Stability analysis of parametric resonance in spar-buoy based on Floquet theory

Parametric resonance is a phenomenon caused by time-varying changes in the parameters of a system which may result in undesirable motion responses and instability. Floating bodies like ships and spar-buoys are prone to Mathieu instability mainly due to the instantaneous change of the metacentric height. With the fast-growing developments in Ocean Renewable Energy systems, spar-buoys are commonly used for wave energy convertors and floating wind turbines. Undesirable, unstable motions as a result of the parametric resonance can be problematic as it may cause inefficiency in operations and structural risk integrity. In this research, a new approach has been developed to investigate these nonlinear oscillations and analyze the conditions when parametric resonance occurs. The hydrodynamic loads are calculated using the linear approach, and the motion responses of the floating body coupled in heave, pitch and surge are determined. It is shown that the eigen values obtained from Floquet Theory can be used as indicators of stability under different wave conditions. This procedure can be practically used with little computational cost to determine factors affecting the equilibrium status of a system in regular waves.