Spectral response surfaces, designer waves and the ringing of offshore structures

The purpose of this paper is to apply the spectral response surface method to the ringing problem. We have re-formulated Newman's results for diffraction force on a column in terms of the frequency components of the ocean surface and their Hilbert transforms. The resulting expression, together with a single degree of freedom model for the structure, allows us to generate hyper-surfaces of constant dynamic response as functionals in the Hilbert space of the spectral components of the ocean surface. As the components are uncorrelated, linear processes, it is straightforward to treat the response surfaces as limit states in a FORM (first order reliability method) type of analysis. This provides a very efficient means of calculating the ocean surface history most likely to generate an extreme ringing response (the `designer wave' for ringing) and the ringing response history.