Kim and Mercier 



The Wave-Exciting Forces and Moments for Twin Cylinders 



Figure 18 illustrates the behavior of the sway- and heave- 

 exciting forces on Body a due to odd and even wave potentials as func- 

 tions of the wave frequency. The vectorial sums of the forces such as 

 f(o+e) = f (o)+ f (e) on ajbj and ( a+b ) are s hown in Figures 19 and 20. 



In this connection, refer to Tables 12 and 13. 



The Has kind -method was applied to the evaluations of the re- 

 sultant wave-exciting forces on the twin bodies and the results confirm 

 exactly the corresponding values obtained by the present method. 

 (See Figures 19, 20 and 21). A relevant discussion of this matter will 

 be given in the following section. 



It is interesting to observe the behavior of the sway-exciting 

 forces on a and b (Figure 19). Ohkusu [35] recently reported on the 

 hydrodynamic interaction between three vertical cylinders. His Fig. 13 

 on page 108 of Reference 35 shows behavior similar to that of the sway- 

 exciting forces on Bodies a and b . A relevant discussion of this mat- 

 ter will be given in the following section. 



The Radiated and Diffracted Waves 



For the twin bodies, the radiated waves A_ and the dif- 

 fracted waves Aj° e ^ were evaluated according to the formulas in 

 Eqs. (24 and 26) (see Figure 21). The radiated wave amplitudes AJ_ m ) 

 are very useful in evaluating the damping force coefficients N^ 1 * 1 ' or 

 5' m ' and the wave-exciting forces f'° +e ^ (see Eqs. 2 7, 28). By compar- 

 ing Figures 15, 19,20 and 21, one can readily confirm the validity of 

 the formulas in Eqs. (27), (28). The diffracted wave amplitude ratio 

 A\° eJ i 3 applied to estimating the mean wave force on the fixed twin 

 bodies in the given incident wave, Eq.(15). The sudden drop of the 

 value of Aj_° e ' at frequency around 0.45 may be ascribed to the ef- 

 fect of the hydrodynamic interaction between the bodies in that close 

 proximity. 



The Wave-Exciting Forces on Some Semi-Submersible Cross Sections 



We chose two simple cross sections : one submerged and the 

 other surface piercing. Figures 22a and 22b represent the sway- 

 and heave -exciting forces on the submerged circular cross section. It 

 is seen from these figures that the interaction effects are negligibly 

 small for the given frequency range. The wave-exciting forces on 

 surface -piercing twin bodies are plotted against the wave frequency in 

 Figures 23a, 23b. It is readily seen that the influence of the interaction 

 effect on the sway-exciting forces is remarkable while the influence on 



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