基于辛本征空间的线性阻尼振动系统动力学分析

李明武; 赵岩; 钟万勰

doi:10.3879/j.issn.1000-0887.2015.01.001

基于辛本征空间的线性阻尼振动系统动力学分析

doi: 10.3879/j.issn.1000-0887.2015.01.001

大连理工大学工程力学系;工业装备结构分析国家重点实验室(大连理工大学), 辽宁大连 116024

基金项目: 国家自然科学基金（面上项目）（11472067）；国家重点基础研究发展计划（973计划）（2014CB046803）

详细信息

作者简介:
李明武(1990—)，男，湖南浏阳人，硕士生(E-mail: limingwu0601@126.com);赵岩(1974—)，男，吉林公主岭人，副教授(通讯作者. E-mail: yzhao@dlut.edu.cn);钟万勰(1934—)，男，浙江德清人，教授，院士(E-mail: zwoffice@dlut.edu.cn).

中图分类号: O322
计量
- 文章访问数: 1664
- HTML全文浏览量: 133
- PDF下载量: 940
- 被引次数: 0
出版历程
- 收稿日期: 2014-09-17
- 修回日期: 2014-11-29
- 刊出日期: 2015-01-15

Dynamic Analysis of Linear Damped Systems With the Symplectic Eigenspace Expansion Method

State Key Laboratory of Structural Analysis for Industrial Equipment(Dalian University of Technology); Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China

Funds: The National Natural Science Foundation of China（General Program）（11472067）; The National Basic Research Program of China(973 Program)（2014CB046803）

摘要

摘要: 对于考虑阻尼项和陀螺项的一般线性动力学振动系统，建立基于辛本征空间展开求解的一般方法.基于Rayleigh商本征值的模态展开方法被广泛应用于复杂结构动力系统振动分析，但对于很多机械系统，由于其不能有效考虑陀螺效应的影响，其适用性却受到很大限制.该文首先讨论了无阻尼系统Rayleigh商本征值问题与辛本征值问题的对应关系，表明前者实际可由后者的一种退化形式给出（也即忽略陀螺效应），而后者更具有一般性.在此基础上，进一步基于辛本征空间本征向量展开，推导了同时考虑阻尼和陀螺系统的一般线性动力学系统的有效求解方法.数值算例选取不考虑陀螺效应及考虑陀螺效应的两种线性阻尼振动系统对所提出的方法进行了验证，分析结果表明了该文所建立方法的正确性和有效性.
- 阻尼系统 /
- 陀螺项 /
- Rayleigh商 /
- 辛本征值
Abstract: A symplectic eigenspace expansion method was proposed for the dynamic analysis of linear systems with damping and gyroscopic effect. The modal expansion method based on the Rayleigh quotient had been widely used in the dynamics of complex structures. However, the applicability of the modal expansion method was restricted since the gyroscopic effect was not taken into account. Herein, the relation between the Rayleigh quotient eigenvalue problems and the symplectic eigenvalue problems was established firstly. For these two types of problems, it was found that the latter was more general and can be reduced to the former through neglection of the gyroscopic effect. Then, the symplectic eigenspace expansion method was derived to conduct the dynamic analysis of linear damped gyroscopic systems. Finally, effectiveness of the proposed method is shown with the numerical examples of damped systems with and without gyroscopic effect simulated respectively.
- damped system /
- gyroscopic term /
- Rayleigh quotient /
- symplectic eigenvalue

HTML全文

参考文献(12)

