随机参数结构系统特征对的随机性及其关系分析

以随机参数结构系统为对象,分析并揭示了结构特征值与特征向量二者随机性之间的关系。利用瑞利商公式分析了结构特征值的随机性;利用结构动力特征方程分析了特征值与特征向量随机性之间的联系;从正则振型的表达式出发,导出了结构正则振型的随机性表达式。通过十杆桁架和三盘两轴扭转系统两个算例考察了结构各个参数的随机性对特征对随机性的影响,通过与MonteCarlo数值模拟法结果比较,验证了理论分析和计算方法的正确性。

Eigenvalues, Eigenvectors and Their Relationship Analysis of Stochastic Parameter Structure

The random factor method for probability analysis of the eigenvalues and eigenvectors of stochastic structure was discussed. Considering the randomness of the structural physical parameters and the geometric dimensional parameters, the mean value and the variance of the eigenvalues were educed from the Rayleigh formula. And then putting the random eigenvalue into the dynamic characteristic equation, the connection between the randomness of eigenvalues and that of eigenvectors was gained. Furthermore, the randomness of canonical eigenvector was analyzed from its educing process. Finally, the influences of randomness of structural physical and geometric dimensional parameters on the structural eigenvalues and eigenvectors was analyzed by two examples with the method and the Monte Carlo method, validating the feasibility of this method discussed by the paper.