Course information

Historical development of ship stability theory. Moseley s concept of dynamic stability. Overview of ship dynamic stability problems. Interface with classical nonlinear dynamical systems’ stability theory. General stability analysis of equilibrium positions and of periodic responses. Coexistence of responses. Modeling the effect of wind on a ship (steady and gusty). The basic equation of ship roll motion for beam seas. The classical Froude approach with the analog of the rotational oscillator. Solution of the linear problem, qualitative and quantitative effect of non-linear terms, permanent and transient behavior, effect of ship loading bias on dynamic stability. Stability consideration for large heel angles. Nonlinear resonance and hysteretic effects. Predictions of roll motions through numerical simulation and approximate analytical solutions based on perturbation theory. Instabilities due to time-varying righting-arm in longitudinal waves. The phenomenon of parametric instability, types and design features of ships where it occurs. Development of a simplified mathematical model and analytical determination of the principal region of parametric instability. Effect of damping and motion coupling. Design criteria. Conditions for ""pure loss of stability"" in following waves. Other instability phenomena and description of the IMO guidelines to avoid dangerous situations. The scientific background of the ""weather criterion"" of ship stability according to IMO. Review of other criteria in force and future trends. Basic concepts of probabilistic approach and application examples. Introduction to damage Stability, historical development, comparison of the deterministic and the probabilistic approach. Calculation of subdivision index according to Wendel’s theory. Current regulations, design aids, and modern developments.