西南交通大学学报Issue(2)：220-226,7.DOI:10.3969/j.issn.0258-2724.2014.02.006
非线性随机振动分析的概率密度演化方法
Probability Density Evolution Method of Nonlinear Random Vibration Analysis
摘要
Abstract
In order to reveal the applicability of the probability density evolution method in nonlinear random vibration analysis,a comparative research of the probability density evolution method and the classical nonlinear random vibration analysis was carried out by investigating the nonlinear responses of a class of randomly base-driven Duffing oscillators using the probability density evolution method (PDEM),the adaptive polynomial chaos expansion (APCE)and the Monte Carlo simulation (MCS). A physically based stochastic ground motion model was employed,and represented by a Karhunen-Loève expansion in the application of the APCE. This discrete representation can be viewed as a projection of the physical vector space into the Gaussian vector space. Numerical results reveal that the solution processes of the three approaches are identical to weakly nonlinear systems,while they are approximately identical to strongly nonlinear systems though errors resulted from numerical techniques and artificial truncations are amplified,indicating that the solution of the PDEM is equivalent to that of the classical nonlinear random vibration analysis in the mean-square sense. The PDEM,moreover, goes a step further than the classical nonlinear random vibration analysis since the probability density function of responses and the dynamic reliability of systems can be simultaneously provided by the PDEM. The other methods,however,need much more computational efforts to obtain high order statistics of responses.关键词
概率密度演化方法/混沌多项式展开/Monte Carlo模拟/随机地震动/Karhunen-Loève分解Key words
probability density evolution method/polynomial chaos expansion/Monte Carlo simulation/random ground motion/Karhunen-Loève expansion分类
数理科学引用本文复制引用
彭勇波,李杰..非线性随机振动分析的概率密度演化方法[J].西南交通大学学报,2014,(2):220-226,7.基金项目
国家自然科学基金资助项目（51108344）；土木工程防灾国家重点实验室探索性研究课题资助项目（SLDRCE11-B-04）；中央高校基本科研业务费专项资金资助项目 （）
