外文翻译--一个在垂直的圆筒的表示为极限力量的新的直接演算 英文版

Barbaroaccepted14instantnegligibleatimmediately appreciate the effects of variations of the parameters in play: the sections of the cylinder, the depth of the sea floor and theEither due to the support of cylinders or to the supportfor cinand 0.62 for cdg. It concerns the substantial valueseven more recently confirmed by Sumer and Fredsoeare in general the supports, which protrude from thebeing rather complex, and therefore the isolation of themaximum of this force in the practice design is undertaken in aARTICLE IN PRESS(1997), even if there are some differences in the rule numerical manner. In this study, we will analyse this functionaldependence and we will arrive at obtaining an expression forthe direct calculation of the aforementioned maximum.0029-8018/$-see front matter r 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.oceaneng.2006.10.013E-mail address: giuseppe.barbarounirc.it.(leg) of the reticular platforms, the KeuleganCarpenter(KE number is usually greater than 2 so that thecalculation of the force can be undertaken with theformula of Morison et al. (1950). Furthermore, therelationship between the Reynolds (RE number andKeuleganCarpenter number normally surpass 104(excep-tions are made for cases of small cylinders) so that they canassume asymptotic values of inertia coefficient cinand ofdrag coefficient cdg(Boccotti, 1997). According to Sarp-kaya and Isaacson (1981), these asymptotic values are 1.85surface of the water). The maximum of this force is realizedfor an instant between the zero-up crossing and the crest ofthe wave, that is in the phase in which the component ofinertia and the component of drag have the same direction.(Actually, even in the interval comprising the zero-downcrossing and the concave the two components have thesame direction, but the total force is inevitably less than theinterval between the zero-up crossing and crest, in as muchas the portion of the loaded cylinder is less).The dependence of wave heights on the total force results inr 2007 Elsevier Ltd. All rights reserved.Keywords: Force； Cylinder； Wave1. IntroductionThe vertical cylinders in the sea typically function as asupport. It is concerned with, in the large majority of cases,circular-section cylinders that represent the fundamentalcomponents of the support structure of offshore jetties orplatforms with a reticular structure.5oKEo20 where the asymptotic values of cinare shown tobe less than 1.85 and the asymptotic values of cdgareshown to be greater than 0.62.The instantaneous horizontal force on the cylinder isobtained by the integration of the unitary force (suppliedby Morisons formula) between the sea floor and thesurface of the water (this, naturally, for cylinders, as theycharacteristics of the waves.Ocean Engineering 34 (2007)A new expression for the directwave force on verticalGiuseppeDepartment of Mechanics and Materials, Via GraziellaReceived 19 April 2006；Available onlineAbstractHere, an easy analytical solution for the direct calculation of theplatform is realized, and for the direct estimation of the aforementionedThe instant is expressed tmof the maximum force as limits of a successioninterests the successions converge very quickly: tm tm1, less thanThe solution allows the estimate of useful synthesis to be arrived17061710calculation of the maximumcylindersLoc. Feo de Vito, 89060 Reggio Calabria, Italy5 October 2006February 2007in which the maximum wave force on a support of an offshoremaximum force. The solution is obtained thanks to an artifice.tm0, tm1, tm2； .； and it is proved that in cases of practicalerrors.in the preliminary phase of the project. In fact, it allows one /locate/oceanengNowadays, with any PC, it is easy to obtain the totalmaximum force on a cylinder. Anyway, the analyticalsolution carries a doubtless advantage for the synthesis； anadvantage that is appreciated above all in the planningstage. In fact, in many cases, the analytical solution allowsone to see, simply and clearly, the effect of the variation ofthe various parameters in play: sections of the girder, depthof the sea-floor and characteristics of the waves.ARTICLE IN PRESSG. Barbaro / Ocean Engineerind2Rz2. Analysis of the total forceWith reference to Fig. 1, the force per unit of length at adepth z isftC0cinrpR2gH2kfzsinotcdgrC2Rg2H24oC02k2f2zcosotjcosotj, 1where the first term in the right-hand side represents theinertia component and the second one the drag component,and where it is definedfzC17coshkd zC138=coshkd. (2)Moreover, introducing the coefficients A and BA C17 cinrpR2gH2k, 3B C17 cdgrRg2H24oC02k2. 