Abstract
This paper examines the influence of stability characteristics on roll motion in the main parametric resonance region. For this purpose, parametrically exited roll motion was modeled as a single degree of freedom system considering heave and pitch effects by means of time varying restoring moment. In addition, restoring moment variations in waves with respect to time and instantaneous roll angle was modeled analytically using the restoring moment curves for the wave crest and wave trough conditions. Roll responses were evaluated in frequency domain by solving the model with an averaging method. Notable correlation between the stability of roll responses and moment curves were observed. The results revealed that, the ratio of metacentric height (GM)between the wave trough and wave crest affects the stability of the trivial solution. Furthermore, the shape of the restoring moment curves in wave trough and wave crest conditions affects the stability of the non-trivial solution or, in other words, the pitchfork bifurcations.
Similar content being viewed by others
References
Watanabe Y (1934) On the dynamic properties of the transverse instability of a ship due to pitching. J Soc Nav Archit Jpn 53:51–70
Kempf G (1938) Die Stabilität Beanspruchung der Schiffe Durch Wellen und Schwingungen. Werft Reederei Hafen 19:200–202
Graff W, Heckscher E (1941) Widerstand und Stabilität Versuche mit Drei Fischdampfer Modellen. Werft Reederei Hafen 22:115–120
Kerwin JE (1955) Note on rolling in longitudinal waves. Int Shipbuild Prog 2(16):597–614
Paulling JR, Rosenberg RM (1959) On unstable ship motions resulting from nonlinear coupling. J Ship Res 3:36–46
Paulling JR, Kastner S, Schaffran S (1972) Experimental Studies of capsizing of intact ships in heavy seas. U.S. Coast Guard Technical Report (also IMO Doc. STAB/7, 1973)
France WN, Levaduo M, Treakle TW, Paulling JR, Michel RK, Moore C (2003) An investigation of head-sea parametric rolling and its influence on container lashing systems. Mar Technol 40(1):1–19
Spyrou KJ (2000) Designing against parametric instability in following seas. Ocean Eng 27:625–653
Neves MAS, Rodriguez CA (2006) Influence of non-linearities on the limits of stability of ships rolling in head seas. Ocean Eng 34:1618–1630
Bulian G, Francescutto A, Lugni C (2004) On the nonlinear modeling of parametric rolling in regular and irregular waves. Int Shipbuild Prog 51:205–220
Shin YS, Belenky VL, Paulling JR, Weems KM, Lin WM (2004) Criteria for parametric roll of large containerships in longitudinal seas. SNAME Trans 112:14–47
ABS (2004) Guide for the assessment of parametric roll resonance in the design of container carriers. American Bureau of Shipping, Houston (as amended 2008)
Belenky VL (2004) On risk evaluation at extreme seas. In: Proceedings of the 7th international stability workshop, Shanghai, China, pp 188–202
Hashimoto H, Umeda N, Matsuda A (2006) Experimental and numerical study on parametric roll of a Post-Panamax container ship in irregular wave. In: Proceedings of STAB’06 9th international conference on stability of ships and ocean vehicles, Rio de Janeiro, Brazil, pp 181–190
Bulian G, Francescutto A, Lugni C (2006) Theoretical, numerical and experimental study on the problem of ergodicity and ‘practical ergodicity’ with an application to parametric roll in longitudinal long crested irregular sea. Ocean Eng 33:1007–1043
IMO SLF 50/4/12 (2007) Review of the intact stability code. Comments on the development of new generation intact stability criteria. http://legacy.sname.org/committees/tech_ops/O44/50/50-4-12.pdf
IMO SLF 51 (2008) Revision of the intact stability code. Report of the Working Group (Part 1), London 2008
Francescutto A (2007) Intact stability of ships recent developments and trends. In: Proceedings of 10th international symposium on practical design of ships and other floating structures PRADS’07, Houston, vol 1, pp 487–496
Mathieu E (1868) Mémoiresur Le Mouvement Vibratoired’une Membrane de forme Elliptique. Journal des Mathématiques Pureset Appliquées 13:137–203
Neves MAS, Rodríguez CA (2005) A coupled third order model of roll parametric resonance. In: Proceedings of the maritime transportation and exploitation of ocean and coastal resources, London, pp 243–253
Levadou M, Van’t Veer R (2006) Parametric roll and ship design. In: Proceedings of the ninth international conference on stability of ships and ocean vehicles STAB’06, vol 1, pp 191–206
Bulian G (2004) Approximate analytical response curve for a parametrically excited highly nonlinear 1-DOF system with an application to ship roll motion prediction. Nonlinear Anal Real World Appl 5(4):725–748
Bulian G (2006) Development of analytical nonlinear models for parametric roll and hydrostatic restoring variations in regular and irregular waves. Ph.D. thesis, University of Trieste, Trieste
Thompson JMT, Rainey RC, Soliman MS (1990) Ship stability criteria based on chaotic transients from incursive fractals. Philos Trans R Soc Lond 332:149–167
Hayashi C (1964) Nonlinear oscillations in physical systems. McGraw Hill, New York
Nayfeh AH, Mook DT (1979) Nonlinear oscillations. Wiley, New York
Nayfeh AH (1985) Problems in perturbation. Wiley, New York
Bogoliubov NN, Mitropolsky YA (1961) Asymptotic methods in the theory of non-linear oscillations. Hindustan Publishing Corp, Delhi
Nyquist H (1928) Certain topics in telegraph transmission theory. Trans AIEE 47:617–644 (reprint as classic paper in: Proc. IEEE, vol 90, No. 2, Feb 2002)
Taylan M (2000) The effect of nonlinear damping and restoring in ship rolling. Ocean Eng 27:921–932
Ikeda Y, Himeno Y, Tanaka N (1978) A prediction method for ship roll damping. Report No. 00405 of Department of Naval Architecture, University of Osaka Prefecture
Bishop RC, Belknap W, Turner C, Simon B, Kim JH (2005) Parametric investigation on the influence of GM, roll damping and above-water form on the roll response of model 5613. Technical Report NSWCCD-50-TR-2005/027, Naval Surface Warfare Center, Carderock Division, Hydromechanics Department
McCue LS, Campbell BL, Belknap WF (2007) On the parametric resonance of tumblehome hull forms in a longitudinal seaway. Am Soc Nav Eng J 3:35–44
Meyers WS, Applebee TR, Baitis AE (1981) User’s manual for the standard ship motion program, SMP. David Taylor Naval Ship Research and Development Center No. SPD-0936-01
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Peşman, E., Taylan, M. Influence of varying restoring moment curve on parametric roll motion of ships in regular longitudinal waves. J Mar Sci Technol 17, 511–522 (2012). https://doi.org/10.1007/s00773-012-0179-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00773-012-0179-9