[1]	Ziegler H.Principles of Structural Stability [M]. Waltham, MA: Blaisdell, 1968.
[2]	Timoshenko S, Young D H.Vibration Problems in Engineering [M]. 3rd ed. D. Van Nostrand Company, 1955.
[3]	Meirovitch L. A new method of solution of the eigenvalue problem for gyroscopic systems[J].AIAA Journal,1974,12(10): 1337-1342.
[4]	隋永枫. 转子动力学的求解辛体系及其数值计算方法[D]. 博士学位论文. 大连: 大连理工大学, 2005.(SUI Yong-feng. A sympletic systematic methodology for rotor dynamics and the corresponding numerical computational methods[D]. PhD Thesis. Dalian: Dalian University of Technology, 2005.(in Chinese))
[5]	钟万勰. 应用力学的辛数学方法[M]. 北京: 高等教育出版社, 2006.(ZHONG Wan-xie.Symplectic Method in Applied Mechanics [M]. Beijing: Higher Education Press, 2006.(in Chinese))
[6]	钟万勰, 高强, 彭海军. 经典力学辛讲[M]. 大连: 大连理工大学出版社, 2013.(ZHONG Wan-xie, GAO Qiang, PENG Hai-jun.Classical Mechanics-Its Symplectic Description [M]. Dalian: Dalian University of Technology Press, 2013.(in Chinese))
[7]	隋永枫, 钟万勰. 大型不正定陀螺系统本征值问题[J]. 应用数学和力学, 2006,27(1): 13-20.(SUI Yong-feng, ZHONG Wan-xie. Eigenvalue problem of a large scale indefinite gyroscopic dynamic system[J].Applied Mathematics and Mechanics,2006,27(1): 13-20.(in Chinese))
[8]	钟万勰. 结构动力方程的精细时程积分法[J]. 大连理工大学学报, 1994,34(2): 131-136.(ZHONG Wan-xie. On precise time-integration method for structural dynamics[J].Journal of Dalian University of Technology,1994,34(2): 131-136.(in Chinese))
[9]	汪梦甫, 周锡元. 结构动力方程的高斯精细时程积分法[J]. 工程力学, 2004,21(4): 13-16.(WANG Meng-fu, ZHOU Xi-yuan. Gauss precise time-integration of structural dynamic analysis[J].Engineering Mechanics,2004,21(4): 13-16.(in Chinese))
[10]	林家浩, 沈为平, 宋华茂, 孙东科. 结构非平稳随机响应的混合型精细积分[J]. 振动工程学报, 1995,8(2): 127-135.(LIN Jia-hao, SHEN Wei-ping, SONG Hua-mao, SUN Dong-ke. High-precision integration of mixed type for analysis of non-stationary random responses[J].Journal of Vibration Engineering,1995,8(2):127-135.(in Chinese))
[11]	曾亮, 李琳. 阻尼陀螺系统动力响应的有限元复模态分析方法[J]. 航空动力学报, 2008,23(10): 1847-1853.(ZENG Liang, LI Lin. Dynamic response of damped gyroscopic system with complex modal method[J].Journal of Aerospace Power,2008,23(10): 1847-1853.(in Chinese))
[12]	张文. 转子动力学理论基础[M]. 北京: 科学出版社, 1990.(ZHANG Wen.Fundamental Theories of Rotor Dynamics [M]. Beijing: Science Press, 1990.(in Chinese))

施引文献

资源附件(0)

访问统计

计量

文章访问数: 1664
HTML全文浏览量: 133
PDF下载量: 940
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

基于辛本征空间的线性阻尼振动系统动力学分析

doi: 10.3879/j.issn.1000-0887.2015.01.001

作者简介:
李明武(1990—)，男，湖南浏阳人，硕士生(E-mail: limingwu0601@126.com);赵岩(1974—)，男，吉林公主岭人，副教授(通讯作者. E-mail: yzhao@dlut.edu.cn);钟万勰(1934—)，男，浙江德清人，教授，院士(E-mail: zwoffice@dlut.edu.cn).

计量

Dynamic Analysis of Linear Damped Systems With the Symplectic Eigenspace Expansion Method

计量

目录

留言板

基于辛本征空间的线性阻尼振动系统动力学分析

doi: 10.3879/j.issn.1000-0887.2015.01.001

作者简介: 李明武(1990—)，男，湖南浏阳人，硕士生(E-mail: limingwu0601@126.com);赵岩(1974—)，男，吉林公主岭人，副教授(通讯作者. E-mail: yzhao@dlut.edu.cn);钟万勰(1934—)，男，浙江德清人，教授，院士(E-mail: zwoffice@dlut.edu.cn).

计量

出版历程

Dynamic Analysis of Linear Damped Systems With the Symplectic Eigenspace Expansion Method

计量

出版历程

目录

作者简介:
李明武(1990—)，男，湖南浏阳人，硕士生(E-mail: limingwu0601@126.com);赵岩(1974—)，男，吉林公主岭人，副教授(通讯作者. E-mail: yzhao@dlut.edu.cn);钟万勰(1934—)，男，浙江德清人，教授，院士(E-mail: zwoffice@dlut.edu.cn).