Importance of Accurately Modeling Nonlinear Damping in Predicting Parametric Ship Rolling

Parametric rolling has become an important design issue in the safe operation of large high-speed container ships. This interest is partly based upon the well-published large amplitude rolling incident of the APL China several years ago and numerous other incidents which have also since come to light. What we have found in our research is that a simple linear model of roll damping does not accurately predict the threshold nature of this phenomenon. However, when we accurately include nonlinear damping we are able to capture the qualitative nature of this phenomenon. Moreover the Mathieu Ince-Strutt stability diagram is limited to linear harmonic excitation. What we have done in this work is to extend the Mathieu Ince-Strutt stability diagram to include non-harmonic excitation and nonlinear damping.

Analysis of ship parametric rolling has generally been restricted to simple analytical models and sophisticated time domain simulations. However, simple analytical models do not capture all the critical dynamics while time-domain simulations are time consuming to implement. Our model captures the essential dynamics of the system without over simplification. This work incorporates important aspects of the system and assesses the significance of including or ignoring these aspects. Many of the previous works on parametric rolling make the assumption of linearized and harmonic behaviour of the time-varying restoring arm or metacentric height. This assumption enables modelling the roll as a Mathieu equation.