非线性弹性杆中纵波传播过程的数值模拟  

Numerical simulation on the longitudinal wave in nonlinear elastic rod

作　　者：胡伟鹏[1] 韩爱红[2] 邓子辰[1,3] 

机构地区：[1]西北工业大学力学与土木建筑学院,西安710072 [2]华北水利水电学院,郑州450011 [3]大连理工大学工业装备结构分析国家重点实验室,大连116023

出　　处：《计算力学学报》2010年第1期8-13,共6页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(10972182;10772147;10632030);高校博士点基金(20070699028);陕西省自然科学基金(2006A07);川引智计划项目(B07050);西北工业大学基础研究基金;大连理工大学工业装备结构分析国家重点实验室开放基金(GZ0802)资助项目

摘　　要：基于Hamilton空间体系的多辛理论研究了包含材料非线性效应和几何弥散效应的非线性弹性杆中纵波传播问题。导出了其Bridges意义下的多辛形式及其多种守恒律,并构造了等价于Box多辛格式的隐式多辛格式对不考虑材料非线性效应和几何弥散效应、只考虑材料非线性效应、只考虑几何弥散效应、同时考虑材料非线性效应和几何弥散效应四种情况下不同截面参数的圆杆中的纵波传播过程进行数值模拟,模拟结果不仅全面地反映了非线性效应和几何弥散效应对纵波传播的影响,而且也反映了多辛方法的两大优点:精确的保持多种守恒律和良好的长时间数值行为。Based on the Bridges＇s multi-symplectic tion in a nonlinear elastic rod with lateral inertia theory in Hamiltonian space, the longitudinal oscilla- is investigated in this paper. The multi-symplectic for- mulations 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-sym- plectic 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 repor- ted. The results showed that the dispersion effect as well as the material nonlinear effect of the longitu- dinal oscillation in a nonlinear elastic rod can be found clearly. In addition, from the results, we can con- clude that the multi-symplectic method is an efficient algorithm with excellent long-time numerical behaviors.

关 键 词：数值模拟 多辛 非线性弹性杆 纵波方程 

分 类 号：O322[理学—一般力学与力学基础] O241.8[理学—力学]