多自由度非线性随机参数振动系统响应分析的概率摄动有限元法  

Probability perturbation finite element method for response analysis of multi-degree-of-freedom nonlinear vibration systems with random parameters

作　　者：张义民[1] 刘巧伶[1] 闻邦椿[2] 

机构地区：[1]吉林大学南岭校区力学系,长春130025 [2]东北大学机械工程与自动化学院,沈阳110004

出　　处：《计算力学学报》2003年第1期8-11,共4页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(19990510;50175043);973项目(1998020320);教育部高等学校骨干教师资助计划资助项目.

摘　　要：提出了一般概率摄动有限元法,并用以解决了具有向量值和矩阵值函数的多自由度非线性随机结构系统承受随机激励的响应分析问题,应用Kronecker代数,矩阵微分理论,向量值和矩阵值函数的二阶矩技术,矩阵摄动理论和概率统计方法系统地扩展了国际上通用的随机有限元法,随机变量和系统导数很方便地排列到二维矩阵中,得到了优美的数学表达式。A generalized probabilistic perturbation finite element method is presented, and the method is employed to solve the response analysis of multi-degree-of-freedom nonlinear vibration systems with random parameters and vector-valued and matrix-valued functions. The current stochastic finite element method is extended using the Kronecker algebra, the matrix calculus, the generalized second moment method, the matrix perturbation theory, the probability theory and the statistics method. The random variables and system derivatives are conveniently arranged into 2D matrices. The elegant mathematical expressions are developed.

关 键 词：多自由度 非线性 随机参数 振动响应 向量值和矩阵值函数 概率摄动有限元法 

分 类 号：O324[理学—一般力学与力学基础]