密集模态量化判别准则的一种新方法  

New Quantitative Criterion to Define Closely Spaced Modes

作　　者：刘伟[1,2] 于岩磊[1] 高维成[1] 李惠[2] 

机构地区：[1]哈尔滨工业大学航天科学与力学系,哈尔滨150001 [2]哈尔滨工业大学土木工程学院,哈尔滨150090

出　　处：《振动．测试与诊断》2013年第4期578-581,721-722,共4页Journal of Vibration,Measurement & Diagnosis

基　　金：国家自然科学基金资助项目(51108128;50878064);高等学校博士学科点专项科研基金资助项目(20112302120013);中国博士后科学基金特别资助项目(201003455);中国博士后科学基金资助项目(20090460914);中央高校基本科研业务费专项资金资助项目(HIT.NSRIF.2010068)

摘　　要：矩阵摄动法是变参数系统或密集模态系统分析的重要方法,其首要任务是明确系统模态分布状况,即判别是否为孤立特征值、重特征值或密集特征值,尤其是密集特征值的判别尤为重要。在对比分析以往结构密集模态判别方法的基础上,基于数学上差分和标准方差的概念,提出一种新的密集模态量化判别准则。以特征值组中最大特征值为模对特征值组进行无量纲化,对其进行差分构造,以差分后特征值组的标准方差来表征该特征组的密集性。模态密集程度不同的两个结构分析算例表明,提出的方法适用于全部特征值组及部分特征值组的模态密集程度判别,准确实用且有效可行,尤其适合于大量自由度系统或密集低频结构的模态分布状况判别。Matrix perturbation method is an important method for analyzing the variable parameter systemor the dense mode system.Its primary task is to distinguish the distributed characteristic of the modal eigenvalues of the system clearly,such as isolated eigenvalues,repeated eigenvalues or close eigenvalues.It is especially important for the case of the close modes.Based on reviewing the past methods and the concept of difference and standard deviation,a new modal identification criterion is presented to determine the modal densities of the closely spaced modes structures quantitatively.Firstly the eigenvalue group is nondimensionalized by dividing the largest eigenvalue.Then its differential eigenvalue group is established.Finally the standard deviation of the differential eigenvalue group is used to define the closely spaced modes.The two different simulation examples show that the new quantitative criterion proposed can be applied to not only all eigenvalues group but also segmental eigenvalues group.It is effective and feasible,especially for the identification of the mode distributed characteristics of the system with a large number of degreesof-freedom or the close low-frequency structures.

关 键 词：密集模态 判别准则 频率 方差 矩阵摄动 

分 类 号：O32[理学—一般力学与力学基础]