Parametric Roll Motion Reduction of a Ship with a Passive Anti-Roll Tank

Abstract

In this study, the influence of a U-tube passive anti-roll tank on parametric roll motion has been investigated as a mechanical absorber of a dynamic system. Specifically, this paper concentrates on how the initial conditions of a coupled roll motion and fluid motion in the tank act on the performance of an anti-roll tank. Parametrically excited roll motion was modeled as a single degree of freedom system incorporating heave and pitch effects by means of a time-varying restoring moment. Fluid motion in the tank was modeled as a single degree of freedom system. Coupled equations of motion were solved numerically and the results were presented in the time domain. Furthermore, the results were comparatively depicted as maximum roll amplitudes vs. initial values for a ship with and without an anti-roll U-tube tank.

Keywords

• Parametric roll motion
• Initial values
• anti-roll tanks
• passive tanks

Pasif Yalpa Tankı ile Gemilerde Parametrik Yalpa Hareketinin Sönümlenmesi

Öz

Bu çalışmada U tüp şeklindeki pasif yalpa tankının parametrik yalpa hareketi üzerindeki sönümleyici etkisi incelenmiştir. Bu çalışmada özellikle adi diferansiyel denklem olan yalpa hareketi ve tank içindeki sıvı hareketi denklemlerinin başlangıç şartlarının yalpa sönümle üzerindeki performansına dikkat çekilmiştir. Parametrik yalpa hareketi, dalıp çıkma ve baş kıç vurma hareketlerinin zamanla değişen doğrultma moment terimi içine gömüldüğü bir serbestlik dereceli lineer olmayan bir denklem olarak modellenmiştir. Tank içindeki sıvı hareketi de 1 serbestlik derecesinde modellenmiştir. Denklem çifti sayısal olarak çözülmüş ve sonuçları zamana bağlı olarak gösterilmiştir. Ayrıca başlangıç şartlarının pasif yalpa tanklı ve tanksız durumlar üzerindeki etkisi karşılaştırmalı olarak sunulmuştur.

Anahtar Kelimeler

• Paramatrik yalpa hareketi
• başlangıç değerleri
• yalpa önleme tankları
• pasif tanklar

References

1. ABS. (2004). Guide for the assessment of parametric roll resonance in the design of container carriers. American Bureau of Shipping, Houston, (as amended 2008).
2. Barr, R.A. and Ankudinov, V. (1977). Ship rolling, its prediction and reduction using roll stabilization. Marine Technology. Vol.14, No.1, pp. 19–41.
3. Belenky, VL. (2004). On risk evaluation at extreme seas. Proceedings of the 7th international stability workshop. Shanghai, China, pp. 188–202.
4. Bell, J. and Walker, W.P. (1966). Activated and passive controlled fluid tank system for ship stabilization. SNAME Transaction. Vol. 74, pp. 150–193.
5. 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 Analysis of Real-World Application. Vol. 5, No.4 pp.725–748.
6. Bulian, G., Francescutto, A. and Lugni, C. (2004). On the nonlinear modeling of parametric rolling in regular and irregular waves. International Shipbuilding Progress. Vol. 51, pp.205–220.
7. Falzarano, J.M., Esparza, I., Taz U.I. and Mulk, M. (1995). A combined steady-state and transient approach to study large amplitude ship rolling motion and capsizing. Journal of Ship Research. Vol. 39, No.3, pp. 213–224.
8. Field, S.B. and Martin, J.P. (1976). Comparative effects of U-tube and free surface type passive roll stabilization systems. Royal Institute of Naval Architects. Vol. 2, pp. 73–92.

