Abstract
This study deals with the asymmetry of stochastic response of a linear system under external and parametric random excitations. The random excitations are modeled by zero-mean Gaussian processes possessing a non-white power spectral density with bandwidth and dominant frequency parameters. The correlation between the two excitations is characterized by their correlation coefficient. In order to examine the effect of the excitation correlation coefficient on response asymmetry, bispectral density is utilized, which is a generalization of a traditional power spectral density. The response asymmetry is evaluated in terms of skewness. First, the analytical method developed in our previous study for obtaining an approximate analytical solution of response bispectral density is extended to the case where the two excitations have arbitrary cross-spectral density. The analytical method consists of a Fourier series representation of the excitation based on the spectral representation theorem and a perturbation technique. In this study, the response bispectral density is normalized by using the response variance. The normalized bispectral density is the distribution of skewness in the frequency domain, and by integrating it over the entire frequency range, the response skewness is obtained. The validity of the approximate analytical solution is confirmed by comparing it with the Monte Carlo simulation result. Then, using the approximate solutions of the bispectral density and skewness, the following findings are made regarding the relationship between the response skewness and the correlation coefficient: (i) the response skewness changes approximately linearly with the correlation coefficient; (ii) the slope of the change can be approximated by the response skewness in the case that the correlation coefficient is equal to 1, i.e., the two excitations are identical.
