Non-linear spectral analysis of offshore structures

The Author has developed two finite element codes to analyse offshore lattice structures. The first code, SPECLIN, uses linear spectral theory to compute spectra of displacement responses due to incident random storms; the second code, NONLIN, uses non-linear spectral theory to compute spectra of displacement responses due to incident random storms. In both analyses the random storm events are characterised by Pierson-Moskowitz spectra using representative storm wind speeds. The linear approach develops a linear relationship between incident waves and platform displacement through equivalent linearisation of the quadratic drag force term in Morrison's equation. In the non-linear approach, the drag force terms is expanded using Hermite polynomials and the perturbation technique is used to formulate response spectra in terms of higher order velocity spectra through the convolution integral. The cumulant neglect closure technique is used and illustrates how some of the terms in the perturbation series can be set to zero. In this paper some of the details of the development of the non-linear model are presented. The paper also focuses on comparing results from the non-linear solution with the linear solution for both a cantilever and a frame structure. It is seen that for cantilever type structures both sets of results are quite similar; however, there are significant differences when the two solutions are applied to a cantilever. Also, results are presented for different sea state spectra, this illustrates that the higher order, non-linear effects are more significant when sea state spectra resonate with the higher harmonic responses.