Higher order nonlinear transfer functions are applied to model the computed nonlinear responses obtained from dynamic analysis of offshore structures. The structural systems developed for this study are a single degree of freedom system with mass and stiffness and a multi degree of freedom standing cylinder which undergoes large displacement. Also an existing TLP model is used. The structural systems are subjected to single harmonic, two wave combination and irregular wave loading. The wave kinematics are based on the linear wave theory and the wave forces are calculated based on the Morison’s equation. Different sources of nonlinearities examined are the drag force nonlinearity from Morison’s equation, the displaced position calculation due to the movement of the structures and the effect of the addition of current velocity. Higher order nonlinear transfer function models based on Volterra series representation are used to model nonlinear responses which appear at the low or high frequency region where virtually no wave energy exists.
The dynamic analysis of the structures yields the time history response and the Fourier transform of the response gives the frequency components of the response. It is shown that the nonlinear low frequency response appears at the resonance frequencies of horizontal degrees of freedom from the dynamic analysis of the SDOF, MDOF and TLP. Also the nonlinear high frequency response appears at the resonance frequencies of the vertical and rotational degrees of freedom of the MDOF and TLP. The transfer function model clearly shows the degrees of nonlinearity of these high and low frequency responses either as quadratic or cubic. When the quadratic transfer functions obtained from a wave spectrum and the corresponding responses were applied to other wave spectra with different magnitude of wave power, the linear part of the response was matched almost exactly but the quadratic nonlinear parts in the low frequency region overestimated the actual response for higher significant wave heights and underestimated it for lower values of the significant wave heights.