Non-linear roll dynamics of a Ro-Ro ship in waves

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.