Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bogoliubov N N, Mitropolsky Y A (1961) Asymptotic methods in the theory of nonlinear oscillations. Intersciense NY
Cardo A, Francescutto A et al. (1981) Ultra harmonics and subharmonics in the rolling motion of a ship: steady state solution. Int Shipbuild Prog 28:234-251
Cotton B, Bishop S R et al. (2000) Sensitivity of capsize to a symmetry breaking bias. In: Vassalos D, Hamamato M et al. (eds). Contemp Ideas on Ship Stab. Elsevier Oxford
Grochowalski S (1989) Investigation into the physics of ship capsizing by combined captive and free running model tests. Trans of Soc of Nav Archit and Mar Eng 97:169-212
Jiang C, Troesch A W et al. (1996) Highly nonlinear rolling motion of biased ships in random beam seas. J of Ship Res 40 2:125-135
Macmaster A G, Thompson J M T (1994) Wave tank testing and the capsizability of hulls. Proc of the R Soc London A 446:217-232
Nayfeh A H (1979) Nonlinear oscillations. John Wiley NY
Nayfeh A H, Khdeir A A (1986) Nonlinear rolling biased ships in regular beam waves. Int Shipbuild Prog 33:84-93
Spyrou K J, Cotton B et al. (1996) Analytical expressions of capsize boundary for a ship with roll bias in beam waves. J of Ship Res 46 3:125-135
Wright J H G, Marshfield W B (1980) Ship roll response and capsize behavior in beam seas. Trans of RINA 122:129-149
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Odabasi, A.Y., Uçer, E. (2011). Effect of Initial Bias on the Roll Response and Stability of Ships in Beam Seas. In: Almeida Santos Neves, M., Belenky, V., de Kat, J., Spyrou, K., Umeda, N. (eds) Contemporary Ideas on Ship Stability and Capsizing in Waves. Fluid Mechanics and Its Applications, vol 97. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1482-3_7
Download citation
DOI: https://doi.org/10.1007/978-94-007-1482-3_7
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-1481-6
Online ISBN: 978-94-007-1482-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)