Effect of initial bias on the roll response and stability of ships in beam seas

A. Yucel Odabasi, Erdem Uçer*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


This study intended to evaluate the behavior of a biased ship under main, sub and super harmonic resonant excitation. For the sake of simplicity Duffing's equation is used for un-biased roll equation. In the first part of this study, first and second order approximate solutions of biased roll equation have been obtained for different equation parameters in main, sub and super harmonic resonance regions by using method of multiple scales and Bogoliubov-Mitropolsky asymptotic method. It was found that second order approximate solutions had a better compliance with numerical results when the solution is stable. In the second part, stable solution bounds of the biased roll equation were obtained for different equation parameters by using numerical methods. It was found that the size of the bounds are highly dependent on initial bias angle, linear damping coefficient, amplitude and frequency of wave excitation and phase angle of the excitation force and also the symmetry of the bounds were dependent on the magnitude of the initial bias angle. From the results obtained it can be concluded that Lyapunov's stability theory provides the most reliable results.

Original languageEnglish
Title of host publicationContemporary Ideas on Ship Stability and Capsizing in Waves
EditorsMarcelo Almeida Santos Neves, Jean Otto de Kat, Naoya Umeda, Vadim Belenky, Kostas Spyrou
Number of pages22
Publication statusPublished - 2011

Publication series

NameFluid Mechanics and its Applications
ISSN (Print)0926-5112


Dive into the research topics of 'Effect of initial bias on the roll response and stability of ships in beam seas'. Together they form a unique fingerprint.

Cite this