7/28/2019 Abstract-Inundation Effect of Wave Forces on Jack-Up Platforms.pdf

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roceedings of the Tenth 2000) nternational Off shore and Polar Engineering ConferenceSeattle , USA, May 28.June 2, 2000Copyright 2000 by The nternational Society f Offshore and P olar EngineersISB N 1-880653-46-X (Set); ISB N 1.880653-49-4 (VoL HI); ISSN 1098-6189 (Set)

I n u n d a t i o n E f f e ct o f W a v e F o r c e s o n J a ck - U p P l a t fo r m sC . Y . L i a w

National University of SingaporeSingapore

A c o n c e n t r a t e d f o r c e a c t i n g o n t h e p l a t f o r m a t t h e m e a n w a t e rs u s e d to r e p r e s e n t t h e i n u n d a t i o n e f f e c t o f t h e v a r i a b l e w a v e

s e ff e c t s o n t h e t o t a l a n d t h e m a x i m u m w a v e f o r c e s a r ea t i o n s . T h e s e c o n d - o r d e r t r a n s fe r f u n c t i o n o f th e/ W i e n e r r e p r e s e n t a t i o n f o r t h e n o n l i n e a r w a v e f o r c e , w i t h

s o f t w o t y p i c a l j a c k - u p p l a t f o r m se f f ec t o n t h e d y n a m i c r e s p o n s es o f t h e s tr u c t u re s .

platform, inundat ion effect, nonlinear waveerra series.

Considerable works have already been carried out by manychers on the study of nonl inear wave forces on jack -up platforms.monly accepted that nonlinear dynamics has significant effectstructures, and there are mainly twoear effects attributable to wave forces. One is the nonl inear dragce, which is usually the predominant wave force component for theructural members of a jack-up platform and can be evaluatedrmula. The other important nonlinear

rs near the free water surface, or the inundation effect. Thetice for includ ing the nonl inear effects in dynamicperform time-history simulat ions of the structuralses. In order to have statistically meaningful results, many such

nsuming simulations are usually required. A more directch is, of course, to carry out the stochastic analysis in the. However, nonlinear analysis in frequency domain islinear assumptions.One well-known method of modelling nonlinear systems instic analysis is the Volterra /Wiener representation based on theies (Schetzen, 1980; Rugh, 1981). The nonl inearity isresented by a polynomial expansion, and nonlinear transfer ~nc tio ns

are derived for the different terms of various orders of the polynomseries. Since the procedure invo lves multivariable Fourier Transfothe derivation and numerical evaluat ion of high-order nonlinea r systecan be very tedious. Borgman (1969) considered the non linea r dterm in the Morison equation for wave force and studied a curepresentation of the drag term withou t current. Gudmestad, et (1983) included the effect of current using a fourth order expansiThe third-order Volterra series and the related transfer functions of nonlinear drag term were studied by Li et al., (1995). It has been shoby the above authors that, with the cubic drag term included, structural response spectrum exhibits a significant resonaphenomenon near the frequency of 3OOp, where COpis the peak frequeof the wave spectrum.

The nonl inear inundation effect due to variable surface, on the othand, produces even-order harmonic force components (Gudmes1988) which cause the force spectra to have peaks at 2O)p. Typica lly, fundamental frequency of a jack-up offshore platform is in the range0.25 to 0.12 Hz (Kjeoy, et al., 1990), which is about two to three timthe peak wave frequency. The nonl ine ar responses near 2OOp therefore be very significant, especially if we consider the fact that wave energy is usual ly higher near 2COp than near 3oop. The inundateffect, however, was not included in the above-mentioned worksnonlinear frequency domain representation of jack-up platforms. In tpaper, the inundation efffect of sinusoidal wave is studied. In ordercompare the effects o f drag and inundation, the modal forces, which be related directly to the structural responses, is evaluated based onassumed structural mode shape. The second-order nonlinear transfunction, with the inundation effect included, and the power specdensity functions of the modal force and di splacement are then derivThe results of nonl inear stochastic analyses of two typical jackplatforms are then presented.

INUNDATION EFFECTThe Morison wave force, f, per unit length of a structural membegiven typically as

f =k~ , OU+kDUlU0t

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