裝甲車水上轉(zhuǎn)向系統(tǒng)液壓擺動油缸及液壓系統(tǒng)設計【水陸兩用的裝甲車在水中浮動時的驅(qū)動裝置設計】,水陸兩用的裝甲車在水中浮動時的驅(qū)動裝置設計,裝甲車水上轉(zhuǎn)向系統(tǒng)液壓擺動油缸及液壓系統(tǒng)設計【水陸兩用的裝甲車在水中浮動時的驅(qū)動裝置設計】,裝甲車,坦克車,水上,轉(zhuǎn)向,系統(tǒng),液壓,擺動,設計,水陸,兩用,水中 Barbaro accepted 14 instant negligible at immediately appreciate the effects of variations of the parameters in play: the sections of the cylinder, the depth of the sea floor and the Either due to the support of cylinders or to the support for c in and 0.62 for c dg . It concerns the substantial values even more recently confirmed by Sumer and Fredsoe are in general the supports, which protrude from the being rather complex, and therefore the isolation of the maximum of this force in the practice design is undertaken in a ARTICLE IN PRESS (1997), even if there are some differences in the rule numerical manner. In this study, we will analyse this functional dependence and we will arrive at obtaining an expression for the direct calculation of the aforementioned maximum. 0029-8018/$-see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2006.10.013 E-mail address: giuseppe.barbarounirc.it. (leg) of the reticular platforms, the KeuleganCarpenter (K E number is usually greater than 2 so that the calculation of the force can be undertaken with the formula of Morison et al. (1950). Furthermore, the relationship between the Reynolds (R E number and KeuleganCarpenter number normally surpass 10 4 (excep- tions are made for cases of small cylinders) so that they can assume asymptotic values of inertia coefficient c in and of drag coefficient c dg (Boccotti, 1997). According to Sarp- kaya and Isaacson (1981), these asymptotic values are 1.85 surface of the water). The maximum of this force is realized for an instant between the zero-up crossing and the crest of the wave, that is in the phase in which the component of inertia and the component of drag have the same direction. (Actually, even in the interval comprising the zero-down crossing and the concave the two components have the same direction, but the total force is inevitably less than the interval between the zero-up crossing and crest, in as much as the portion of the loaded cylinder is less). The dependence of wave heights on the total force results in r 2007 Elsevier Ltd. All rights reserved. Keywords: Force; Cylinder; Wave 1. Introduction The vertical cylinders in the sea typically function as a support. It is concerned with, in the large majority of cases, circular-section cylinders that represent the fundamental components of the support structure of offshore jetties or platforms with a reticular structure. 5oK E o20 where the asymptotic values of c in are shown to be less than 1.85 and the asymptotic values of c dg are shown to be greater than 0.62. The instantaneous horizontal force on the cylinder is obtained by the integration of the unitary force (supplied by Morisons formula) between the sea floor and the surface of the water (this, naturally, for cylinders, as they characteristics of the waves. Ocean Engineering 34 (2007) A new expression for the direct wave force on vertical Giuseppe Department of Mechanics and Materials, Via Graziella Received 19 April 2006; Available online Abstract Here, an easy analytical solution for the direct calculation of the platform is realized, and for the direct estimation of the aforementioned The instant is expressed t m of the maximum force as limits of a succession interests the successions converge very quickly: t m t m 1 , less than The solution allows the estimate of useful synthesis to be arrived 17061710 calculation of the maximum cylinders Loc. Feo de Vito, 89060 Reggio Calabria, Italy 5 October 2006 February 2007 in which the maximum wave force on a support of an offshore maximum force. The solution is obtained thanks to an artifice. t m 0 , t m 1 , t m 2 ; .; and it is proved that in cases of practical errors. in the preliminary phase of the project. In fact, it allows one