陀螺系统随机振动分析的辛本征展开方法

赵岩; 李明武; 林家浩; 钟万勰

doi:10.3879/j.issn.1000-0887.2015.05.001

陀螺系统随机振动分析的辛本征展开方法

doi: 10.3879/j.issn.1000-0887.2015.05.001

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:
赵岩(1974—)，男，吉林公主岭人，副教授(E-mail: yzhao@dlut.edu.cn);李明武(1990—)，男，湖南浏阳人，硕士生(通讯作者. E-mail: limingwu0601@126.com);林家浩(1941—)，男，广东中山人，教授(E-mail: jhlin@dlut.edu.cn);钟万勰(1934—)，男，浙江德清人，教授，中科院院士(E-mail: zwoffice@dlut.edu.cn).

中图分类号: O324
计量
- 文章访问数: 1729
- HTML全文浏览量: 240
- PDF下载量: 1204
- 被引次数: 0
出版历程
- 收稿日期: 2014-12-30
- 修回日期: 2015-01-10
- 刊出日期: 2015-05-15

Symplectic Eigenspace Expansion for the Random Vibration Analysis of Gyroscopic Systems

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: 探讨了受随机载荷作用下陀螺阻尼系统随机动力响应问题.虚拟激励法作为随机振动分析的一种高效、精确方法已经广泛应用于结构抗震、抗风等工程领域.在以单类物理变量描述的Lagrange(拉格朗日)体系框架下，振型分解方法已被有效应用于上述随机振动问题的模型自由度缩减.然而，对于陀螺系统的随机振动问题，由于陀螺效应的存在，基于Rayleigh商本征值的振型分解方法受到很大限制.对此，首先给出了陀螺系统辛本征值问题的一般形式.然后对于受平稳随机载荷激励的陀螺系统(无阻尼或有阻尼)引入虚拟激励法，基于辛本征空间展开推导了系统随机振动响应功率谱的求解列式；对于仅考虑陀螺效应的保守系统(无阻尼)，该求解列式可以表述为一个显式表达式.在数值算例中，应用该文提出的方法分析了平稳随机载荷作用下一类阻尼陀螺系统的随机振动响应问题，通过与其它方法进行对比，验证了该方法的精确性和有效性.
- 陀螺系统 /
- 辛本征空间 /
- 随机振动 /
- 虚拟激励法
Abstract: The random dynamic responses of the damped gyroscopic system were investigated under random loads. The pseudo-excitation method, as a highly efficient and accurate method for random vibration analysis, had been widely used in the fields of structural seismic and wind engineering. In the Lagrange framework based on a single physics variable the method of modal superposition is effective to reduce the degrees of freedom for complex structures in the numerical random vibration analysis. However, for the random analysis of gyroscopic systems, given the existing gyroscopic effects, application of the modal superposition method based on the Rayleigh quotient eigenvalues will be quite limited. Therefore, the general description of the symplectic eigenvalue problem was introduced firstly. Furthermore, for the damped gyroscopic system subjected to stationary random loads, the pseudo-excitation method was used and the solution formulae were derived based on the symplectic eigenspace expansion. For the conservative gyroscopic system, the solution expression was in an explicit form. In the numerical examples, the stationary random responses of a gyroscopic system were computed with the present method, of which the accuracy and efficiency were verified through comparison of the results with those out of other methods. The present method is of significance for the random vibration problems about mechanical engineering equipments with gyroscopic systems.
- gyroscopic system /
- symplectic eigenspace /
- random vibration /
- pseudo-excitation method

HTML全文

参考文献(12)

[1]	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))
[2]	毕世华, 黄文虎, 荆武兴, 郑钢铁. 油膜轴承动态特性参数及转子不平衡的统一识别[J]. 强度与环境, 1995(2): 8-15, 21.(BI Shi-hua, HUANG Wen-hu, JING Wu-xing, ZHENG Gang-tie. Identification of both the dynamic characteristics of the journal bearings and the unbalances of the rotor[J]. Structure & Environment Engineering,1995(2): 8-15, 21.(in Chinese))
[3]	Clough R W, Penzien J. Dynamics of Structures[M]. 3rd ed. University Ave: Computers & Structures, Inc, 1995.
[4]	钟万勰, 林家浩. 不对称实矩阵的本征对共轭子空间迭代算法[J]. 计算结构力学及其应用, 1990,7(4): 1-10.(ZHONG Wan-xie, LIN Jia-hao. Adjoint subspace for large scale eigenvalue problems of asymmetric real matrices[J]. Computational Structural Mechanics and Applications,1990,7(4): 1-10.(in Chinese))
[5]	钟万勰, 林家浩. 陀螺系统与反对称矩阵辛本征解的计算[J]. 计算结构力学及其应用,1993,10(3): 237-253.(ZHONG Wan-xie, LIN Jia-hao. Computation of gyroscopic system and the symplectic eigensolution of anti-symmetric matrix[J]. Computational Structural Mechanics and Applications,1993,10(3): 237-253.(in Chinese))
[6]	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))
[7]	李明武, 赵岩, 钟万勰. 基于辛本征空间的线性阻尼振动系统动力学分析[J]. 应用数学和力学, 2015,36(1): 1-15.(LI Ming-wu, ZHAO Yan, ZHONG Wan-xie. Dynamic analysis of linear damped systems with the symplectic eigenspace expansion method[J]. Applied Mathematics and Mechanics,2015,36(1): 1-15.(in Chinese))
[8]	林家浩, 张亚辉. 随机振动的虚拟激励法[M]. 北京: 科学出版社, 2004.(LIN Jia-hao, ZHANG Ya-hui. Pseudo Excitation Method in Random Vibration[M]. Beijing: Science Press, 2004.(in Chinese))
[9]	LIN Jia-hao, ZHAO Yan, ZHANG Ya-hui. Accurate and highly efficient algorithms for structural stationary/non-stationary random responses[J]. Computer Methods in Applied Mechanics and Engineering,2001,191(1/2): 103-111.
[10]	赵岩, 项盼, 张有为, 林家浩. 不确定车轨耦合系统辛随机振动分析[J]. 力学学报, 2012,44(4): 769-778.(ZHAO Yan, XIANG Pan, ZHANG You-wei, LIN Jia-hao. Symplectic random vibration analysis for coupled vehicle-track systems with parameter uncertainties[J]. Chinese Journal of Theoretical and Applied Mechanics,2012,44(4): 769-778.(in Chinese))
[11]	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))
[12]	胡海昌. 多自由度结构固有振动理论[M]. 北京: 科学出版社, 1987.(HU Hai-chang. Natural Vibration Theories of Multi-Degree-of-Freedom Structures[M]. Beijing: Science Press, 1987.(in Chinese))