Dynamical response analysis of tubular offshore platform structures to wave forces is considered. The non-Gaussianity of the response in terms of its coefficient of excess is predicted via the separability assumption. Further statistical information is generated implementing the mixture technique. Results are presented for the case study of two-degrees-of-freedom system.
The Morison-type fluid force is known to have a non-Gaussian probability distribution with thick tails (high kurtosis). If the equations of motion were quasi-static, the high kurtosis of the exciting force would pass unabated into the response. When the dynamics is taken into account, it is found that the motion becomes more Gaussian. This is beneficial in terms of the reliability analysis of offshore platform structures. For example, in the present study, where a range of dynamic responses were analysed, from the very resonant to the nearly quasi-static case, the response coefficient of excess (defined as kurtosis-3 always remained between 0.0 and 2.5 whereas the quasi-static response would have a coefficient of excess in the range 2.48 to 4.96. An exact method does exist for analysing the kurtosis, but it is too cumbersome to be undertaken routinely. In previous work a simplification of this task was proposed, and its performance was assessed. The previous study was valid for a 1 degree of freedom (1 DOF) system. Here, the method is extended to more than one DOF structures. Section 2 recalls the earlier 1 DOF relations and develops the new theory providing the formulation of the general N degrees of freedom problem. The predicted quantity is the 4th order statistical moment of the platform displacement; other response statistics such as level exceedance probabilities, distributions of maxima (envelope statistics) can be estimated subsequently, leading to probabilistic fatigue life evaluations.
