NONLINEAR DYNAMICS ON PARAMETRIC ROLL RESONANCE WITH REALISTIC NUMERICAL MODELLING

Abstract

This paper describes latest collaborative researches between Japan and the UK on parametric roll resonance of a container ship in following and head seas with realistic modelling of restoring moment as a nonlinear function of wave steepness in experimental, geometrical and analytical approaches. Firstly, captive model experiments were conducted, and demonstrated that the Froude-Krylov prediction could overestimate the amplitude of its variation. Secondly, Poincare mapping technique applied to the numerical model with measured time-varying restoring moment was used for tracing stable steady states, and revealed symmetry-breaking, period-doubling, chaos and capsizing associated with parametric roll resonance. Thirdly, an averaging method was applied to the same numerical model, and confirmed good agreement with the Poincare mapping as well as subcritical bifurcation. Finally, by utilising the present numerical model and methodology, it is shown that a requirement of higher metacentric height does not always improve safety for capsizing associated with parametric roll resonance.