首页 | 本学科首页   官方微博 | 高级检索  
     

三类保辛摄动及其数值比较
引用本文:钟万勰,孙雁. 三类保辛摄动及其数值比较[J]. 动力学与控制学报, 2005, 3(2): 1-9
作者姓名:钟万勰  孙雁
作者单位:大连理工大学工程力学系,大连,116023;上海交通大学工程力学系,上海,200030;上海交通大学工程力学系,上海,200030
基金项目:中国科学院资助项目;高等学校博士学科点专项科研项目
摘    要:摄动法近似应当保辛.本文指出,有限元位移法自动保辛,有限元混合能表示也保辛.摄动法的刚度阵Taylor级数展开能证明保辛;混合能的Taylor级数展开摄动也证明了保辛.但传递辛矩阵的Taylor级数展开摄动却不能保辛.辛矩阵只能在乘法群下保辛,故传递辛矩阵的保辛摄动必须采用正则变换的乘法.虽然刚度阵加法摄动、混合能矩阵加法摄动与传递辛矩阵正则变换乘法摄动都保辛,但这3种摄动近似并不相同.最后通过数值例题给出了对比.

关 键 词:摄动法  保辛摄动  有限元刚度阵摄动法  混合能矩阵摄动  传递辛矩阵保辛摄动
收稿时间:2005-01-20
修稿时间:2005-01-20

Numerical comparison for three different symplectic perturbation methods
Zhong Wanxie and Sun Yan. Numerical comparison for three different symplectic perturbation methods[J]. Journal of Dynamics and Control, 2005, 3(2): 1-9
Authors:Zhong Wanxie and Sun Yan
Abstract:The perturbation approximation should be symplectic conservative. The FEM displacement method is naturally symplectic conservative, the mixed energy representation is also shown symplectic conservative. The stiffness matrix, as well as the mixed energy matrix, perturbations based on the Taylor series expansion are all proved symplectic conservative. However, the Taylor series expansion perturbation for the symplectic transfer matrix is not able to reach symplectic conservative. The symplectic conservative perturbation for a transfer symplectic matrix should be based on the canonical transformation method. Although, the perturbation methods of the stiffness matrix, of the mixed energy matrix and of the transfer symplectic matrix multiplicative perturbation are all symplectic conservative, however, they are not identical. Therefore, numerical comparison is given for an example.
Keywords:perturbation method  symplectic conserved perturbation  FEM perturbation  mixed energy matrix perturbation  transfer matrix symplectic conserved perturbation method
本文献已被 CNKI 维普 万方数据 等数据库收录!
点击此处可从《动力学与控制学报》浏览原始摘要信息
点击此处可从《动力学与控制学报》下载全文
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号