Abstract
Based on the Bridges' 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.
| Original language | English |
|---|---|
| Pages (from-to) | 8-13 |
| Number of pages | 6 |
| Journal | Jisuan Lixue Xuebao/Chinese Journal of Computational Mechanics |
| Volume | 27 |
| Issue number | 1 |
| State | Published - Feb 2010 |
Keywords
- Longitudinal oscillation
- Multi-symplectic
- Nonlinear elastic rod
- Numerical simulation