EFFECTS OF NONNORMALITY ON STOCHASTIC STRUCTURAL DYNAMICS AND FATIGUE

Abstract

The use of stochastic process theory in a structural dynamic analysis is usually restricted to normal processes. Recent studies have shown that the influence of nonnormality on both fatigue failures and first-excursion failures cannot be neglected. Basically, the aim of this study is to understand the effects of nonnormality on structural dynamics and fatigue, particularly as related to offshore structures. Several related aspects of the problem are studied. The fourth order cumulant function is taken as a reasonable measure of the departure of a process from normality. However, in practice, it is not easy to see the degree of nonnormality of a process directly from the fourth order cumulant function, because of its multidimensional nature. Therefore, the kurtosis or the coefficient of excess is used as a simpler index to represent the degree of nonnormality. The study significantly extends the usual description of wave forces by deriving a description for the nonnormal part of the wave force. An approximation for the fourth cumulant function (and corresponding three-dimensional power spectral density) of a wave force is obtained. Because the degree of nonnormality of the response of a linear structure subjected to a wave force is not easily obtained, analytical studies are also made for a linear SDF structure subjected to somewhat simpler nonnormal forces. An efficient technique for calculating the response kurtosis is derived. Another aim of this study is to estimate the effect of nonnormality of fatigue damage. Both analytical and simulation results confirm that the effect of nonnormality should not be neglected. Simulation studies are also made for the dynamic response of an idealized structure subjected to a stochastic wave force. It is found the degree of nonnormality of the response is quite substantial, but never exceeds the degree of nonnormality of the excitation, at least for the situations considered