9. France, W.N., Levaduo, M., Treakle, T.W., Paulling, J.R., Michel, R.K. and Moore, C. (2003). An investigation of head-sea parametric rolling and its influence on container lashing systems. Marine Technology,.Vol. 40, No.1, pp. 1–19.
10. Francescutto, A. (2007). Intact stability of ships recent developments and trends. Proceedings of 10th international symposium on practical design of ships and other floating structures PRADS’07, Houston, Vol 1, pp. 487–496.
11. Graff, W. and Heckscher, E. (1941). Widerstand und Stabilita¨t Versuche mit Drei Fischdampfer Modellen. Werft Reederei Hafen, Vol.22 pp.115–120.
12. Gawthrop, P.J., Kountzeris, A. and Roberts, J.B. (1988). Parametric identification of nonlinear ship roll motion from forced roll data. Journal of Ship Research, Vol. 32 No.2, pp. 101–111.
13. Gawad, A.F.A., Ragab, S.A., Nayfeh, A.H. and Mook, D.T. (2001). Roll Stabilization by Anti Roll Passive Tanks. Ocean Engineering, Vol.28, pp. 457-469.
14. Hashimoto, H., Umeda, N. and Matsuda, A. (2006). Experimental and numerical study on parametric roll of a Post-Panamax container ship in irregular wave. Proceedings of STAB’06 9th international conference on stability of ships and ocean vehicles, Rio de Janeiro, Brazil, pp. 181–190.
15. Ikeda, Y., Himeno, Y. and Tanaka, N. (1978). A prediction method for ship roll dampin., Report No. 00405 of Department of Naval Architecture, University of Osaka Prefecture.
16. Kempf, G. (1938). Die Stabilita¨t Beanspruchung der Schiffe Durch Wellen und Schwingungen. Werft Reederei Hafen, Vol.19 pp. 200–202.
17. Kerwin, J.E. (1955). Note on rolling in longitudinal waves. International Shipbuilding Progress. Vol. 2, No. 16, pp. 597–614.
18. Lee, B.S. and Vassalos, D. (1996). An investigation into the stability effects of anti-roll tanks with flow obstructions. International Shipbuilding Progress. Vol. 43, No. 433, pp. 70–88.
19. Lewison, B.A. (1975). "Optimum Design of Passive Roll Stabilizer Tanks. The Royal Institution of Naval Architects, pp. 31–45.
20. Lloyd, A.R.J.M. (1989). Seakeeping-Ship Behaviour in Rough Weather. Ellis Horwood Limited, Chichester.
21. Mathieu, E. (1868). Me´moiresur Le Mouvement Vibratoired’une Membrane de forme Elliptique. Journal des Math´matiques Pureset Applique´es, Vol. 13, pp. 137–203.
22. Nayfeh, A.H. and Oh, I.G. (1995). Nonlinearly coupled pitch and roll motions in the presence of internal resonance; part 1, theory. International Shipbuilding Progress, Vol. 42, pp. 295–324.
23. Neves, M.A.S. and Rodriguez, C.A. (2006). Influence of non-linearities on the limits of stability of ships rolling in head seas. Ocean Engineering, Vol. 34, pp. 1618–1630.
24. Paulling, J.R., Kastner, S. and 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).
25. Paulling, J.R. and Rosenberg, R.M. (1959). On unstable ship motions resulting from nonlinear coupling. Journal of Ship Research, Vol. 3 pp. 36–46.
26. Peşman, E. and Taylan, M. (2011). Effect of Encounter Angle on Parametric Roll Motion in Regular Waves. INT-NAM 2011, İstanbul, 24, 25 October, pp. 337-345.
27. Peşman E. and Taylan M., (2012). Influence of varying restoring moment curve on parametric roll motion of ships in regular longitudinal waves. Journal of Marine Science and Technology, vol. 17, pp 511–522.
28. Sanchez, N.E. and Nayfeh, A.H. (1990). Nonlinear rolling motions of ships in longitudinal waves. International Shipbuilding Progress, Vol.37, No. 411, pp. 247–272.
29. Shin, Y.S., Belenky, V.L., Paulling, J.R., Weems, K.M. and Lin, W.M. (2004). Criteria for parametric roll of large containerships in longitudinal seas. SNAME Transactions, Vol. 112, pp. 14–47.
30. Spyrou, K.J. (2000). Designing against parametric instability in following seas. Ocean Engineering, Vol. 27, pp. 625–650.
31. Stigter, C. (1966). The performance of U-tanks as a passive anti-rolling device. The Royal Institution of Naval Architects ISP, Vol.13, No.144, pp. 249–275.
32. Vasta, J., Giddings, A.J., Taplin, A. and Stilwell, J.J. (1961). Roll stabilization by means of passive tanks. SNAME Transactions, Vol. 69, pp. 411–460.
33. Vugts, I.R.J.H. (1969). A comparative study on four different passive roll damping tanks—part II. International Shipbuilding Progress, Vol. 16, pp. 212–223.
34. Watanabe, Y. (1934). On the dynamic properties of the transverse instability of a ship due to pitching. Journal of Society of Naval Architects Japan, Vol. 53, pp.51–70.
35. Webster, W.C. (1967). Analysis of the control of activated antiroll tanks. SNAME Transactions, Vol. 75, pp. 296–331.
36. Webster, W.C., Dalzell, J.F. and Barr, R.A. (1988). Prediction and measurement of the performance of freeflooding ship antirolling tanks. SNAME Transactions, Vol. 96, pp. 333–364.