Full Scale Measurements of the Hydro-Elastic Response of Large Container Ships for Decision Support

The overall topic of this thesis is decision support for operation of ships and several aspects are covered herein. However, the main focus is on the wave-induced hydro-elastic response of large container ships and its implications on the structural response. The analyses are based mainly on full scale measurements from four container ships of 4,400 TEU, 8,600 TEU, 9,400 TEU and 14,000 TEU Primarily, strains measured near the deck amidships are used.

Furthermore, measurements of motions and the encountered sea state are available for one of the ships. The smallest ship is in operation on the North Atlantic, while the three largest ships are operated on the Europe - Asia route. In the design rules of the classification societies for container ships the minimum design sagging bending moment amidships is larger than the hogging bending moment.

Due to their design (full midship section and slender bow and stern sections) and their normal cargo loading condition, container ships are typically operated in a still-water hogging condition (tension in deck and compression in the bottom structure). The wave-induced bending moment is added to the still-water bending moment, which, together with the smaller design hogging bending moment, generally makes the wave-induced hogging bending moment more critical than the sagging bending moment in the operation of container ships.

As container ships of today become larger, their natural vibration frequencies become lower and approach the typical encounter frequency with the waves. Together with the relatively high design speed and often pronounced bow flare this makes large container ship more sensitive to slamming and, consequently, the effects of wave-induced hull girder vibrations.

From full scale strain measurements of individual, measured hull girder responses in the four container ships, the wave-induced hull girder vibrations are found to increase the vertical bending moment amidships by 100% or more. From the full scale measurements the amplification, due to the hull girder flexibility, is found to be largest for the 8,600 TEU and the 9,400 TEU ships, but, in addition to ship size, speed and bow flare angle are also believed to be important factors contributing to the hull girder vibrations.

The hull girder vibrational response is found to be dominated by the 2-node vertical bending mode. No torsional vibrations are found but torsion may, however, still be a concern for ultra large container ships. The damping of the 2-node vertical bending mode is estimated from full scale measurements for the four ships to 1.3-2.5% of the critical damping.

No effect of ship size on the damping is identified. In some cases the hogging bending moment is more amplified by the effect of the hull girder flexibility than the sagging bending moment. No general trend in the amplification of the response is found from the full scale measurements. In some cases, the rigid-body hogging bending moment, found from full scale measurements and model tests, is considerably larger than the corresponding sagging bending moment.

Generally, the difference between the design sagging and hogging bending moments is not reflected in the full scale measurements considered here. The extreme value of the vertical hogging bending moment, as estimated from full scale measurements, is investigated using the peak-over-threshold method for different periods.

The tails of the peak distributions for the four different ships are found to be very different from case to case. The irregularity of the tail behaviour makes it difficult to determine an appropriate extreme value distribution for the hogging bending moment. The Gumbel distribution is believed to be the appropriate extreme value distribution, but it may be necessary to fit other types of extreme value distributions to the largest peaks.

From the full scale measurements it is difficult to assess the influence of operational parameters (ship speed, heading relative to the waves and wave height) on the extreme response because these data are not readily available in all cases. Model tests indicate that bow-quartering sea may induce larger structural loads on the ship than direct head sea and that the amplification of the response due to the hull girder flexibility is largest in bow-quartering waves.

However, this fact is not necessarily reflected in the behaviour of ship masters who seemingly tend to prefer bow-quartering sea to head sea when encountering adverse weather. Numerical design tools are widely used in ship design, but may not be able to fully capture the effect of the hull girder flexibility and are here found to significantly underestimate the effect compared to model tests and full scale measurements.

Hence, full scale measurements from ships are highly valuable in the evaluation of existing designs and may reveal effects that cannot be assessed numerically. For decision support, accurate knowledge of the encountered sea state parameters (wave height, period and relative wave direction) is crucial.

One means to estimate the on-site sea state from an advancing ship is to use the wave buoy analogy, i.e. use the motions of the ship and the associated motion transfer functions to derive the sea state parameters. The method is promising but needs further refinement before it can be implemented in decision support systems on board ships.

Fatigue damage is estimated from full scale strain measurements from two of the container ships with focus on the assessment of the influence of the wave-induced high-frequency hull girder vibrations. In several cases, the high-frequency contribution to the fatigue damage is dominating the estimated fatigue damage.

Spectral formulations for estimating fatigue damage from bi-modal processes are explored and found to yield results fairly similar to the outcome of classical fatigue damage estimation from rainflow counting. However, in a few cases higher fatigue damage rates were estimated from rainflow counting than from narrow-band approximations.

In summary and only considering larger container ships, the new and original contributions of the thesis are believed to be: •From full scale measurements the hull girder vibrational response is generally found to be dominated by the 2-node vertical bending mode even when the ship is sailing in oblique seas. •The vertical bending moment in hogging and sagging is amplified considerably by the effect of the hull girder flexibility and the wave-induced hull girder vibrations are found capable of increasing the vertical wave bending moment amidships by 100% or more. •The vertical hogging bending moment can be as critical as the sagging bending moment in design. •From comparison of models tests and numerical methods, it seems that the numerical methods are not capable of fully capturing the effect of hull girder flexibility seen in model tests. •The peak-over-threshold method is found to be the most useful method for extreme value prediction of the vertical bending moment in combination with an appropriate asymptotic extreme value distribution.