Non-Gaussian Response Evaluation of Nonlinear System Subjected to Non-white Random Excitation Using Higher-Order Statistical Values

Non-Gaussian response characteristics of an asymmetric nonlinear system subjected to nonwhite random excitation are investigated. Applying a previously developed analytical method, which contains moment equations method and non-Gaussian equivalent linearization technique, stationary responses are numerically computed. Non-Gaussian indicators i.e. skewness, kurtosis and equivalent linear coefficients which are defined by the 3rd and 4th order moments are considered to evaluate the non-Gaussianity of the responses. Skewness and kurtosis of the response in a family of the asymmetric parameter of the system and the dominant frequency of the excitation are plotted onto a diagram as the map of non-Gaussianity. The non-Gaussian map indicates the variation of the shape of probability density function. The equivalent linear coefficients are illustrated in the same way. These numerical results demonstrate the effects of the asymmetric properties of the system and the dominant frequencies of the excitation upon the non-Gaussian response characteristics.