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Simple Analytical Criteria for Parametric Rolling

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Contemporary Ideas on Ship Stability and Capsizing in Waves

Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 97))

Abstract

Analytical design criteria are sought for predicting the parametric rolling behavior of ships, taking into account: the growth rate during the inception stage of parametric rolling; and the steady amplitude that is reached when regular parametric excitation is assumed. The connection with the shape of the restoring curve and the effect of roll damping are shown. The results of the current deterministic treatment are transferred to the domain of probabilistic analysis by use of the concept of wave groups which seems to provide a powerful basis for criteria development.

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References

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  • Bulian G, Francescutto A and Lugni C (2003) On the nonlinear modeling of parametric rolling in regular and irregular waves, Proc, 8th Int Conf, Stab of Ships and Ocean Veh, 305-324, Madrid.

    Google Scholar 

  • Blocki W (1980) Ship safety in connection with parametric resonance of the roll. Int Shipbuilding Prog, 27, 36-53.

    Google Scholar 

  • Esparza I and Falzarano JM (1993) Nonlinear rolling motion of a statically biased ship under the effect of external and parametric excitations. Proc, Symposium on Dyn and Vibration of Time-Varying Systems, OE, 56, ASME, 111-122.

    Google Scholar 

  • Francescutto A and Dessi (2001) Some remarks on the excitation of parametric rolling in nonlinear modeling. Proc, 5th Int Workshop, Stab and Oper Safety of Ships, Trieste, 4.9.1-4.9.8.

    Google Scholar 

  • Goda Y (1976) On wave groups. Proc, BOSS’76, Vol. 1, 115-128.

    Google Scholar 

  • Gray M (2001) Rolling case for more research, Lloyd’s List (Section: Insight and Opinion), February 18, London.

    Google Scholar 

  • Grim O (1952) Rollschwingungen, Stabilität und Sicherheit im Seegang. Schiffstechnik, 1 (1), 10-21.

    Google Scholar 

  • Hayashi C (1985) Nonlinear Oscillations in Physical Systems, Princeton Univ Press, ISBN 0-691-08383-5, Princeton, New Jersey.

    Google Scholar 

  • Kerwin JE (1955) Notes on rolling in longitudinal waves. Int Shipbuilding Prog, 2 (16) 597-614.

    Google Scholar 

  • Kimura A (1980) Statistical properties of random wave groups. Proc, 1st Coastal Eng Conf, Vol. 2, 2955-2973.

    Google Scholar 

  • Longuet-Higgins MS (1975) On the joint distribution of the periods and amplitudes of sea waves. J of Geophys Res, 80, 6778-6789.

    Article  Google Scholar 

  • Longuet-Higgins MS (1983) On the joint distribution of wave period and amplitudes in a random wave field. Proc of the Royal Soc, London, Series A, 310, 219-250.

    Google Scholar 

  • Longuet-Higgins MS (1984) Statistical properties of wave groups in a random sea state. Proc of the Royal Soc, London, Series A, 389, 241-258.

    Article  MathSciNet  Google Scholar 

  • Myrhaug D, Dahle EA, Slaattelid OH (2000) Statistics of successive wave periods with application to rolling of ships. Int Shipbuilding Prog, 47, 451, 253-266.

    Google Scholar 

  • Neves M (2002) On the excitation of combination modes associated with parametric resonance in waves. Proc, 6th Int Ship Stab Workshop, Webb Inst, Long Island.

    Google Scholar 

  • Paulling JR and Rosenberg RM (1959) On unstable ship motions resulting from nonlinear coupling. J of Ship Res, 3, 1, 36-46.

    Google Scholar 

  • Shin YS, Belenky VL, Paulling JR, Weems KM, Lin WM (2004) Criteria for parametric rolling of large containerships in longitudinal seas, SNAME Annual Meeting, Sept 30 – October 1, Washington D.C. (early copy).

    Google Scholar 

  • Skalak R and Yarymovych MI (1960) Subharmonic oscillations of a pendulum. J of Appl Mech, 27, 159-164.

    MathSciNet  MATH  Google Scholar 

  • Soliman M and Thompson JMT (1992) Indeterminate sub-critical bifurcations in parametric resonance. Proc of the Royal Soc of London, Series A, 438, 433-615.

    Article  MathSciNet  Google Scholar 

  • Spyrou KJ (2000) Designing against parametric instability in following seas, Ocean Eng, 27, 625-653.

    Article  Google Scholar 

  • Stansell P, Wolfram J and Linfoot B (2002) Statistics of wave groups measured in the northern North Sea: comparisons between time series and spectral predictions. Appl Ocean Res, 24, 91-106.

    Google Scholar 

  • Tayfun A (1983) Effects of spectrum bandwidth on the distribution of wave heights and periods. Ocean Eng, 10, 107-118.

    Article  Google Scholar 

  • Tinsley, D. 2003 DNV Project thinks about the box. Lloyd’s List (Section: Shipbuilding and Shiprepair). November 18, London.

    Google Scholar 

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    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Naval Architecture and Marine Engineering, National Technical University of Athens, 9 Iroon Polytechneiou, Zographos, Athens, 157 80, Greece

    K. J. Spyrou

Authors
  1. K. J. Spyrou
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Editor information

Editors and Affiliations

  1. , Department of Naval Architecture and Oce, Federal University of Rio de Janeiro, Parque Tecnologico, Quadra 7, Rio de Janeiro, 21941-972, Brazil

    Marcelo Almeida Santos Neves

  2. Naval Surface Warfare Center Carderock D, MacArthur Blvd 9500, West Bethesda, 20817-5700, Maryland, USA

    Vadim L. Belenky

  3. A. P. Moeller - Maersk A/S, Esplanaden 50, Copenhagen, 1098, Denmark

    Jean Otto de Kat

  4. , School of Naval Architecture and Marine, National Technical University of Athens, Iroon Polytechnion, Zographou 9, Athens, 157 73, Greece

    Kostas Spyrou

  5. , Department of Naval Architecture and Oce, Osaka University, Graduate School of Eng, Yamadaoka Suita 2-1, Osaka, 565-0971, Japan

    Naoya Umeda

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Spyrou, K.J. (2011). Simple Analytical Criteria for Parametric Rolling. 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_13

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