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| Numerical simulation on the longitudinal wave in nonlinear elastic rod |
| Received:October 23, 2007 |
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| DOI：10.7511/jslx20101002 |
| KeyWord:numerical simulation multi-symplectic nonlinear elastic rod longitudinal oscillation equation |
| Author | Institution |
| 胡伟鹏 |
西北工业大学 力学与土木建筑学院,西安 |
| 韩爱红 |
华北水利水电学院,郑州 |
| 邓子辰 |
西北工业大学 力学与土木建筑学院,西安 ;大连理工大学 工业装备结构分析国家重点实验室,大连 |
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| Abstract: |
| Based on the Bridges's multi-symplectic theory in Hamiltonian space, the longitudinal oscillation in a nonlinear elastic rod with lateral inertia is investigated in this paper. The multi-symplectic formulations and several conservation laws of the longitudinal oscillation equation are presented firstly. Then the equivalent formula of the multi-symplectic Box scheme is constructed to solve the multi-symplectic partial differential equations that are derived from the longitudinal oscillation equation. Finally, the numerical simulations on the longitudinal oscillation equation in four different cases are also reported. The results showed that the dispersion effect as well as the material nonlinear effect of the longitudinal oscillation in a nonlinear elastic rod can be found clearly. In addition, from the results, we can conclude that the multi-symplectic method is an efficient algorithm with excellent long-time numerical behaviors. |
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