结构非平稳随机响应方差矩阵的直接精细积分计算

英文篇名：Precise Integration of the Variance Matrix of Structural Non stationary Random Responses
中文刊名：振动工程学报
英文刊名：JOURNAL OF VIBRATION ENGINEERING
作者：林家浩 ; 钟万勰 ; 张文首
英文作者：Lin Jiahao Zhong Wanxie (State Key Laboratory of Structural Analysis of Industrial Equipment ; Dalian University of Technology Dalian ; 116023) Zhang Wenshou (Department of Civil and Structural Engineering ; Hong Kong
中文关键词：非平稳随机振动 ; 方差 ; 随机分析 ; 精细积分
英文关键词：non stationary random vibration ; variance ; random analysis ; precise integration
出版日期：1999-03-30
机构：大连理工大学工业装备结构分析国家重点实验室,香港理工大学土木系
年：1999
期：01
出版单位：振动工程学报

摘要

对于受演变随机白噪声或有色噪声激励的结构，对其方差矩阵推导了相应的微分Ｌｙａｐｕｎｏｖ方程，并用精细积分方法建立了倍步长与等步长积分格式，使一大类以往难于得到精确解的问题，能迅速地在计算机上得到具有很高精度的解答。并用其它文献上的例题验证了本文给出方法的精确性及极高的计算效率。
For most engineering structures subjected to stationary/nonstationary random excitations, the computations of their response variances are usually very difficult and time consuming. The PEM(pseudo excitation methods)have partly solved this problem by means of accurate and very efficient computations of various response power spectral densities which are used in the integration of the corresponding variances. This article shows that for some kinds of evolutionary white or colored random excitations, the Lyapunov equation of any arbitrary response variance matrix can be quickly and accurately computed in terms of the “precise integration scheme”, and thus further remarkably accelerates such computations. The corresponding stationary response variances can be conveniently obtained by using the double step formulas.

引文

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