Analyses of Multiple-Float-Supported Platforms in Waves 



sum of the far field waves induced by the pulsating sources Q^' di- 

 stributed on the sectional contours, where 7 = m (mode number) for 

 the radiation, and 7 = /3(0 + e) for the diffraction problem. 



The asymptotic expression of the velocity potential tpW' at 

 for both 

 in their forms 



y— * _°o for both radiation (7= m) and diffraction (7= /3 ) are identical 



(7) . A ± <7) „ ^"1") 



<p + — e e (23) 



where - suffix refers to y— >-oo . 



It is to be noted that <£+' 'denotes both the potential per unit amplitude 

 of displacement in forced oscillation for 7 = m and that per unit 

 amplitude of the incident wave for 7 = j3 , A? ' and A} are evaluat- 

 ed in a fashion similar to that given in Ref. 30 where the arbitrarily 

 shaped geometry and both symmetric and asymmetric flow conditions 

 will require that the term with (-1) in the formula Eq. (25) of the 

 above reference should be taken as zero. Hence, 



+ D + (7) 



v 7) - Vs 



1 LT^)- J 



,(*) 



(7) 

 tan 



\t t Q (7) K. + Q W L ., 



3" 1 3 3 N+j ]j a 



+ \£ tQ W K.^l ) L, h 



3 =1 3 3 N+j j^b 



+ 



J E + Q (7) L - Q (7) 



N 



+ J T + o (T) t n (7) k- I 



+ \k ±Q 3 L j" Q N + j K j(b (24) 



K = e cos(j^77 . , + a.) -e cos(j^n. + a.) 



j 3 +1 3 2 2 



815 



