随机结构系统的一般实矩阵特征值问题的概率分析

由于工程实际结构的复杂性和所用材料在统计上的离散性以及测量、加工、制造误差的存在，必然导致具有随机参数的随机结构振动系统，按结构参数的性质来划分，随机振动问题包括两方面内容：(1)确定结构问题；(2)随机结构问题。本文以现代数学理论为依托，研究了随机结构系统的一般实矩阵的特征值问题。根据Kronecker代数、向量值和矩阵值函数的灵敏度分析、一般二阶矩法和概率摄动技术给出了计算随机结构系统的一般实矩阵的特征值和特征向量的数值方法，可以有效地得出随机结构系统的一般实矩阵的特征向量的统计量，发展了2D矩阵值函数的随机结构系统的特征值问题概率分析理论。

Probability Analysis of Eigenvalue Problem with General Real Matrices in Random Structural Systems

Uncertainties in material properties and structural geometry are due to the manufacturing error, measurement inaccuracies or structure complexities. The uncertainties may be materialized by the randomness of the structural parameters, such as mass and stiffness. Inherent uncertainties in material properties and structural geometry certainly bring randomness of the mass and stiffness and stochastic eigenvalue problem. In random vibration, two main problems are compartmentalized by parameter uncertainties: (1)certain structures and (2)stochastic structures. The eigenvalue problem of general real matrices was researched in random structure system that it is from depending on modern mathematics theories. On the basis of Kronecker algebra, matrix calculus, generalized second-moment method, and probabilistic perturbation technique, the numerical method for stochastic eigenvalues and eigenvectors of general real matrices was given. The method can be used to solve the statistics values of stochastic eigenvalues and eigenvectors in random structure systems accurately and effectively. Probability analysis theory for eigenvalue problem of general real matrices with 2D matrix functions in random structural systems has been developed.