具随机刚度梁结构的重特征值计算

利用一种新的方法来研究具随机刚度梁结构的重特征值问题。将材料物理量的随机场扩展为K．L（Karhtmen-Loeve）正交展式，运用矩阵技巧处理重特征值对应的特征向量，采用二阶收敛的非正交多项式展开式表示梁结构的重特征值和特征向量，建立了类似于摄动法的一系列确定性的递推方程，求解这些递推方程，得到了重特征值的均值和均方差。悬臂、简支和固支梁的算例表明：递推随机有限元法的结果能在较宽的随机涨落范围内较好地逼近蒙特卡罗模拟法的结果，而且相对于蒙特卡罗模拟法而言可以节省大量计算时间。

Computation of Repeated Eigenvalues of Beam''''s Structures with Stochastic Stiffness

A new random finite element method for solving repeated eigenvalues problems involving beams' structures with stochastic stiffness was proposed.The random material properties,such as the modulus of elasticity,were represented by the Karhunun-Loeve orthogonal expansions.Random beam's eigenvalues and eigenvectors were expressed as quadratic nonorthogonal polynomials expansions.Utilizing the finite element method,a set of deterministic recursive equations was set up to deal with the repeated eigenvalues problems according different orders.Then the explicit statistical expansion of eigenvalues was derived.Using the new method,in terms of accuracy and efficiency,is exemplified by considering the cantilever,two-simply-supported and two-clamped beams with random rigidity.The derived results about the statistics of the response are found in very good agreement with those obtained by a Monte-carlo simulation.Furthermore,it is still effective in the condition of large-size fluctuation.