In this work a combined analytical-numerical approach is proposed to address the problem of the ship roll motion under the combined action of wind and waves. Roll motion is modelled as a one-degree-of-freedom system non-linear in both damping and restoring. The approach is modular, allowing an easy update of the methodology on the basis of new research outcomes. Realistic environmental conditions regarding the effects of both wind and waves are taken into account and can be easily changed. The spatial correlation of wind gusts is taken into account by means of an ‘aerodynamic admittance’ function, whereas the moment due to waves is obtained from the sea slope spectrum using the concept of effective wave slope, leading to a ‘hydrodynamic admittance’ function. Both static and dynamic aspects of the problems are taken into account. The proposed analytical procedure, based on statistical linearization technique, allows approximate statistical averages of the roll motion, assumed to be Gaussian, to be obtained without necessarily resorting to time-consuming Monte Carlo simulations. On the basis of the results obtained, an estimation of the capsize probability can be carried out. It seems that the effect of wind gustiness could be considered very small when compared with the effects of waves and mean wind speed when the metacentric height is sufficiently large. Finally, the presented approach moves towards the concept of ‘performance-based analysis’, recently introduced at the International Maritime Organization as the basis for future developments of intact stability, in a clear and formal way.
Code on Intact Stability for all Types of Ships Covered by IMO Instruments, 2002 (International Maritime Organization, London).
2.
FrancescuttoAIntact ship stability: The way aheadMar. Technol., 2004, 41, 31–37.
3.
CardoAFrancescuttoANabergojROn damping models in free and forced rolling motion, Ocean Engng, 1982, 9, 171–179.
4.
VugtsJ HThe hydrodynamic coefficients for swaying, heaving and rolling cylinders in a free surface. Report 194, Technical University of Delft, The Netherlands, January 1968.
5.
BlagoveshchenskyS NTheory of Ship Motions (English Translation), 1962 (Dover Publications, New York).
6.
BlendermannWWind loading of ships—collected data from wind tunnel tests in uniform flow. IFS Bericht 574, Institut für Schiffbau, Universität Hamburg, 1996.
7.
BertagliaGSerraAFrancescuttoABulianGExperimental evaluation of the parameters for the weather criterion. In Proceedings of the 8th International Conference onStability of Ships and Ocean Vehicles (STAB2003), Madrid, Spain, September 2003, pp. 253–263.
8.
DeakinBThe development of stability standards for U.K. sailing vessels. In Proceedings of the Spring Meeting of the Royal Institution of Naval Architects, London, April 1990, pp. 1–19.
9.
Scheltema De HeereR FBakkerA RBuoyancy and Stability of Ships, 1969 (Technical Publications H. Stam, Culemborge).
10.
DeakinBModel test techniques developed to investigate the wind heeling characteristics of sailing vessels and their response to gusts. In Proceedings of the 10th Chesapeake Sailing Yacht Symposium, 1991, pp. 83–93.
11.
BulianGFrancescuttoASome considerations on the opportunity of considering a dependence on the ship length of the gust level prescribed by the IMO Res.A562 (in [1]) (in Italian). Internal Report, Department of Naval Architecture, Ocean and Environmental Engineering, University of Trieste, April 2003.
12.
DavenportA GSpectrum of horizontal gustiness near the ground in strong windsJ. R. Meteorol. Soc., 1961, 87, 194–211.
13.
de KatJ OPaullingR JPrediction of extreme roll motions and capsizing of a ship and offshore marine vehicles. In Proceedings of the 20th International Conference onOffshore Mechanics and Arctic Engineering (OMAE2001), Rio de Janeiro, Brazil, June 2001, pp. 1–12.
14.
WichersJ. E.W.DevlinP VEffect of coupling of mooring lines and risers on the design values for a turret moored FPSO in deep water of the Gulf of Mexico. In Proceedings of the 11th International Symposium onOffshore and Polar Engineering (ISOPE), Stavanger, Norway, June 2001, pp. 1–8.
15.
