An Energy Conservation Algorithm for Nonlinear Dynamic Equation
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 st...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/453230 |
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| author | Jian Pang Yu Du Ping Hu Weidong Li Z. D. Ma |
| author_facet | Jian Pang Yu Du Ping Hu Weidong Li Z. D. Ma |
| author_sort | Jian Pang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2fc5fa367e2448838f1356433006ae1f |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-2fc5fa367e2448838f1356433006ae1f2025-08-20T02:07:57ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/453230453230An Energy Conservation Algorithm for Nonlinear Dynamic EquationJian Pang0Yu Du1Ping Hu2Weidong Li3Z. D. Ma4Changan Auto Global R&D Center, State Key Laboratory of Vehicle NVH and Safety Technology, Chongqing 401120, ChinaSchool of Automotive Engineering, Dalian University of Technology, Dalian 116024, ChinaSchool of Automotive Engineering, Dalian University of Technology, Dalian 116024, ChinaSchool of Automotive Engineering, Dalian University of Technology, Dalian 116024, ChinaCollege of Engineering, University of Michigan, Ann Arbor, MI 48109-2133, USAAn 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.http://dx.doi.org/10.1155/2012/453230 |
| spellingShingle | Jian Pang Yu Du Ping Hu Weidong Li Z. D. Ma An Energy Conservation Algorithm for Nonlinear Dynamic Equation Journal of Applied Mathematics |
| title | An Energy Conservation Algorithm for Nonlinear Dynamic Equation |
| title_full | An Energy Conservation Algorithm for Nonlinear Dynamic Equation |
| title_fullStr | An Energy Conservation Algorithm for Nonlinear Dynamic Equation |
| title_full_unstemmed | An Energy Conservation Algorithm for Nonlinear Dynamic Equation |
| title_short | An Energy Conservation Algorithm for Nonlinear Dynamic Equation |
| title_sort | energy conservation algorithm for nonlinear dynamic equation |
| url | http://dx.doi.org/10.1155/2012/453230 |
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