to Nowadays, with any PC, it is easy to obtain the total maximum force on a cylinder. Anyway, the analytical solution carries a doubtless advantage for the synthesis; an advantage that is appreciated above all in the planning stage. In fact, in many cases, the analytical solution allows one to see, simply and clearly, the effect of the variation of the various parameters in play: sections of the girder, depth of the sea-floor and characteristics of the waves. ARTICLE IN PRESS G. Barbaro / Ocean Engineerin d 2R z 2. Analysis of the total force With reference to Fig. 1, the force per unit of length at a depth z is ftC0c in rpR 2 g H 2 kfzsinotc dg r C2Rg 2 H 2 4 o C02 k 2 f 2 zcosotjcosotj, 1 where the first term in the right-hand side represents the inertia component and the second one the drag component, and where it is defined fzC17coshkd zC138=coshkd. (2) Moreover, introducing the coefficients A and B A C17 c in rpR 2 g H 2 k, 3 B C17 c dg rRg 2 H 2 4 o C02 k 2 . 4 The expression (1) can be rewritten in the form ftC0AfzsinotBf 2 zcos 2 ot. (5) Integrating the ft per z in C0d;Z and making explicit the term fz one has Ft Z Z C0d C0A coshkd zC138 coshkd sinotdz Z Z C0d B cosh 2 kd zC138 cosh 2 kd cos 2 otdz, 6 defining the coefficients A 0 C17 A coshkd c in rpR 2 g H 2 k 1 coshkd , (7) Fig. 1. Reference scheme. B 0 C17 B cosh 2 kd c dg rRg 2 H 2 4 o C02 k 2 1 cosh 2 kd (8) one has Ft C0A 0 sinot Z Z C0d coshkd zC138dz B 0 cos 2 ot Z Z C0d cosh 2 kd zC138dz 9 and solving the integrals Ft C0A 0 sinot 1 k sinhkd ZC138 B 0 cos 2 ot 1 4k fsinh2kd ZC138 2kd Zg. 10 Using the following linear approximations: sinhkd ZC138 sinhkd kZsinhkdcoshkdkZ (11) expression (10) becomes Ft C0 A 0 k sinotsinhkdcoshkdkZC138 B 0 4k cos 2 otfsinh2kdcosh2kd2kZ 2kd 2kZg. 12 Substituting in (12) the values of A 0 and B 0 and using the following definitions: W 1 C17 c in rpR 2 g H 2 tanhkd, 13 W 2 C17 c in rpR 2 g H 2 4 k, 14 W 3 C17 c dg rRg 2 H 2 16 o C02 k 1 cosh 2 kd sinh2kd2kdC138, 15 W 4 C17 c dg rRg 2 H 3 16 o C02 k 2 1 cosh 2 kd cosh2kd1C138. 16 Expression (12) of the total force on the cylinder Ft can be rewritten in the form Ft C0W 1 sinotC0W 2 cosotsinot W 3 cos 2 otW 4 cos 3 ot. 17 The maximum of the function Ft does not change if the sign of the first two addends to the second member is changed. Naturally, however, with such a change of sign, the maximum falls in the domain 0potpp=2. In conclusion, the maximum of the function (17), or rather the maximum horizontal force on the cylinder, is equal to the maximum of the function FxW 1 x W 2 x 1 C0 x 2 p W 3 1 C0 x 2 W 4 1 C0 x 2 p 1 C0 x 2 . 18 For 0pxp1 , where, with evidence, x stands for sinot. g 34 (2007) 17061710 1707 Of the four terms in expression (18) of Fx, the first term expresses the inertia force under m.w.l, the second the ARTICLE IN PRESS inertia force above m.w.l , the third the component of drag under m.w.l. and the fourth the component of drag above m.w.l. Here, it is better not to consider the problem purely from a mathematical point of view. It is better, instead, to keep present the physical meaning of various terms that present themselves in the second member of (18). Doing so, one manages on one hand to skirt round the mathematical problem that presents itself as rather complex, and on the other hand one can investigate the same mechanics of the force on the cylinder. It is better to rewrite (18) in the form FxF 1 xF 2 x (19) defining F 1 xC17W 1 x W 3 1 C0 x 2 , 20 F 2 xC17 W 2 1 C0 x 2 p x W 4 1 C0 x 2 p 1 C0 x 2 , 21 where F 1 x is the force on the portion of the cylinder between the sea-floor and the average level.F 2 x is the force on the portion of the cylinder between the average level and the water surface. If the component of inertia is neatly predominant compared to the component of drag, the maximum Fx is realized for x 1 (zero of the elevation of the wave). If, vice versa, the component of drag is neatly predominant over