Kim and Mevciev 



S , S, = amplitudes of displacement in the mode of motion 



where 



, (ma, 



>a ' ~b 



S„S 



a°b 



m a and m, , respectively (m or m, = 2,3,4 

 correspond to sway, heave, roll) 



phase difference between the motions of bodies 

 a and b 



For certain kinds of problems such as the relative heaving motions 

 between adjacent bodies, it may be convenient to refer the phases of 

 the motions to, for instance, the wave-exciting force. 



The space coordinate system is defined in Figure 14a ; the 

 y-axis lies on a calm water surface, the z-axis points vertically up- 

 ward and the origin is taken at the midpoint between the two walls 

 of a and b . 



The body contours C a and C^ of a and b are approximat- 

 ely represented by polygons with a finite number of segments. A puls- 

 ating source of unknown strength is uniformly distributed on each se- 

 gment to represent the flow induced by the motions of the two bodies. 

 The velocity potential for the source of unit strength at (*? , f ) may be 

 written [29] : 



G(y,z i r,,r)e" iu ' t (12) 



where (y,z) is the coordinate of a field point. The resultant velocity 

 potential is represented as a sum of all of the discrete source se- 

 gments of the polygonal approximation to the contours C a and C^ , 



(m a ,m b , e s s ) N 



*(y.z) = A Q. / G(y,z;r 7 ,r)dS 



J 2 si 



M 3a 



S<5k Jaiy.'ii.tHS (13: 



where S-; , S^ = j and k polygonal segments of a,b, respect- 

 ively 



Q. , Q = (uniform) complex source intensity of the j and 

 k* n polygonal segments of a,b, respectively 



The unknown source intesities Q are determined numerically, 

 satisfying the kinematic boundary conditions, 



808 



