工程结构的随机特征问题研究及其在梁结构中的应用

采用子结构模态综合和摄动随机有限元相结合求解工程结构的随机特征问题。为求出随机特征对的方差，借助于模态截断概念推出诸特征值与特征向量对随机变量的偏导数。以染结构为典型算法，定量研究了子结构动模态的选取个数与随机特征对的计算精度间关系，以梁的长细比首次确定使用Timoshenko梁和Euler-Bernoulli梁两模型求解梁类工程结构随机特征问题的适用范围。

Study on The Random Eigen-Problem of Engineering Structures and its Application To Beam

In this paper, the component mode synthesis, combined with the perturbation and stochastic finite element, is used to study the random eigen problem of large and complicated structures. Partial derivatives of eigenvalues and eigen vectors with respect to random variables for structures are deduced by means of the concept of mode truncation. Through numerical study, the relation between the number of dynamic modes chosen and the computational accuracy to meet the engineering requirement is obtained quantitatively. The effects of Euler Bernoulli beam and Timoshenko beam on the stochastic eigen problem and the computing accuracy of beam structures are studied. Finally, with the ratio of length to gyration radius of cross sectional area for a uniform beam, the applicable range of Euler Bernoulli beam and Timoshenko beam models for solving the random eigen problem of beam structures is determined for the first time.