894-9166
EISSN: 1860-2134
DOI: 10.1007/s10338-006-0635-3
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