S. Murashige et al., Bifurcation and resonance of a mathematical model for non-linear motion ofa flooded ship in waves, J SOUND VIB, 220(1), 1999, pp. 155-170
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.