Approximate analytical response curve for a parametrically excited highly nonlinear 1-DOF system with an application to ship roll motion prediction

Nonlinear Analysis: Real World Applications

Volumn 5, Issue 4, 2004, Pages 725-748

  Bulian, Gabriele ^a  

^a UNIVERSITY OF TRIESTE   (Italy)

Author keywords

Bifurcations; Mathieu; Nonlinear roll; Parametric excitation; Parametric roll; Ship safety; Stability

Indexed keywords

EID: 3042603109     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2004.03.002     Document Type: Article

References (30)

1. V. Belenky, K.M. Weems, W.M. Lin, J.R. Paulling, Probabilistic analysis of roll parametric resonance in head sea, Proceedings of the Eighth International Conference on Stability of Ships and Ocean Vehicles (STAB2003), Madrid, September 2003, pp. 325-340.
2. Blagoveshchensky S.N. Theory of Ship Motions, (English translation) 1962 Dover New York
3. G. Bulian, Parametric roll in regular and irregular sea, Graduation Thesis, University of Trieste, October 2002 (in Italian).
4. G. Bulian, Nonlinear parametric rolling in regular waves-A general procedure for the analytical approximation of the GZ curve and its use in time domain simulations, Technical Report PHD1-2003, DINMA, University of Trieste, Submitted for publication.
5. G. Bulian, Nonlinear parametric rolling in regular waves-An approximate analytical solution for the response curve in the region of first parametric resonance, Technical Report PHD2-2003, DINMA, University of Trieste, Submitted for publication.
6. G. Bulian, A. Francescutto, C. Lugni, A theoretical and experimental study of the threshold and amplitude of parametric rolling in regular and irregular waves, Proceedings of the International Conference on Ship and Shipping Research-NAV2003, Vol. 2, Palermo, June 2003, pp. 7.6.1-7.6.12.
7. G. Bulian, A. Francescutto, C. Lugni, On the nonlinear modeling of parametric rolling in regular and irregular waves, Proceedings of the Eighth International Conference on Stability of Ships and Ocean Vehicles (STAB2003), Madrid, September 2003, pp. 305-323.
8. Cardo A. Francescutto A. Nabergoj R. Ultraharmonics and subharmonics in the rolling motion of a ship: steady-state solution Int. Shipbuild. Prog. 28 326 1981 234-251
9. Cardo A. Francescutto A. Nabergoj R. On damping models in free and forced rolling motion Ocean Eng. 9 2 1982 171-179
10. J.M. Falzarano, Complete six-degrees of freedom nonlinear ship rolling, Proceedings of STAB94, Florida, November 1994, pp. 1430-1455.
11. France W.N. Levadou M. Treakle T.W. Paulling J.R. Michel R.K. Moore C. An investigation of head-sea parametric rolling and its influence on container lashing systems Mar. Technol. 40 1 2003 1-19
12. A. Francescutto, An experimental investigation of parametric rolling in head waves, Proceedings of ETCE/OMAE2000 Joint Conference: Energy for New Millenium, New Orleans, February 2000.
13. A. Francescutto, Theoretical study of the roll motion in longitudinal waves, Technical Report, Department of DINMA, University of Trieste, 2002 (in Italian).
14. A. Francescutto, G. Bulian, Nonlinear and stochastic aspects of parametric rolling modelling, Proceedings of the Sixth International Ship Stability Workshop, Webb Institute, New York, October 2002.
15. A. Francescutto, G. Bulian, Theoretical and experimental study of roll motion in longitudinal irregular waves, Technical Report, Department of DINMA, University of Trieste, 2003 (in Italian).
16. Francescutto A. Contento G. Bifurcations in ship rolling: experimental results and parameter identification technique Ocean Eng. 26 1999 1095-1123
17. A. Francescutto, D. Dessi, R. Penna, Some remarks on the nonlinear modelling of parametric rolling, Proceedings of 11th International Symposium on Offshore and Polar Engineering-ISOPE'2001, Vol. 3, Stavanger, May 2001, pp. 317-320.
18. A. Francescutto, S. Naito, Large amplitude rolling in a realistic sea, Proceedings of the Eighth International Conference on Stability of Ships and Ocean Vehicles (STAB2003), Madrid, September 2003, pp. 495-505.
19. Hayashi C. Nonlinear Oscillations in Physical Systems 1964 McGraw Hill New York
20. IMO Document SLF 45/6/2, Proposals with regard to the scope of revising the IS Code and the related MSC/Circ.707, submitted by Germany.
21. MSC/Circ.707, Guidance to the master for avoiding dangerous situations in following and quartering seas, IMO, London, 1995.
22. Nayfeh A.H. Problems in Perturbation 1985 Wiley New York
23. Nayfeh A.H. Mook D.T. Nonlinear Oscillations 1979 Wiley New York
24. VOh I.G. Nayfeh A.H. Mook D.T. A theoretical and experimental investigation of indirectly excited roll motion in ships Philos. Trans. R. Soc. 15 358 1771 2000 1853-1881
25. Press W.H. Flannery B.P. Teukolsky S.A. Vetterling W.T. Numerical Recipes-The Art of Scientific Computing (FORTRAN Version) 1990 Cambridge University Press Cambridge
26. H. Sadakane, A criterion for ship capsize in beam sea, Proceedings of the Third International Conference on Stability of Ships and Ocean Vehicles (STAB'86), Paper, 3.1, Gdansk, September 1986, pp. 119-124.
27. Spyrou K.J. Designing against parametric instability in following seas Ocean Eng. 27 2000 625-653
28. K.J. Spyrou, A basis for a developing a rational alternative to the weather criterion: problems and capabilities Proceedings of the Sixth International Ship Stability Workshop, Webb Institute, New York, October 2002.
29. Tondl A. Ruijgrok T. Verlhust F. Nabergoj R. Autoparametric Resonance in Mechanical Systems 2000 Cambridge University Press Cambridge
30. N. Umeda, H. Hashimoto, D. Vassalos, S. Urano, K. Okou, Nonlinear dynamics on parametric roll resonance with realistic numerical modelling, Proceedings of the Eighth International Conference on Stability of Ships and Ocean Vehicles (STAB2003), Madrid, September 2003, pp. 281-290