Study on The Random Eigen-Problem of Engineering Structures and its Application To Beam
Cao Jiayu, Fang Zhichu
(School of Civil Engineering and Mechanics, Shanghai Jiaotong University, Shanghai 200030)

Abstract: 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 o f 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 o f Euler-Bernoulli beam and Timoshenko beam models for solving the random eigen-problem of beam structures is determined for the first time.
Keywords: Engineering structures, random eigen-problem, component mode synthesis, perturbation and stochastic finite element, Timoshenko beam, Euler-Bernoulli beam, ratio of length to gyration radius of cross-sectional area for a uniform beam.