随机参数平面刚架结构频率特性分析的随机因子法

对物理和几何参数均为随机变量的平面刚架结构，提出频率特性数字特征计算的随机因子法。首先将结构的刚度矩阵分解为各参数因子幂相等的矩阵之和形式，再由求解结构频率的瑞利商公式出发，将结构频率展成部分频率分量和的形式，利用求解随机函数数字特征的代数综合法求解结构频率的数字特征，并对矩形截面梁给出具体的计算公式，通过算例与其精确解及数值模拟结果的比较，验证方法的可行、有效和正确性。

RANDOM FACTOR METHOD FOR FREQUENCY CHARACTERISTIC ANALYSIS OF STOCHASTIC FRAME STRUCTURES

For the frame structures with the physical parameters and geometrical parameters as random variables, an algorithm for calculating the numerical characteristics of the structural frequency is put forward. The stiff matrix of frame structure is disassembled to four partial matrixes, so the structural parameters can be taken out from the separate matrixes easily. Taking the stiff matrix into Rayleigh formula, the structural frequency can be written as the sum of four parts with explicit random factor. And then the expressions of the mean value and the variance of stoehastic frame are educed utilizing the algebra synthesis method. Finally, the influence of the randomhess of structural physical and geometrical parameters on the structural frequency is analyzed by two examples, validating the feasibility of this method discussed.