摘要
为分析随机结构系统固有频率的统计特性,提出一种基于分解法的随机有限元最大熵法。该法利用单变量分解将高维随机变量特征值函数分解成单维随机变量特征值函数的组合形式,从而将求解随机结构特征值统计矩的多维积分表达式转化为单维积分式,对单维积分采用高斯-埃尔米特积分格式数值求解。在获得随机结构系统固有频率的前四阶原点矩之后,利用最大熵原理求得结构固有频率概率密度函数的解析表达式。算例分析表明:该方法结果与Monte-Carlo法结果相比,误差很小,具有令人满意的计算精度和效率。
In order to analyze the statistical characteristic of eigenfrequencies of stochastic structural systems, a stochastic fmite element maximum entropy method was proposed on the basis of the dimension-reduction method. In this method, the multi-dimensional random eigenvalue functions were decomposed into the combination of one-dimensional random eigenvalue functions by the univariate dimension-reduction method, so the multi-dimensional integrations, which were employed to calculate statistical moments of eigenvalues of stochastic structural systems, were transformed into one-dimensional integrations, and the one-dimensional integration was calculated by the Gauss-Hermite numerical integration. After getting the first four origin moments of eigenfrequencies of stochastic structural systems, the explicit expressions of the probability density function of eigenvalues of structures were obtained using the Maximum Entropy Principle（MEP）. The comparison of results between proposed method and Monte-Carlo simulation method demonstrates that the proposed method has small error, satisfactory computational accuracy and efficiency.
出处
《工程力学》
EI
CSCD
北大核心
2009年第12期58-63,共6页
Engineering Mechanics
基金
国家863高技术研究发展计划项目(2006AA04Z402)
关键词
随机结构
固有频率特性
分解法
最大熵原理
Gauss-Hermite积分
概率密度函数
stochastic structures
eigenfrequencies characteristic
dimension-reduction method
maximum entropy principle
Gauss-Hermite integration
probability density functions
