Integrity Diagrams of the Ship/U-Tank System Undergoing Parametric Rolling

Unstable rolling motions in regular head seas are investigated in the case of a ship stabilized with an U-type anti-rolling tank (ART). A transom stern small vessel, well-known for her tendency to develop strong parametric excitation is investigated. Nonlinear equations are employed to describe the liquid motion inside the tank, the forces and moments generated by the tank on the ship and the coupled ship motions (heave, roll and pitch). These are numerically solved for different initial conditions. Nonlinear dynamics techniques are applied to the coupled ship/tank system. In particular, it is verified that the nonlinear system, despite the fact that the ship is stabilized with a tuned ART, as wave amplitude is increased there exists a process of erosion of the safe basin which is not smooth. Similarly to the case of the unstabilized ship, the integrity diagrams show a clear cliff tendency at some critical wave amplitudes. The implication of this aspect is relevant to the design of ART’s against parametric rolling, in the sense that it allows for the definition and quantification of a critical wave amplitude for distinct tank designs in the context of an analysis that takes into account all the relevant nonlinearities of the coupled ship and tank motions under the influence of a whole set of initial conditions.