摘要
研究了随机过程的随机谐和函数表达及其性质.首先证明了当随机谐和函数的频率分布与目标功率谱密度函数形状一致时,随机谐和函数过程的功率谱密度函数等于目标功率谱密度函数.进而,证明了随机谐和函数过程的渐进正态性,讨论了趋向正态分布的速率,并采用Pearson分布研究了一维概率密度函数的性质.与已有的随机过程谱表达方式相比,采用随机谐和函数表达,仅需要很少的展开项数,即可获得精确的目标功率谱密度函数,从而大大降低了与之相关的随机动力系统分析的难度.最后,以多自由度体系的线性和非线性响应分析为例,验证了随机谐和函数模型的有效性和优越性.
Stochastic harmonic functions and their properties are studied.In the paper,it is firstly proved that as the distributions of the random frequencies are consistent with the target power spectral density function, the power spectral density of the stochastic harmonic process is identical to the target power spectral density. Further,it is proved that the stochastic harmonic process is asymptotically Gaussian.The rate of approaching Gaussian distribution is discussed by adopting Pearson distribution to describe the one-dimensional distribution of the stochastic harmonic process.Compared to existing representations of stochastic process,very few stochastic harmonic components can capture the exact target power spectral density.This greatly reduces the number of the random variables and thus eases the difficulty of stochastic dynamics.Finally,linear and nonlinear responses of a multi-degree-of-freedom system subjected to random ground motions are carried out to exemplify the effectiveness and advantages of the stochastic harmonic representations.
出处
《力学学报》
EI
CSCD
北大核心
2011年第3期505-513,共9页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金(10872148
90715033)
国家高技术研究发展计划(2008AA05Z413)
教育部新世纪优秀人才支持计划资助项目~~
关键词
随机谐和函数
功率谱密度
相关函数
平稳过程
非线性
stochastic harmonic function
power spectral density function
covariance function
stationary process
nonlinearity
作者简介
E-maihchenjb@tongji．edu．cn
