Slowly varying damped oscillations of moored vessels

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Lab. y. Schepsboiwkun*

Technische HojeschooI DeIfL 2.

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SLOWLY VARYING DAMPED OSCILLATIONS f

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OF MOORED VESSELS

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YOSHIYUKI INOtJE

Offshore Design Department

Ishikawajima -Harima

Heavy Ind. Co., Ltd.

ABSTRACT

The problems on The Slow Drift Oscillations of Moored Vesselst' have

already been studied by many resarchers, such as Pinkstermery

8) 7) ₉₎

& Hermans, 1-isu & Blenkern, Rye and others.

These researchers studies are seemed. to be ba.sed on the comnTon assumption that there exist slowlyvarying drifting forces acting on

vessels and to be predicted slowly varying oscillations as response motions due to the exciting forces.

According to the theoretical explanation by J.N. NewmanVthese slowly varying forces exist as 2nd order wave forces. But, these forces are very difficult to be directly confirmed by measuring them from model test, because of very small and. slowly varying forces compa±ed to the first order huge and varying exciting ones.

Therefore, nowadays, those forces are to be confirmed by some numerical treatments for the measuring data of response motions of the exciting fOrces.

Now, as you well know

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response motions of forced damped

oscillation systems are the superposed motions of damped oscillations and so -called forced oscillations.

-ARCHIEF

BOSS'76

Behaviour of Off-Shore Structures The Norwagian Institute of Technology

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The damped oscillations are transient motions to vanish after an infinitely long time, and forced oscillations are contiftued infinitely. For the period of finite time, the damped oscillations does exist,

especially under the conditions of long natural period and small damping, I suppose that we can not neglect the existence of the damped oscillations of the response motions at usual model basin tests.

According to the simple analysis for the simple harmonic forced oscillation of a system with one degree of freedom, we know that the initial amplitudes of damped oscillations are directly proportional to the frequencies of the exciting forces.

Roughly speaking, on the other hand, slowly varying drifting forces are increasing when their frequencies are increasing.

Therefore, we can consistently explain that phenomena of so-callslowly varying oscillations are not only forced oscillations caused by slowly varying exciting forces, but also some transient damped osciallations of long natural periods.

Supposing that slowly varying oscillations are damped oscillations, I could confirm from the test results of the moored vessels in regular beam waves that amplitudes of slowling varying oscillations were

directly proportional to the frequency of exciting force.

Fig. 1 shows the test result of two dimensional model with Lewis section in the regular beam waves, which has been carried out at Kyushu UniversIty. As you can see on this figure, the experimental values are lined up to a straight line and the amplitude of slowly varying damped osciallation is proportional to the frequency of exciting force (a). Fig. 2 shows the :test result of two dimensional rectangular model as

similar to Fig. 1 and this test has been undertaken at IHI Ship Model Basin in Yokohama. Andiwe have got the similar result.

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However, under the tight mooring with high initial tensions on normal lines,(Test No. 8), there is almost no slowly varying damped oscillation can be seen. Under the conditions of low initial tensions on mooring lines (Test No. 7:) and high initial tension on mooring line with sinker for shock absorber (Test No. 12), we can observe the existence of siowj

varying damped oscillations in regular waves.

Fig. 3 shows an example of the test records of the slowly varying damped oscillations in the regular waves. Its characteristic can be found very well in sways record.

Fig. 4 shows the result of spectrum analysis of the test record in Fig. 3. The existence of the slowly varying oscillations can be found from the low frequency domain of this spectrum density.

Fig. 5 shows the results of spectrum analyses of Il-Li's Test No. 8 and 12, we can see the slowly varying oscillations of Test No. 12. in this figure, but under the condition of Test No. 8 there is almost no slowly varying oscillations can be seen.

Thus, there is interesting tendency that the slowly varying damped oscillations are also likely to appear in the irregular waves when they are likely to appear in regular waves.

In the above mentioned test results, there are some doubts of the effects of the 2nd-order exciting forces. And becuase of the different amplitude of the slowly varying damped oscillations which are primarily induced by the initial wave condition, I also tried to conduct simulated calculations of moored vessels in beam seas.

In these calculations, the 2nd-order slowly varying exciting forces were neglected and the hydrodynamic forces are to be independent of the frequency.

And the exciting forces are to be increased by the first-order lag element of time.

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An example of these calculations can be seen in Fig. 6.

From this figure, I could say that even if slowly varying exciting forces do not even exist, slowly varying oscillations will be caused by motion response itself.

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References

H.Maruo "The Drift of a Body Floating on Waves" Journal of Ship Reseach

(Dec.1960)

H.Maruo "Resistance in Waves" The Society of Naval Architects of Japan, 60th Anniversary Series Vol.8 (1963)

H.Maruo "A Note on the Higher Order Theory of Thin Ships" Bulletin of the Faculty of Engineering, Yokohama National University Vol. 15 (1966)

J.N.Néwman "Second-order, Slowly-varying Forces on Vessels in Irregular Waves" International Symposium on the Dynamics of Marine Vehcles and Structures in Waves, University College, London (1974)

J.A.Pinkster "Low Frequency Phenomena Associated with Vessels Moored at Sea" Soc. of Petroleum Engineers, SPE-4837, SPE-European Spring Meeting

,Arnsterdam (1974)

J.A.Pinkster "Low Frequency Second Order Forces on Vessels Moored at Sea"

11th Symposium on Naval Hydrodynamics, London (1976)

7) F.H.I-isu & K.A.Blenkarn "Analysis of Peak Mooring Force Caused by Slow Vessel Drift Oscillation in Random Sea" OTC-1159, Offshore Technology

Conference, Houston (1970)

F.M.Remery & A.J.Hermans "The Slow Drift Oscillations of a Moored

Object in Random Seas" OTC-1500 (1971)

H.Rye, S.Rynriing & H.Moshagen " On the Slow Drift Oscillations of Moored

Structures" OTC-2366 (1975) .

(for example). FrankS. Crawford, Jr. "Berkeley Physics Course Volume 3 - Waves -" McGraw-Hill Book Company, New York (1968)

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