随机结构复合随机振动分析的概率密度演化方法  

THE PROBABILITY DENSITY EVOLUTION METHOD FOR COMPOUND RANDOM VIBRATION ANALYSIS OF STOCHASTIC STRUCTURES

作　　者：陈建兵[1] 李杰[1] 

机构地区：[1]同济大学土木工程学院建筑工程系,上海200092

出　　处：《工程力学》2004年第3期90-95,共6页Engineering Mechanics

基　　金：国家杰出青年科学基金资助项目(59825105)

摘　　要：提出了随机结构复合随机振动分析的概率密度演化方法。通过引入扩展状态向量,构造具有随机初始条件的状态方程,导出了复合随机振动反应的概率密度演化方程。结合精细时程积分方法和Lax-Wendroff差分格式对概率密度演化方程提出了数值求解方法。进行了八层层间剪切框架结构复合随机振动反应的概率密度演化分析,证明提出的方法具有计算高效、收敛性稳定与精度高的特点。研究表明随着时间的增长,复合随机振动反应概率密度曲线趋于复杂,基于正态分布假定的二阶矩分析方法可能造成可靠度分析结果的显著偏差。与仅考虑结构参数随机性和仅考虑输入随机性时的结构反应相比,复合随机振动反应概率密度曲线峰值降低、分布变宽,且随机涨落显著增强。A probability density evolution method for compound random vibration analysis of stochastic structures is proposed. The augmented state vector is introduced to construct a state equation with random initial conditions. The probability density evolution equation (PDEE) for the response of compound random vibrations is deduced. With the precise integration method and the Lax-Wendroff difference scheme, the PDEE is solved numerically. An example is studied where the probability densities of the response of an 8-story floor shear frame structure are evaluated, verifying the high computational efficiency, stable convergence and high accuracy of the present method. The investigations demonstrate that the probability density curves tend to be complex with time, which means that the widely applied second moment method for reliability evaluation based on normal distribution assumption may have great deviation. In addition, compared with the response when only the randomness of the structural parameter is taken into account and only the randomness of the input is considered, the probability density curves of the response of compound vibration have lower peak and wider distribution, and the fluctuation of the response of compound vibration is enlarged in contrast to that of response of vibration with single randomness source.

关 键 词：结构工程 随机结构 复合随机振动 概率密度演化:精细积分方法 差分方法 

分 类 号：TU311[建筑科学—结构工程] O324[理学—一般力学与力学基础]