非线性随机动力系统的概率密度演化分析  

Probability density evolution analysis of nonlinear dynamical systems

作　　者：陈建兵[1] 刘章军[1,2] 李杰[1] 

机构地区：[1]同济大学土木工程学院土木工程防灾国家重点实验室,上海200092 [2]三峡大学土木水电学院,宜昌443002

出　　处：《计算力学学报》2009年第3期312-317,共6页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金创新研究群体科学基金(50621062);教育部新世纪优秀人才支持计划联合资助项目

摘　　要：阐述了基于概率密度演化理论进行多自由度结构非线性随机动力反应分析的基本思想。采用随机过程的正交分解或物理系统建模的思想,实现随机激励的随机函数表述。对由此获得的随机状态方程采用概率密度演化理论求解,可以获得随机动力系统反应的概率密度函数及其演化。以某剪切型框架结构的非线性随机地震反应分析为例,说明了所发展方法的可行性和有效性。The basic idea of stochastic response analysis of multi-degree-of-freedom nonlinear structures is outlined. Employing the orthogonal decomposition or physical modeling, the stochastic excitation can be represented by random combination of a set of deterministic functions. The probability density evolution theory can then be applied to the resulted stochastic dynamical system and the instantaneous probability density function and its evolution can thus be obtained. Stochastic response analysis of a shear frame subjected to random ground motions is exemplified, showing the feasibility and validity of the proposed method.

关 键 词：随机动力系统 非线性 概率密度演化 概率守恒 正交分解 

分 类 号：O313.7[理学—一般力学与力学基础]