4The expression (1) can be rewritten in the formftC0AfzsinotBf2zcos2ot. (5)Integrating the ft per z in C0d；Z and making explicit theterm fz one hasFtZZC0dC0Acoshkd zC138coshkdsinotdzZZC0dBcosh2kd zC138cosh2kdcos2otdz, 6defining the coefficientsA0C17Acoshkd cinrpR2gH2k1coshkd, (7)Fig. 1. Reference scheme.B0C17Bcosh2kd cdgrRg2H24oC02k21cosh2kd(8)one hasFt C0A0sinotZZC0dcoshkd zC138dz B0cos2otZZC0dcosh2kd zC138dz 9and solving the integralsFt C0A0sinot1ksinhkd ZC138 B0cos2ot14kfsinh2kd ZC138 2kd Zg. 10Using the following linear approximations:sinhkd ZC138 sinhkd kZsinhkdcoshkdkZ(11)expression (10) becomesFt C0A0ksinotsinhkdcoshkdkZC138B04kcos2otfsinh2kdcosh2kd2kZ 2kd 2kZg. 12Substituting in (12) the values of A0and B0and using thefollowing definitions:W1C17 cinrpR2gH2tanhkd, 13W2C17 cinrpR2gH24k, 14W3C17 cdgrRg2H216oC02k1cosh2kdsinh2kd2kdC138, 15W4C17 cdgrRg2H316oC02k21cosh2kdcosh2kd1C138. 16Expression (12) of the total force on the cylinder Ft canbe rewritten in the formFt C0W1sinotC0W2cosotsinot W3cos2otW4cos3ot. 17The maximum of the function Ft does not change if thesign of the first two addends to the second member ischanged. Naturally, however, with such a change of sign,the maximum falls in the domain 0potpp=2. Inconclusion, the maximum of the function (17), or ratherthe maximum horizontal force on the cylinder, is equal tothe maximum of the functionFxW1x W2x1 C0 x2p W31 C0 x2 W41 C0 x2p1 C0 x2. 18For 0pxp1 , where, with evidence, x stands for sinot.g 34 (2007) 17061710 1707Of the four terms in expression (18) of Fx, the firstterm expresses the inertia force under m.w.l, the second theARTICLE IN PRESSinertia force above m.w.l , the third the component of dragunder m.w.l. and the fourth the component of drag abovem.w.l.Here, it is better not to consider the problem purely froma mathematical point of view. It is better, instead, to keeppresent the physical meaning of various terms that presentthemselves in the second member of (18). Doing so, onemanages on one hand to skirt round the mathematicalproblem that presents itself as rather complex, and on theother hand one can investigate the same mechanics of theforce on the cylinder.It is better to rewrite (18) in the formFxF1xF2x (19)definingF1xC17W1x W31 C0 x2, 20F2xC17 W21 C0 x2px W41 C0 x2p1 C0 x2, 21where F1x is the force on the portion of the cylinderbetween the sea-floor and the average level.F2x is theforce on the portion of the cylinder between the averagelevel and the water surface.If the component of inertia is neatly predominantcompared to the component of drag, the maximum Fxis realized for x 1 (zero of the elevation of the wave). If,vice versa, the component of drag is neatly predominantover the force of inertia, the maximum of Fx is realizedfor x 0 (crest of the wave).F1x has a maximum in (0.1) if W1o2W3, otherwisethe maximum of F1x is realized for x 1. In cases ofpractical interest, if the maximum of F1x is realizedfor x 1, also the maximum of Eq. (19) is realized inx 1 or extremely near to x 1, so that one can rightlyassumeif W1X2W3: Fmax W1. (22)It concerns, as mentioned, cases in which the inertialcomponent is neatly predominant over the component ofdrag.We now come to the case in which W1o2W3. In thiscase the maximum of F1x is realized in x C17 xm, or ratherW1C0 2W3xm 0 ) xmW12W3. (23)Here, to derive the maximum of the total force, it is best togo back to the following series of functions:FixW1x W21 C0 x2iC01q W31 C0 x2W41 C0 x2iC01q1 C0 x2, 24with i 1；2； ., xmprovided by (23) and xi, abscissa of themaximum of Fixx 1W1 W21 C0 x2iC01qq . (25)G. Barbaro / Ocean Engineerin1708i2W3 W41 C0 x2iC01It can easily be verified that FixEq. (24)has the sameform as FxEq. (18) with the only difference being thatthe factor1 C0 x2pis substituted by1 C0 x2iC01q. Thesuccession of xiconverges and the value limit of thesuccession coincides with the abscissa of the maximum ofFx . In cases of practical interest, the convergence is veryfast, in as much as one can assume with a good degree ofcertainty that x1coincides with the limit of succession. As aresult, the desired maximum value of the functions on thecylinder, or rather the value maximum of Fx can beestimated as equal to Fx1.Or ratherif W1o2W3: Fmax W1x1 W21 C0 x21qx1 W31 C0 x21W41 