非线性弦振动方程的多辛算法  

MULTI-SYMPLECTIC METHOD FOR THE NONLINEAR VIBRATING STRING EQUATION

作　　者：胡伟鹏[1,2] 邓子辰[1,3] 韩松迎[4] 范玮[2] 

机构地区：[1]西北工业大学力学与土木建筑学院,西安710072 [2]西北工业大学动力与能源学院,西安710072 [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 [4]陕西理工学院材料科学与工程学院,汉中723003

出　　处：《动力学与控制学报》2009年第2期104-107,共4页Journal of Dynamics and Control

基　　金：国家自然科学基金(10572119;10772147和10632030);高校博士点基金(20070699028);陕西省自然科学基金(2006A07);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资助项目~~

摘　　要：利用Hamiltonian空间体系下的多辛理论研究了非线性弦微小横向振动问题的数值解法。基于Bridges意义下的多辛积分理论,首先推导了非线性弦振动方程的一阶多辛偏微分方程组及其多种守恒律,随后构造了一种等价于Box多辛格式的新隐式多辛格式,最后,运用该多辛格式对非线性弦振动方程进行了数值模拟,并将模拟结果与吕克璞等人得到的解析解进行比较。数值实验结果显示利用本文构造的多辛格式得到的数值解与吕克璞等人得到的解析解非常接近,这说明该多辛格式能够较为精确地模拟非线性弦振动问题,同时数值结果也反映出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＇ multi-symplectic theory in Hamihonian space, the longitudinal oscillation in a nonlinear elastic string was investigated. Firstly, the multi-symplectic formulations and several conservation laws of the longitudinal oscillation equation were presented. Then, a new equivalent formula of the multi-symplectic Box scheme was constructed. Finally, the numerical experiments on the longitudinal oscillation equation were also reported. The results are in good agreement with the exact solution obtained by Lu et al, which implies that the scheme can simulate the nonlinear elastic string vibration problem accurately. In addition, from the results, we can conclude that the multi-symplectic method is an efficient algorithm with excellent long-time numerical behaviors.

关 键 词：多辛积分 非线性弦 守恒律 

分 类 号：O322[理学—一般力学与力学基础]