区间随机桁架结构动力特性分析方法研究

A method of dynamic characteristic analysis for interval stochastic truss structures

针对区间随机桁架结构的动力特性分析,提出了一种区间随机有限元方法。当结构的物理参数和几何尺寸同时具有区间随机性时,利用区间因子法和随机因子法建立了结构的刚度矩阵和质量矩阵;从结构振动的瑞利商表达式出发,利用区间运算推导了结构动力特性区间随机变量的计算式;进而利用随机变量的矩法和代数综合法,推导出了结构特征值的数字特征的计算式。最后通过算例分析了区间随机桁架结构参数的区间随机性对其动力特性的影响,计算结果表明该方法是可行和有效的。

A new interval stochastic finite element method based on the interval factor method and the random factor method was given and an analysis of structural dynamic characteristic for an interval stochastic truss structure was presented. Considering interval randomness of structural physical parameters and geometric sizes simultaneously, the structural stiffness and mass matrices were constructed based on the interval factor method and the random factor method; from Rayleigh’s quotient of structural vibration,the structural interval random dynamic characteristic was obtained by means of the interval arithmetic; the interval numerical characteristics of the dynamic characteristic were then derived by using the random variable’s moment function method and the algebra synthesis method.Two numerical examples were provided to illustrate the validity and feasibility of the proposed method.