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