Abstract
We examine the non-Gaussianity of joint response probability distributions of a linear system subjected to non-Gaussian random excitation. In our previous study, we calculated the joint response probability distribution of the displacement and velocity of the system. It was revealed that the distribution concentrates on a straight line (x′ axis), and the marginal distribution on the x′axis has the same non-Gaussianity as the excitation. In addition, we derived the solution of the straight line analytically. In this paper, first, we calculate the marginal probability density function on the x′ axis in order to investigate how the non-Gaussianity on the x′ axis varies with time and excitation bandwidth parameter. In this regard, we also derive the analytical solution of the marginal distribution when the excitation bandwidth is zero, and then, use it for comparison with the marginal distribution in the non-zero bandwidth case. It is found that the marginal distribution exhibits non-Gaussianity similar to that of the excitation at almost any time, however, the degree of the non-Gaussianity decreases temporarily with a period of 2π. Next, we calculate the marginal probability density function on the straight line perpendicular to the x′ axis and show that it does not have non-Gaussianity. This fact indicates that the excitation non-Gaussianity appears only on the x′ axis.
