关键词: 随机结构, 孤立特征值, K-L正交展式, 非正交多项式混沌, 摄动法

Abstract: A new random finite element method for solving eigenvalue problems involving material variability is given. The random material properties, such as the modulus of elasticity, are represented by Karhunun-Loeve expansion. Random structural eigenvalues are expressed as nonorthogonal polynomials chaos. With the aid of the finite element method, a set of deterministic recursive equations is set up to deal with eigenvalue problems through nonorthogonal polynomials of the same order. The statistics of eigenvalues is derived. A beam problem and a plate problem are investigated by the new method. The derived second-order statistics of eigenvalues is found in good agreement with those obtained by Monte-Carlo simulation.

Key words: random structure, isolated eigenvalue, Karhunen-Loeve expansion, nonorthogonal polynomials chaos, perturbation method