复模态正交性理论的异常现象及对策分析

张淼; 于澜; 鞠伟

doi:10.3879/j.issn.1000-0887.2014.10.002

复模态正交性理论的异常现象及对策分析

doi: 10.3879/j.issn.1000-0887.2014.10.002

张淼¹,
于澜¹,
鞠伟²

¹长春工程学院理学院, 长春 130012;²中国第一汽车股份有限公司技术中心, 长春 130011

基金项目: 吉林省自然科学基金（201215115）

详细信息

作者简介:
张淼（1972—），男，长春人，副教授，博士(通讯作者. E-mail: zm7209@163.com).

中图分类号: O321;TB122
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出版历程
- 收稿日期: 2014-04-18
- 刊出日期: 2014-10-15

An Unusual Phenomenon in the Complex Mode Orthogonality Theory and the Strategy Against It

¹School of Science, Changchun Institute of Technology, Changchun 130012, P.R.China;²R&D Center, China FAW Group Corporation, Changchun 130011, P.R.China

摘要

摘要: 利用复模态正交性理论的数值实验发现并提出了标号现象.首先根据复模态理论在两种状态空间格式下，对不同振动系统的状态向量解耦功能进行分析，其次提出了对称及非对称重频系统的状态向量正交性的相关结论并进行了数值验证；继而发现并提出了标号现象，并指出了克服标号现象的方法；最后以工程应用中的一个常见的灵敏度分析问题为例，用数值算例的结果说明了忽略标号现象可能存在的风险.
- 复模态理论 /
- 标号现象 /
- 正交性 /
- 解耦 /
- 对角化
Abstract: The label phenomenon was revealed through verification of the correctness of the complex mode orthogonality theory used in engineering with numerical experiment. Firstly, the decoupling function of the state vectors under different state space schemes was theoretically analyzed. The related conclusions were also proposed on the orthogonal properties of the state vectors in the cases of symmetric and asymmetric structures with repeated frequencies. Secondly, the label phenomenon was found out and the method to eliminate its undesirable influence was given. Finally, through a general example of sensitivity analysis, the likely risk out of ignorance of the label phenomenon was demonstrated. The research indicates that, through necessary orthogonality check and adjustment of the state vectors’ orders, the decoupling of the state vectors is realized and the adverse effect of the label phenomenon on the calculation accuracy is eliminated.
- complex mode theory /
- label phenomenon /
- orthogonal property /
- decouple /
- diagonalization

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参考文献(13)

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