On the Occurrence of Mathieu Instabilities of Vertical Cylinders

Large offshore platforms with vertical circular cylindrical hull shapes have been designed and employed in recent times. Classical spar platforms and mono-column concepts are just two examples of designs with such simple configuration, supposed to perform limited motion responses in waves. Reports on investigations on the occurrence of parametric resonance of spar platforms have been published recently in which the relevance of Mathieu amplifications have been assessed making use of different mathematical models. However, some uncertainties still remain on the influence of crucial design parameters as, for instance, metacentric height, draft/diameter ratio, associated damping and mooring system. In an attempt to clarify some of these aspects, in this paper the dynamic stability of a vertical cylinder in regular waves is investigated theoretically and experimentally. A coupled non-linear mathematical model is employed to model and simulate the coupled heave, roll and pitch motions. Theoretical aspects related to the development of resonant motions are discussed. In addition to the numerical and theoretical investigations, an extensive series of experiments with a model of a typical mono-column have been recently conducted at LabOceano. The findings of these investigations are compared and summarized.