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.

Drill ship is a ship-shaped structure with a drilling unit at its center and with oil compartments, which is moored and kept in position using anchors. These ships should be capable of working in deep sea for a long time, hence affected by harsh ocean environment. Drill units are said to have greater heave motion, and the height of the derrick influences the vessel’s stability. MARPOL Oil Outflow Analysis is performed for damaged crude oil carriers or tankers and Mobile offshore drilling units (MODU) in damaged condition. In the present study, probabilistic analysis is performed on drill ship to understand its stability behavior under damaged condition. Stability assessments are carried out by considering single and multiple damage locations. Oil outflow analysis is carried out for different damage cases of oil tank. Probabilistic damage assessment is done for load cases up to 50% flooding, to obtain stability charts. These charts will be useful to understand variations in stability parameters under damaged conditions.

Sloshing affects the intact and damage stability of the ship, which causes variation in dynamic metacentric height (GM) under critical load conditions. The transient flooding soon after the ship damage is analyzed, with floodwater accumulation in large space and causing the ship to suffer huge heel angles. The ship motion and stability changes when sloshing becomes high in partially flooded compartments. Most of the previous researches focus on the motion response of ship alone, hence the variation of stability due to sloshing is to be more critically studied. In the present study, three critical damage locations are identified and flooding through these locations are analyzed using the volume of fluids method. The method focus on finding damage ship motion response, flood water dynamics, and coupled dynamics of both. This is studied using the numerical method FLOW3D. Motion and stability behaviour will be different for different damage locations; hence portside, starboard-side, and aft-end bottom damage cases are considered. The effect of compartment shape and damage location on motion response and stability of the damaged ship is highlighted.