%0 Journal Article
%A CHEN Jian-Bing
%A LI Jie
%T Stochastic harmonic function and spectral representations
%D 2011
%R 10.6052/0459-1879-2011-3-lxxb2010-375
%J Chinese Journal of Theoretical and Applied Mechanics
%P 505-513
%V 43
%N 3
%X Stochastic harmonic function representations 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 normally distributed. The rate of approaching normal
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.
Keywords: Stochastic harmonic function, power spectral density function, covariance function,
stationary process, nonlinearity
%U http://lxxb.cstam.org.cn/EN/10.6052/0459-1879-2011-3-lxxb2010-375