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BIFURCATION AND RESONANCE OF A MATHEMATICAL MODEL FOR NON-LINEAR MOTION OF A FLOODED SHIP IN WAVES

Authors
Journal
Journal of Sound and Vibration
0022-460X
Publisher
Elsevier
Publication Date
Volume
220
Issue
1
Identifiers
DOI: 10.1006/jsvi.1998.1956
Disciplines
  • Mathematics

Abstract

Abstract 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-linear phenomenon, the non-linearly coupled dynamics of a ship and flood water are considered using a mathematical model for the simplified motion of a flooded ship in regular beam waves. This paper describes bifurcation and resonance of this coupled system. A bifurcation diagram shows that large-amplitude subharmonic motion exists in a wide range of parameters, and that the Hopf bifurcation is observed due to the dynamic effects of flood water. Resonance frequencies can be determined by linearization of this model. Comparison between the resonant points and the bifurcation curves suggests that non-linear resonance of this model can bring about large-amplitude subharmonic motion, even if it is in the non-resonate state of the linearized system.

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