The aim of this work is to compare two approaches of taking into account non-linearity of the drag term implied by the modified Morison equation, using spectral analysis. Equivalent linearization method which involves iterative analysis and perturbation method are the two methods chosen for this purpose. Two frequently used examples, i.e., a 31 member plane frame and a 58 member plane frame structure are used to compare the merits and demerits of the two methods. The analysis of results indicate that the spectra obtained by linearization and perturbation differ significantly for shallow water structure and at lower sea states. Also, the major spectral peak is observed at the most dominant wave frequency and not at the fundamental natural frequency of the structure as reported in the literature. Possible explanations have also been discussed.
With a fast depleting oil reserves on-land and shallow seas, increasing attention is being given to the exploration in deep sea. Even with the advent of structures suitable to deep water conditions such as the tension leg platforms, if a jacket turns out to be cost effective, it is of interest worldwide. It is assumed in such a case that, these structures are sufficiently slender and that they are assumed not to alter the incident wave field significantly (otherwise a different formulation involving the diffraction effects would have to be implemented.) If the structure is assumed to be rigid, the Morison equation describes the forces as the non-linear function of the wave particle kinematics. If one uses a stochastic description of random sea waves, one finds that, this non-linear transformation affects the frequency content of the forcing function in the vicinity of three times the characteristic frequency of waves. In particular, the spectral densities of the excitation are increased in the vicinity of these frequencies.
