弹性杆纵波弥散效应数值分析

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振动与冲击 ›› 2011, Vol. 30 ›› Issue (6) : 83-85.

论文

弹性杆纵波弥散效应数值分析

胡秦1; 韩爱红2

作者信息 +

Numerical Analysis on the Dispersion Effect of the Longitudinal Wave in Elastic Bar

Qin Hu1 ; Aihong Han2

Author information +

文章历史 +

摘要

弹性杆中的纵波弥散效应一直是力学界研究的热点问题之一。本文基于Hamiltonian体系变分原
理和Bridges多辛理论采用数值手段研究了弹性杆中纵波的弥散效应。通过引入正交动量，将用以描述计入
弥散效应的线弹性杆中的纵波运动方程转化为满足多种局部守恒律的标准多辛形式，并构造了相应的中点
多辛离散格式。数值试验结果一方面再现了线弹性杆中纵波传播的弥散效应，另一方面也充分体现了多辛
方法能够长时间地保持纵波的局部能量和局部动量特征这一优点

Abstract

In Hamiltonian space, the dispersion effect of the longitudinal wave in elastic bar
is investigated by multi-symplectic method. The multi-symplectic formulations and several local
conservation laws (including the multi-symplectic conservation law, the local energy conservation
law and the local momentum conservation law) of the longitudinal wave equation that describes
the dispersion effect in elastic bar are presented firstly. Then the multi-symplectic midpoint
scheme is constructed to solve the multi-symplectic partial differential equations that are derived
from the longitudinal wave equation. The numerical experiments are also reported finally, the
results of which show that the multi-symplectic scheme can simulate the dispersion effect of the
longitudinal wave in elastic bar well. In addition, the multi-symplectic scheme can satisfy the local
conservation laws exactly, which implies that the multi-symplectic method is an efficient
algorithm with excellent long-time numerical behaviors

导出引用

胡秦;韩爱红. 弹性杆纵波弥散效应数值分析[J]. 振动与冲击, 2011, 30(6): 83-85

Qin Hu;Aihong Han. Numerical Analysis on the Dispersion Effect of the Longitudinal Wave in Elastic Bar [J]. Journal of Vibration and Shock, 2011, 30(6): 83-85