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Research Papers: Structures and Safety Reliability

Estimation of Short-and Long-Term Probability Distributions of Wave-Induced Loads Acting on a Cruise Vessel in Extreme Seas

[+] Author and Article Information
Suresh Rajendran

Centre for Marine Technology and
Ocean Engineering (CENTEC),
Instituto Superior Técnico,
Universidade de Lisboa,
Lisbon 1049-001, Portugal
e-mail: suresh@centec.tecnico.ulisboa.pt

Nuno Fonseca

Centre for Marine Technology and
Ocean Engineering (CENTEC),
Instituto Superior Técnico,
Universidade de Lisboa,
Lisbon 1049-001, Portugal
e-mail: nuno.fonseca@centec.tecnico.ulisboa.pt

C. Guedes Soares

Centre for Marine Technology and
Ocean Engineering (CENTEC),
Instituto Superior Técnico,
Universidade de Lisboa,
Lisbon 1049-001, Portugal
e-mail: c.guedes.soares@centec.tecnico.ulisboa.pt

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received September 13, 2014; final manuscript received October 4, 2017; published online December 6, 2017. Assoc. Editor: Lance Manuel.

J. Offshore Mech. Arct. Eng 140(2), 021602 (Dec 06, 2017) (14 pages) Paper No: OMAE-14-1126; doi: 10.1115/1.4038347 History: Received September 13, 2014; Revised October 04, 2017

A time domain code based on strip theory is applied to calculate the probability distributions of relative motions and bending moments of a cruise ship in a set of extreme seas. The code includes two levels of complexity. The simpler one combines linear radiation and diffraction forces with nonlinear Froude–Krylov forces, hydrostatic forces, and shipping of green water on the bow. Cummins formulation is used to represent the radiation forces. The second approach is a generalization of the first one and, although the formulation is based on the linear assumption (of the radiation forces), the effects of body nonlinearity are considered by a simplified method: the memory functions, infinite frequency added masses, and the radiation restoring coefficients are assessed at each time instant as function of the instantaneous wetted surface. A similar procedure is used to calculate the diffraction forces. The code is used to analyze the responses of a cruise ship in a set of extreme sea conditions. The short-term nonlinear responses are represented by empirical probability distributions, obtained from the nonlinear time domain simulations, and the quality of the predictions is assessed by comparing with model tests experimental data. Finally, the long-term value of the bending moment is calculated from the short-term distribution of the nonlinear loads in a few extreme sea states selected based on coefficient of contribution method, and the results are compared with the International Association of Classification Societies (IACS) rule bending moment.

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References

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Figures

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Fig. 1

Body plan of cruise vessel

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Fig. 2

Coordinate transformation between the original and new coordinate system

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Fig. 3

Probability of exceedance of experimental and numerical wave crests (+ve) and troughs (−ve) for case 1 (top graph) and case 2 (bottom graph). The left graph shows the comparison between experimental wave and numerical waves that is spatially shifted to center of gravity of ship from the measured location using linear dispersion. The right graph shows the experimental waves when used for numerical analysis at the LCG of the ship without any spatial transfer.

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Fig. 4

Probability of exceedance of experimental and numerical hogging (+ve) and sagging (−ve) moment peaks for case 1. Acronyms “TD” and “TDNL” stand for results from partial and fully body nonlinear code, respectively. (M̂5=M5/ρgHsLpp2B).

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Fig. 5

Probability of exceedance of experimental and numerical hogging (+ve) and sagging (−ve) moment peaks for case 2. Acronyms TD and TDNL stand for results from partial and fully body nonlinear code, respectively. (M̂5=M5/ρgHsLpp2B).

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Fig. 6

Probability of exceedance of experimental and numerical relative motion for case 1 (left) and 2 (right). Acronym TDNL stands for results from the fully nonlinear code.

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Fig. 7

Probability of exceedance of experimental and numerical hogging (+ve) and sagging (−ve) moment peaks for case 3 (left) and case 4 (right). Acronym TDNL stands for results from the fully body nonlinear code.

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Fig. 8

VBM RAO of the passenger ship (left plot) and linear long-term distribution of VBN (right plot). Long-term VBM calculated for 20 years is encircled in the plot.

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Fig. 9

PM spectrum (left) and generated time series (right) for case 1

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Fig. 10

Probability of exceedance of numerical hogging and sagging moment peaks for case 1 (left) and case 2 (right) fitted with a two-parameter Weibull distribution

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