DavenportA GThe application of statistical concepts to the wind loading of structuresProc. Instn Civ. Engrs, 1961, 19, 449–472.
16.
VassalosDJasionowskiACichowiczJWeather criterion—questions and answers. In Proceedings of the 8th International Conference onStability of Ships and Ocean Vehicles (STAB2003), Madrid, Spain, September 2003, pp. 695–705.
17.
SimiuEScanlanH RWind Effects on Structures—Fundamentals and Applications to Design, 3rd edition, 1996 (John Wiley, New York).
KijewskiTHaanFKareemAWind-induced vibrations In Encyclopedia of Vibration (Eds BraunS GEwinsD JRaoS S), 2001, pp. 1578–1587 (Academic Press, New York).
20.
OosterhoutG P CThe wind-induced dynamic response of tall buildings, a comparative studyJ. Wind Engng Ind. Aerodynamics, 1996, 64, 135–144.
21.
ZhouYKijewskiTKareemAAlongwind load effects on tall buildings: A comparative study of major international codes and standardsJ. Struct. Engng, Am. Soc. Civ. Engrs, 2002, 128 (6), 788–796.
22.
OchiM KApplied Probability and Stochastic Processes in Engineering and Physical Sciences, 1990 (John Wiley, New York).
23.
ThompsonJ M TTransient basins: A new tool for designing ships against capsize. In Proceedings of the IUTAM Symposium onDynamics of Marine Vehicles and Structures in Waves, Brunel University, Uxbridge, Middlesex, June 1990, pp. 325–331.
24.
RobertsJ BSpanosP DRandom Vibration and Statistical Linearization, 1990 (John Wiley, New York).
25.
FaltinsenO MSea Loads on Ships and Offshore Structures, 1990 (Cambridge University Press, Cambridge).
26.
IkedaYHimenoYTanakaNA prediction method for ship roll damping. Report 00405, Department of Naval Architecture, University of Osaka Prefecture, 1978, p. 21.
27.
BelenkyVSuzukiSYamakoshiYPreliminary results of experimental validation of practical non-ergodicity of large amplitude rolling motion. In Proceedings of the 5th International Workshop onShip Stability and Operational Safety, Trieste, Italy, September 2001, pp. 4.1.1–4.1.8.
28.
CrandallS HMarkW DRandom Vibration in Mechanical Systems, 1973 (Academic Press, New York).
29.
ParkusHRandom Processes in Mechanical Sciences, 1969 (CISM, Udine).
30.
AngA. H.S.TangW HProbability Concepts in Engineering Planning and Design, Vol. 1, Basic Principles, 1975 (John Wiley, New York).
31.
Time-dependent survival probability of a damaged passenger ship, Vol. 1 (Capsizing). HSVA Report CFD 05/2002, Hamburg, February 2002.
DitlevsenOStochastic model for joint wave and wind loads on offshore structuresStructl Safety, 2002, 24, 139–163.
34.
FrancescuttoAContentoGBiotMSchiffrerLThe effect of excitation modelling in the parameter estimation of nonlinear rolling. In Proceedings of the 8th International Offshore and Polar Engineering Conference, Montréal, Canada, May 1998, pp. 490–498.
35.
TuckerM JChallenorP GCarterD J TNumerical simulation of a random sea: A common error and its effect upon wave group statisticsAppl. Ocean Res., 1984, 6, 118–122.
FranceW NLevadouMTreakleT WPaullingJ RMichelR KMooreCAn investigation of head-sea parametric rolling and its influence on container lashing systemsMar. Technol., 2003, 40 (1), 1–19.
GodaYRandom Seas and Design of Maritime Structures, 1985 (University of Tokyo Press, Tokyo).
42.
PanjaitanJ PA study on ship motions and capsizing in severe astern seas. PhD thesis, Department of Naval Architecture and Ocean Engineering, Faculty of Engineering, Osaka University, Osaka, Japan, 1998.
43.
VassalosDA critical look into the development of ship stability criteria based on work/energy balanceTrans. R. Instn Nav. Architects, 1986, 128, 217–234.
