Nonlinear analyses of roll motion of a flooded ship in waves

This paper investigates nonlinear responses of a flooded ship in regular waves. In previous experimental work, we found that the roll motion of a flooded ship can exhibit complicated irregular behaviour even in waves of a moderate height. First, we analyse the fractal dimension and the Lyapunov exponents of the experimental data and show that they have chaotic characteristics. We also show that a radial basis function network obtained directly from the data can reproduce a geometrical structure of the reconstructed attractor and provide good short-term prediction on the dynamical motion. Next, in order to understand this nonlinear phenomenon, we derive a simple mathematical model for the nonlinearly coupled motion of roll and flooded water in regular waves. This model has a form of coupled Duffing's equations with a bistable restoring term and a nonlinear inertial coefficient matrix. We obtain bifurcation diagrams of periodic solutions of this model and examine the intricate structure of this nonlinear system. Chaotic responses are found in wide regions of the parameter space, even if the wave-exciting moment is not large. Furthermore, the attractor structure of the chaotic solution is similar to that of the measured chaotic motion in the experiments. The results suggest that bifurcation analyses in this work help us understand the complex dynamics of nonlinear motion of a flooded ship in waves.