Stability Analysis of Parametric Roll Resonance

For investigation and developing fundamental knowledge about how and why ships and structures behave in an ocean environment Norway started the Centre for Ships and Ocean Structures. One of the research topics of this centre of excellence is parametric roll resonance. Parametric roll resonance is a phenomenon that causes a roll motion to a ship due to longitudinal waves. This roll motion can become so large that capsizing can occur. It is dangerous for ships to encounter this phenomenon. Even when capsizing does not happen this roll motion could cause damage to the ship and can be a threat for the cargo and crew. Although there are very specific conditions when parametric roll resonance can occur there are several examples where it did happen and caused significant damage to the ship and cargo for millions of euro's. To describe this phenomenon the coupled 3 DOF model proposed by Neves and Rodríguez is used. The pitch angle and vertical displacement are assumed to be harmonic and therefore and uncoupled 1 DOF model is derived to describe the roll motion of the ship. For control it is interesting to have an indication what the values of the control parameters could be to prevent parametric roll resonance to occur. To determine these values of the control parameters first the stability regions of the uncoupled 1 DOF are determined. These simulations can easily be used as an indication for the control parameters since it is easy to see what the value of the control parameters should be to reduce the roll angle. Since in this study only an uncoupled 1 DOF model is used, results can be more accurate when a higher degree of freedom model is used to describe the roll motion. Also attention has been paid to a simple velocity controller. One of the control parameters used is the forwards velocity of the ship. Simulations show that an increase or decrease of the forward velocity would lead to a reduction of the roll angle. Decreasing the velocity always leads to a reduction of the roll angle. But increasing the velocity does not always lead to a reduction of the roll angle. The reduction of the roll angle when increasing the velocity seems to be highly dependent on the forward acceleration of the ship. No explanation for this has been found and further investigation is needed.