Bifurcation and resonance of a mathematical model for non-linear motion ofa flooded ship in waves

A flooded ship can exhibit undesirable non-linear roll motion even in waves of moderate amplitude. In order to understand the mechanism of this non-li near phenomenon, the nan-linearly coupled dynamics of a ship and flood wate r are considered using a mathematical model for the simplified motion of a flooded ship in regular beam waves. This paper describes bifurcation and re sonance of this coupled system. A bifurcation diagram shows that large-ampl itude subharmonic motion exists in a wide range of parameters, and that the Hopf bifurcation is observed due to the dynamic effects of flood water. Re sonance frequencies can be determined by linearization of this model. Compa rison between the resonance points and the bifurcation curves suggests that non-linear resonances of this model can bring about large-amplitude subhar monic motion, even if it is in the non-resonant state of the linearized sys tem. (C) 1999 Academic Press.