抄録
The approximate analytical method combined with equivalent linearization and equivalent non-Gaussian excitation method is proposed to estimate the statistical moments up to the 4th order of the stationary response of a Duffing oscillator subjected to non-Gaussian random excitation. These moments contain information on the mean, the variance, the asymmetry and the tail heaviness of the response distribution. In the previous study, the equivalent non-Gaussian excitation method was applied to a linear system. It was shown that the moments up to the 4th order of the response can be accurately obtained by this method. On the other hand, many of real structures have nonlinear restoring force. Therefore, in this research, equivalent non-Gaussian excitation method is applied to a nonlinear system. In order to obtain the moments, the moment equations for the response, which are derived from the equation of motion of the system and the stochastic differential equation governing the excitation, are used. However, they are not generally closed form due to the complex nonlinearity of the diffusion coefficient of the stochastic differential equations governing the excitation and the nonlinear term of the equation of motion of the system. Therefore, using non-Gaussian excitation method and equivalent linearization, the diffusion coefficient is replaced with the second order polynomial and the nonlinear parameter of the system can be replaced with a linear term, and then the moment equations can be closed. By solving these equations, the moments up to the 4th order can be obtained. Using these obtained moments, the skewness and the kurtosis of the response are also determined. In the analysis, various non-Gaussian distributions, and a wide range of the excitation bandwidth and nonlinearity of a Duffing oscillator are considered. To demonstrate the effectiveness of the method, the results of the proposed method are compared with those of Monte Carlo simulation.
