Analyses of Multiple-Float-Suppovted Platforms in Waves 



the heave-exciting forces is relatively small. Similar behavior was 

 pointed out by Ohkusu [35J as described previously. 



In connection with the present investigation, force measure- 

 ments were made at Davidson Laboratory on twin Motora-type floats. 

 These measurements are plotted in Figures 24a, 24b. Since the tests 

 were carried in a relatively high frequency range, even a rough comp- 

 arison with the present two-dimensional calculations cannot be made. 

 However, the interaction effects appear to be quite small compared to 

 the two-dimensional case, especially considering the very close spac- 

 ing of the floats. 



Interaction effects and the occurence of dramatic variations of 

 force coefficients for particular, characteristic, frequencies should be 

 expected to be weaker for three-dimensional than for two dimensional 

 bodies. We have, however, noted an unusual flow pattern for waves 

 passing a fixed toroidal body ; at a particular wave frequency a pulsat- 

 ing jet erupts in the center of the torus. Of course, the jet also exists 

 for forced heaving oscillations in calm water at the same frequency. 

 The shape of the torus corresponds to that of the profile of the twin 

 cylinders of Figures 15-20 rotated about a vertical central axis, with 

 2S/B = 2. The characteristic frequency described for this three- 

 dimensional case corresponds to i/B/2 = 0.42 , rather close to the 

 frequency shown in Figure 15 where Ctttt and 5 vary dramatical- 



iy. 



Some Hydrodynamic Characteristics of Two Different Cylindrical 

 Bodies Floating in Beam Seas 



Some aspects of the hydrodynamic interaction between two ar- 

 bitrarily shaped cylindrical floats were investigated numerically (see 

 Figures 25a, 25b, 25c). First we evaluated the heaving added mass and 

 damping coefficient C , 5 on bodies a and b for heaving motions with 

 unit amplitude and different phases. The results are plotted against the 

 relative phase angle e^ at two different frequencies v(B a +Bk)/2 = 0.45 

 and 0.26 (Figure 25a). The results show significantly large effects on 

 the hydrodynamic forces due to the hydrodynamic interactions between 

 the two different cylinders floating freely with different phases. 



As a special case of the above, we calculated the hydrodynamic 

 forces on the swaying and heaving Body a in the presence of the fixed 

 Body b (Figure 25b). Two draft ratios T^/Tg = 2 and 15 were taken in 

 order to observe the false wall effect on the hydrodynamic forces. The 

 figure also shows the hydrodynamic inertial forces Cjjjj , Cgg on an 

 isolated swaying and heaving Body a . It is seen that the increment of 



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