To study the rolling motion of a ship in the presence of water on its deck, a linear-plus-quadratic damping term was incorporated into its equation of motion. Ship model tests indicates that the key dynamics of the physical system are preserved in the ship rolling equation with the linear-plus-quadratic type damping term. To take into account the presence of randomness in the excitation and the response, a new method was developed and a Melnikov criterion was obtained to provide an upper bound on the domain of the potential chaotic rolling motion (erratic rocking). Additionally, the Melnikov criterion proposed in this study was verified by the utilization of phase plane diagrams and Poincare maps. Furthermore, this research has made the initial endeavor to systematically modify the system parameters in the rolling equation of motion for ship stability analysis.

ship stability  /  Melnikov criterion  /  erratic rocking  /  Poincare section