On the loss of stability of periodic oscillations and its relevance to ship capsize

TitleOn the loss of stability of periodic oscillations and its relevance to ship capsize
Publication TypeJournal Article
Year of Publication2019
AuthorsA Maki, LN Virgin, N Umeda, T Ueta, Y Miino, M Sakai, and H Kawakami
JournalJournal of Marine Science and Technology (Japan)
Volume24
Start Page846
Issue3
Pagination846 - 854
Date Published09/2019
Abstract

This research revisits the analysis of roll motion and the possible capsize of floating vessels in beam seas. Many analytical investigations of this topic have adopted the softening Duffing equation, which is similar to the ship roll equation of motion. Here we focus on the loss of stability of periodic oscillations and its relevance to ship capsize. Previous researchers have found the thresholds of the saddle-node, flip, and heteroclinic bifurcations. They derived the flip condition from the negative stiffness condition in a Mathieu type variational equation. In our revisited analysis, we show that this threshold is identical to a pitchfork bifurcation. On the other hand, we simultaneously find that the generated asymmetry solution is unstable due to the limitation of the first order analysis.

DOI10.1007/s00773-018-0591-x
Short TitleJournal of Marine Science and Technology (Japan)