随机过程的第二类随机谐和函数表达

Stochastic Harmonic Functions of Second Kind for Spectral Representations

摘要:

发展了随机过程的第二类随机谐和函数表达并研究了其性质.证明当随机频率与相位服从独立均匀分布而幅值由频率与目标功率谱密度决定时,随机谐和函数过程的功率谱密度函数精确地等于目标功率谱密度函数.研究第二类随机谐和函数过程的渐进正态性,讨论趋向正态分布的速率,并采用Pearson分布研究1维概率密度函数的性质.研究表明,第二类随机谐和函数同第一类随机谐和函数具有相似的性质,且由于第二类随机谐和函数频率为均匀分布,应用更为方便.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.

Abstract:

The stochastic harmonic function of the second kind is proposed for representations of stochastic processes.It is firstly proved that,as long as the random phase angles and random circular frequencies are independent and uniformly distributed whereas the amplitudes are related to the target power spectral density function in a specified way,the power spectral density of the process represented by the stochastic harmonic function of the second kind is identical to the target power spectral density.Then,it is demonstrated that the process represented by the stochastic harmonic function of the second kind is asymptotically Gaussian.The rate of approaching Gaussian distribution is further studied by obtaining the onedimensional distribution via Pearson distribution.The study reveals the similarities between the stochastic harmonic functions of the first kind and the second kind.However,the application of the stochastic harmonic function of the second kind is more convenient than that of the first kind because the random circular frequencies are uniformly distributed.Finally,linear and nonlinear responses of a multidegreeoffreedom system subjected to random ground motions are analyzed to exemplify the effectiveness and superiorities of the proposed approach.