C0 x21q1 C0 x2126withx112W1 W21 C0W1=2W32qW3 W41 C0W1=2W32q . (27)The errors which occur when applying expressions (26) and(27) for the estimation of Fmaxin cases of practical interest,are within 1.1%.3. The data used in the applicationThe data used in the applications are taken from thebuoy of Mazara del Vallo, which belongs to the ReteOndametrica Nazionale (RON) of the Servizio Idrogra-fico e Mareografico Nazionale (SIMN), active since July1989.The records are normally acquired for a period of 30minevery 3h and with shorter intervals in the case ofparticularly significant heavy seas. The buoy is in deepwater.Fig. 2 shows, referring to the Mazara buoy, a serious ofstorms with a level of significant wave height for the period1731 December 1997. From the aforementioned figure, itis possible to reveal the presence of some significant heavyseas. The most intense, recorded on the 28th December,presents a maximum value of significant height equal to3.5m.4. Application at the district of Mazara del ValloThe characteristic parameters of the district of Mazaradel Vallo, located in the Sicilian Channel areu 1:256； w 1:012m.Now let us consider the reticular platform of Fig. 3 placedin that district at a depth of 150m and let us estimate themaximum force of the elements of support of dimensionsequal to R 2m.g 34 (2007) 17061710Let us fix a project life L 100 years and a value of 0.10of the probability P that during L the event to assume atARTICLE IN PRESS24 25 25 26 27 28 28 29 303131Mazara del Vallo(17-31 Dicembre 1997)00.511.522.533.5417 17 18 19 20 21 21 22 23Hs (m)G. Barbaro / Ocean Engineerinthe base of the project is realized at least once. From thegraphics in Fig. 4, with the aforementioned data, one caninfer the maximum wave height expected Hmax 16m andthe significant height of the sea state h 8m in which themaximum wave of 16m is realized in the district subjectedto study.As a result, the period of the highest wave in that localityis equal to (Boccotti, 2000)Th 24:5584gs 12s.Therefore, the wave of the project for the structure in Fig. 3in the district of Mazara del Vallo will beHmax 16m； Th 12s.Fig. 2. A series of storms with a levels of significant height recorded in the districtFig. 3. The support structure of a reticular platform.g 34 (2007) 17061710 1709For those conditions we haveREKE 3:33 C2 105.So that one can assume the asymptotic values cin 1:85,cdg 0:62.Using Eqs. (13)(16) one hasW1 187:7t； W2 41:9t； W3 40:2t； W4 17:9t.In this case, W1is greater than 2W3and therefore thecomponent of inertia neatly prevails over that of drag, andthe Fmaxcan be estimated directly through the very simpleof Mazara del Vallo (Sicilian Channel) in the period 1731/12/97.05105 10 15 20 250204060801001200101520250.1168P(Hmax(100 anni)H)- p(Hs=h；HmaxH)H (m)H (m)5Fig. 4. Trend of the probability PHmax100years4HC138 and of the densitypHs h；Hmax x for the district of Mazara del Vallo.x1 0:97 means that the value of sinot for which it isverified that the maximum of force is equal to 0.97； orrather it means that the maximum force has a phase anglearcsin 0:9776C14in regard to the crest of the wave. Weare in a condition in which the drag component prevailsbut the inertia component is not negligible (one shouldremember that the maximum of drag force is realized incorrespondence to the crest of the wave and the maximumof inertia force is realized in correspondence to the zero ofthe wave).ARTICLE IN PRESSd2RG. Barbaro / Ocean Engineering 34 (2007) 170617101710relation (22). Therefore, the maximum force exercised onthe project wave, in the district of Mazara del Vallo, on thediagonals of the platform result:Fmax 187:7t.Now we shall pass to a support pole of ray R 0:25m ofthe jetty in Fig. 5, as always, placed at Mazaro del Vallo ata depth d 15m, and we will estimate the maximum forceof it.Resulting the coefficient of diffraction in the position ofthe jetty equal to 0.25, the height of the wave of the projectresults as equal to 4m. Also in this case resulting condition:REKE 1:13 C2 104.One can assume the asymptotic values cin 1:85,cdg 0:62.From the Eqs. (13)(16) one hasFig. 5. Section of the jetty located in the district of Mazaro del Vallo.W1 0:709t； W2 0:199t； W3 0:357t； W4 0:176t.As W1is less than 2W3, one has to fall back on Eqs. (26)and (27). The value of x1, results equal to 0.97 and themaximum force results equal toFmax 0:76t,5. ConclusionsIn this paper, a new expression for the dire