Evaluating Capsize Boundary of Damaged Ro-Ro Ship Using Chaos Theory and Probabilistic Analysis

Abstract

Instability in intact condition occurs when a ship’s motion changes periodically with time i.e. frequency of motion will match with free-roll frequency or multiples. In case of damage stability, the instability occurs due to flood water sloshing, a series of vibration occur along with free surface effect, which changes the metacentric height of ship. Mathieu's effect is the linear theory behind instability. Probabilistic damage stability analysis is performed in damage cases for the Ro-Ro vessel to understand the most critical loading condition. Phase plots and radial plots are used to find critical stability parameters for ship at intact condition. A new method for modeling the nonlinear dynamic behavior of ship in the chaotic flooded condition is developed and the results indicate that the vessel behaviour of flooded ship is similar to the Duffings oscillation equation and the stability conditions can be captured by this model.