the force of inertia, the maximum of Fx is realized for x 0 (crest of the wave). F 1 x has a maximum in (0.1) if W 1 o2W 3 , otherwise the maximum of F 1 x is realized for x 1. In cases of practical interest, if the maximum of F 1 x is realized for x 1, also the maximum of Eq. (19) is realized in x 1 or extremely near to x 1, so that one can rightly assume if W 1 X2W 3 : F max W 1 . (22) It concerns, as mentioned, cases in which the inertial component is neatly predominant over the component of drag. We now come to the case in which W 1 o2W 3 . In this case the maximum of F 1 x is realized in x C17 x m , or rather W 1 C0 2W 3 x m 0 ) x m W 1 2W 3 . (23) Here, to derive the maximum of the total force, it is best to go back to the following series of functions: F i xW 1 x W 2 1 C0 x 2 iC01 q W 3 1 C0 x 2 W 4 1 C0 x 2 iC01 q 1 C0 x 2 , 24 with i 1;2; ., x m provided by (23) and x i , abscissa of the maximum of F i x x 1 W 1 W 2 1 C0 x 2 iC01 q q . (25) G. Barbaro / Ocean Engineerin1708 i 2 W 3 W 4 1 C0 x 2 iC01 It can easily be verified that F i xEq. (24)has the same form as FxEq. (18) with the only difference being that the factor 1 C0 x 2 p is substituted by 1 C0 x 2 iC01 q . The succession of x i converges and the value limit of the succession coincides with the abscissa of the maximum of Fx . In cases of practical interest, the convergence is very fast, in as much as one can assume with a good degree of certainty that x 1 coincides with the limit of succession. As a result, the desired maximum value of the functions on the cylinder, or rather the value maximum of Fx can be estimated as equal to Fx 1 . Or rather if W 1 o2W 3 : F max W 1 x 1 W 2 1 C0 x 2 1 q x 1 W 3 1 C0 x 2 1 W 4 1 C0 x 2 1 q 1 C0 x 2 1 26 with x 1 1 2 W 1 W 2 1 C0W 1 =2W 3 2 q W 3 W 4 1 C0W 1 =2W 3 2 q . (27) The errors which occur when applying expressions (26) and (27) for the estimation of F max in cases of practical interest, are within 1.1%. 3. The data used in the application The data used in the applications are taken from the buoy of Mazara del Vallo, which belongs to the Rete Ondametrica Nazionale (RON) of the Servizio Idrogra- fico e Mareografico Nazionale (SIMN), active since July 1989. The records are normally acquired for a period of 30min every 3h and with shorter intervals in the case of particularly significant heavy seas. The buoy is in deep water. Fig. 2 shows, referring to the Mazara buoy, a serious of storms with a level of significant wave height for the period 1731 December 1997. From the aforementioned figure, it is possible to reveal the presence of some significant heavy seas. The most intense, recorded on the 28th December, presents a maximum value of significant height equal to 3.5m. 4. Application at the district of Mazara del Vallo The characteristic parameters of the district of Mazara del Vallo, located in the Sicilian Channel are u 1:256; w 1:012m. Now let us consider the reticular platform of Fig. 3 placed in that district at a depth of 150m and let us estimate the maximum force of the elements of support of dimensions equal to R 2m. g 34 (2007) 17061710 Let us fix a project life L 100 years and a value of 0.10 of the probability P that during L the event to assume at ARTICLE IN PRESS 24 25 25 26 27 28 28 29 3 0 3 1 3 1 Mazara del Vallo (17-31 Dicembre 1997) 0 0.5 1 1.5 2 2.5 3 3.5 4 17 17 18 19 20 21 21 22 23 Hs (m) G. Barbaro / Ocean Engineerin the base of the project is realized at least once. From the graphics in Fig. 4, with the aforementioned data, one can infer the maximum wave height expected H max 16m and the significant height of the sea state h 8m in which the maximum wave of 16m is realized in the district subjected to study. As a result, the period of the highest wave in that locality is equal to (Boccotti, 2000) T h 24:55 8 4g s 12s. Therefore, the wave of the project for the structure in Fig. 3 in the district of Mazara del Vallo will be H max 16m; T h 12s. Fig. 2. A series of storms with a levels of significant height recorded in the district Fig. 3. The support structure of a reticular platform. g 34 (2007) 17061710 1709 For those conditions we have R E K E 3:33 C2 10 5 . So that one can assume the asymptotic values c in 1:85, c dg 0:62. Using Eqs. (13)(16) one has W 1 187:7t; W 2 41:9t; W 3 40:2t; W 4 17:9t. In this case, W 1 is greater than 2W 3 and therefore the component of inertia neatly prevails over that of drag, and the F max can be estimated directly through the very simple of Mazara del Vallo (Sicilian Channel) in the period 1731/12/97. 