复模态正交性理论的异常现象及对策分析  

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

作　　者：张淼[1] 于澜[1] 鞠伟 

机构地区：[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

出　　处：《应用数学和力学》2014年第10期1081-1091,共11页Applied Mathematics and Mechanics

基　　金：吉林省自然科学基金(201215115)

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.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. Second- ly, 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 igno- rance of the label phenomenon was demonstrated. The research indicates that, through neces- sary 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 accu- racy is eliminated.

关 键 词：复模态理论 标号现象 正交性 解耦 对角化 

分 类 号：O321[理学—一般力学与力学基础] TB122[理学—力学]