随机桁架结构的非平稳随机动力响应分析

本文研究了随机桁架结构在非平稳随机激励下的动力响应问题。在利用随机因子法分析随机结构动力特性的基础上，给出了一种分析随机结构非平稳随机响应的新方法。从结构非平稳随机响应的表达式出发，同时考虑桁架结构的物理参数、几何尺寸的随机性，利用求解随机变量函数矩的方法和求解随机变量数字特征的代数综合法，导出了随机桁架结构在非平稳随机激励下位移响应均方值和应力响应均方值的均值、方差和变异系数的计算表达式。通过算例，分析了结构物理参数和几何尺寸的随机性对结构位移响应均方值和应力响应均方值随机变量随机性的影响。本文方法具有对随机结构进行一次动力分析便可求得动力响应的数字特征，且可以考察结构任一参数的随机性对结构非平稳随机响应分析结果的影响之优点。

Non-stationary Random Vibration Analysis of Stochastic Truss Structures

The non-stationary random vibration analysis of stochastic turss structures was investigated. Based on the stochastic structural dynamical characteristics that analyzed by using Random Factor Method (RFM) , a new method for the non-stationary random vibration analysis of stochastic structures were proposed. From the expressions of structural stationary random response of the frequency domain, the computational expressions of the mean value, variance and variation coefficient of the mean square value of structural displacement and stress response under the stationary random excitation were developed by means of the random variable's functional moment method and the algebra synthesis method. In which the randomness of the structural physical parameters and geometric dimensions were considered simultaneously. The influences of the randomness of structural physical parameters and geometric dimensions on the randomness of the mean square value of structural displacement and stress response were inspected by examples. The method has the merits that the numerical characteristics of stochastic structural dynamical respose can be obtained by analyzing the stochastic structure one time, and the influences of the randomness of each structural parameter on the non-stationary random vibration analysis results of stochastic structures can be inspected easily.