0 0.25 0.5 0.75 1 05 10 15 20 25 0 20 40 60 80 100 120 010152025 0.1 16 8 P(H max (100 anni ) H ) - p(H s =h;H max H ) H (m) H (m) 5 Fig. 4. Trend of the probability PH max 100years4HC138 and of the density pH s h; H max x for the district of Mazara del Vallo. x 1 0:97 means that the value of sinot for which it is verified that the maximum of force is equal to 0.97; or rather it means that the maximum force has a phase angle arcsin 0:9776 C14 in regard to the crest of the wave. We are in a condition in which the drag component prevails but the inertia component is not negligible (one should remember that the maximum of drag force is realized in correspondence to the crest of the wave and the maximum of inertia force is realized in correspondence to the zero of the wave). ARTICLE IN PRESS d 2R G. Barbaro / Ocean Engineering 34 (2007) 170617101710 relation (22). Therefore, the maximum force exercised on the project wave, in the district of Mazara del Vallo, on the diagonals of the platform result: F max 187:7t. Now we shall pass to a support pole of ray R 0:25m of the jetty in Fig. 5, as always, placed at Mazaro del Vallo at a depth d 15m, and we will estimate the maximum force of it. Resulting the coefficient of diffraction in the position of the jetty equal to 0.25, the height of the wave of the project results as equal to 4m. Also in this case resulting condition: R E K E 1:13 C2 10 4 . One can assume the asymptotic values c in 1:85, c dg 0:62. From the Eqs. (13)(16) one has Fig. 5. Section of the jetty located in the district of Mazaro del Vallo. W 1 0:709t; W 2 0:199t; W 3 0:357t; W 4 0:176t. As W 1 is less than 2W 3 , one has to fall back on Eqs. (26) and (27). The value of x 1 , results equal to 0.97 and the maximum force results equal to F max 0:76t, 5. Conclusions In this paper, a new expression for the direct calculation of the maximum force is proposed, produced by the waves on vertical cylinders. This force is functions of four terms: W 1 ;W 2 ;W 3 ; and W 4 , which represent the force of inertia above and below the level of m.w.l, respectively, and the drag force above and below the level of m.w.l. One application of the new expression of maximum force was proposed in the district of Mazara del Vallo, located in the Sicilian Channel, on the elements of support of a reticular structure and a jetty. In the case of the reticular platform, the component of inertia prevails over that of drag and the value of F max resulted equal to 187.7t. For the jetty, the component of drag slightly prevails over that of inertia and F max resulted equal to 0.76t with a phase angle of 76 C14 compared to the crest of the wave. The difference between the results of maximum force estimated with the method proposed in this paper and of the traditional one is less than 1%. References Boccotti, P., 1997. Idraulica Marittima. UTET, pp. 1522. Boccotti, P., 2000. Wave Mechanics for Ocean Engineering. Elsevier Oceanography Series, pp. 1496. Morison, J.R., OBrien, M.P., Johnson, J.W., et al., 1950. The forces exerted by surface waves on piles. Petroleum Transactions 189, 149156. Sarpkaya, T., Isaacson, M., 1981. Mechanics of Wave Forces on Offshore Structures. Van Nonstrand Reinhold Co., New York, pp. 1650. Sumer, B.M., Fredsoe, J., 1997. Hydrodynamics Around Cylindral Structures. World Scientifc Co. Ltd., Singapore, pp. 1530.