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When formulating a general, non-linear mathematical model of ship dynamics in waves the hydrostatic forces and moments along with the Froude-Krylov part of wave load are usually concerned. Normally radiation and the diffraction forces are regarded as linear ones. The paper discusses briefly few approaches, which can be used in this respect. The concerned models attempt to model the non-linearities of the surface waves; both regular and the irregular ones, and the non-linearities of the restoring forces and moments. The approach selected in the Laidyn method, which is meant for the evaluation of large amplitude motions in the 6 degrees-of-freedom, is presented in a bigger detail. The workability of the method is illustrated with the simulation of ship motions in irregular stern quartering waves.

An inconvenience in the experimental set-up of a FPSO in regular waves highlighted occurrence of parametric-roll events promoted by yaw-roll coupling and motivated a combined physical and numerical analysis on the relevance of this phenomenon on the roll resonance, as well as on the water shipping. The model tests examine the ship in head- and bow-sea waves in the zone of the first parametric resonance. Numerically, it is adopted a 3D Domain-Decomposition (DD) strategy combining a weakly-nonlinear potential-flow solver based on the weak-scatterer theory with a shallow-water approximation for the shipped liquid and with a bottom-slamming solution. Detailed comparisons against these and other seakeeping experiments validated the numerical method in its different aspects with global success. At first, a 2-dof equivalent linearized yaw-roll coupled system is examined and the measurements are used to estimate hydrodynamic coefficients required to complete the mathematical model of the problem. Then the DD method is applied to verify the instability occurrence and compared against the experiments. From the analysis, the parametric-roll instability does not occur if all nonlinearities in the roll restoring load are not accounted for. However the amplitude of the resonant roll is affected by the coupling with the other degrees of freedom. Especially the coupling with yaw tends to increase the steady-state roll amplitude. It also affects the water shipping with the trend in reducing its severity for the vessel, this is opposite to the influence of the parametric roll in head-sea waves on the water on deck, as documented in Greco et al. (2014) [4] . [ABSTRACT FROM AUTHOR]

Abstract: This paper is a continuation of a technical note published in Ocean Engineering in Vol. 30 (2003). Stability of Ro-Ro ships was subjected to rigorous investigation by many researchers recent past. Stability of a ship is to be ensured during design stage for various loading conditions. Two typical conditions of departure and arrival are usually chosen by naval architects. Out of all types of motions of a ship, the critical motion leading to capsize is the roll. Ship roll motions are very complicated and difficult to analyze, as there are various parameters involved in the motion. Large angle roll motions are nonlinear in many aspects. For larger angles of roll many nonlinearties become significant. Various representations of damping and restoring terms found in the literature are investigated and their solutions are analyzed. Data of a Ro-Ro vessel is used to demonstrate the applicability of the proposed procedure. In the present study, the problem of ship safety has been considered with regard to the rolling motion of a ship in beam waves. A parametric investigation is undertaken to identify and quantify the effect of a number of key parameters viz., wave slope, wave frequency etc. on the capsizing conditions of a ship. Nonlinear response of ship is determined in the frequency domain. [Copyright &y& Elsevier]