抄録
In order to obtain statistical moments up to the 4th order of the response of narrow-band non-Gaussian randomly excited systems readily, equivalent non-Gaussian excitation method is extended. The narrow-band non-Gaussian excitation used in this paper is governed by an Ito stochastic differential equation determined by the dominant frequency, bandwidth and probability density function of the excitation. Moment equations which govern the response moments are generally not closed form due to the complex nonlinearity of the diffusion coefficient in the stochastic differential equation expressing the excitation. To make the moment equation closed form, equivalent non-Gaussian excitation method is used. Equivalent non-Gaussian excitation method, which makes the moment equation closed form by approximating the diffusion coefficient to the equivalent diffusion coefficient expressed by a quadratic function, was proposed to calculate the moment equation of systems under non-Gaussian random excitation with zero dominant frequency. In this paper, by proposing new equivalent diffusion coefficient, equivalent non-Gaussian excitation method is extended to apply to the systems under non-Gaussian random excitation with nonzero dominant frequency. In order to assess the validity of the present method, a single degree of freedom linear system under two types of narrow-band non-Gaussian random excitations are considered. By comparing the kurtosis of responses calculated by this method and Monte-Carlo simulation, the validity of this method is demonstrated. Finally, in order to discuss the accuracy of the method, the statistical moments of the equivalent non-Gaussian excitation are investigated.
