Investigation of coupled sway, roll and yaw motions of a floating body: numerical modelling for non-linear roll restoring

The article deals with the numerical modelling of sway, roll and yaw motions of a floating body in time domain and investigates motion instability primarily due to non-linear roll restoring characteristics in the absence of auto piloting mechanism. To compute hydrodynamic forces, we consider non-linear roll restoring characteristics and speed dependent strip theory that are obtained from the Frank's close-fit method. The governing equations are solved numerically by using Runge-Kutta-Gill method with adaptive step size adjustment algorithm. In order to illustrate non-linear roll restoring effect in sway, roll and yaw, numerical experiments have been carried out for a Panamax container ship under the action of sinusoidal wave of periodicity 11.2 s with varying wave height and speed. To emulate the soft spring behaviour in roll, the expression for non-linear restoring moment is represented by an odd order polynomial of roll angle. Further, in the absence of zero restoring mechanism in sway and yaw, the effect of initial condition, wave height and ship's speed is examined in terms of ship's stability. This approach provides an important guideline to model non-linear roll restoring moment for a coupled system in three degrees of freedom.