The dynamic response and fatigue of offshore structures subjected to random wave loadings is studied, with the focus being on the effects of Morison equation nonlinearity. Particular emphasis is given to non-Gaussian aspects of the problem. Simplified analytical and numerical methods for predicting the response and fatigue behavior are developed and are compared with the results of extensive numerical study of the complete nonlinear formulation.
One way of characterizing non-Gaussianity is to use moments higher than the second. Thus, kurtosis or the coefficient of excess and skewness are used to measure the degree of non-Gaussianity in this study. The hydrodynamic wave loading is modeled by the nonlinear Morison equation including fluid-structure interaction effects. Fatigue damage is calculated by using both analytical and simulation methods based on applying the Palmgren-Miner hypothesis to the dynamic response of a linear single degree of freedom structural model.
An improved simulation procedure is developed to generate the random wave force and response time histories for the nonlinear interactive fluid-structure system. Compared to the usual simulation procedure, this method gives a better combination of reduced simulation time and accurate estimates of the high order time average moments which are related to non-Gaussian effects. For both compliant and fixed offshore structures, the response kurtosis is obtained analytically by using the Fourier transform and inverse Fourier transform method and a linear filter approach using state space analysis. An improved analytical model is presented for predicting the fatigue damage induced by the nonlinear interactive Morison equation wave loading.
In addition to the non-Gaussian effect, other characteristics of the stress time history which are related to stochastic fatigue life prediction are also studied. It is found that the response rms has the most significant effect on fatigue damage, the non-Gaussian effect is second in importance, and the effects of using simplified Morison equation models to estimate response average frequency and spectral bandwidth are generally less significant. In particular, neglecting the non-Gaussian effect may result in significantly unconservative fatigue damage prediction while neglecting the spectral bandwidth effect gives results on the conservative side. The skewness is found to be less important than kurtosis for non-Gaussian fatigue like prediction.