Fatigue damage in randomly vibrating jack-up platforms under non-Gaussian loads

The problem of fatigue damage estimation of ageing jack-up platforms is considered, using theories of random processes. The sea-wave excitations are modelled as stationary, Gaussian random processes, with specified power spectral density function. The loads acting on the structure due to the sea waves is calculated using Morison’s equation and are therefore non-Gaussian whose probabilistic properties are not available in explicit form. Assuming linear structure behaviour, the probabilistic properties of the structure response are determined using theories of random vibrations. The simple peak counting method is adopted for estimating the mean fatigue damage. This requires knowledge of the joint probability density function of the structure response and its first and second time derivatives, at the same time instant. A methodology has been presented for developing analytical expressions for this joint pdf. This requires evaluation of multidimensional integrals. A recently developed computational algorithm is presented to deal with integrals for which derivation of closed form analytical expressions may not be feasible. The methodology proposed in this paper provides an alternative and computationally cheaper technique for estimating the fatigue damage in comparison to the Monte Carlo simulation procedure. Numerical results have been presented for illustration of the proposed methodology.