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Journal of Applied Mathematics
Volume 2012, Article ID 453230, 18 pages
Research Article

An Energy Conservation Algorithm for Nonlinear Dynamic Equation

1Changan Auto Global R&D Center, State Key Laboratory of Vehicle NVH and Safety Technology, Chongqing 401120, China
2School of Automotive Engineering, Dalian University of Technology, Dalian 116024, China
3State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116024, China
4College of Engineering, University of Michigan, Ann Arbor, MI 48109-2133, USA

Received 14 July 2011; Revised 19 October 2011; Accepted 27 October 2011

Academic Editor: Ferenc Hartung

Copyright © 2012 Jian Pang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An energy conservation algorithm for numerically solving nonlinear multidegree-of-freedom (MDOF) dynamic equations is proposed. Firstly, by Taylor expansion and Duhamel integration, an integral iteration formula for numerically solving the nonlinear problems can be achieved. However, this formula still includes a parameter that is to be determined. Secondly, through some mathematical manipulations, the original dynamical equation can be further converted into an energy conservation equation which can then be used to determine the unknown parameter. Finally, an accurate numerical result for the nonlinear problem is achieved by substituting this parameter into the integral iteration formula. Several examples are used to compare the current method with the well-known Runge-Kutta method. They all show that the energy conservation algorithm introduced in this study can eliminate algorithm damping inherent in the Runge-Kutta algorithm and also has better stability for large integral steps.