Fieri and Lee 



x-axis, w is the wave frequency, K Q is the wave number given 

 by w Q 2 / g, and A is the wave amplitude. The wave diffraction is 

 represented by (j> n and the fluid disturbance caused by the motion 

 of the body in initially calm water is represented by (J) M . Within 

 a linear approximation to the solution of the velocity potential <P M 

 we can let 



6 



4> = £*.<|> (63) 



M k;2 ko k v ' 



where <$)^ is another set of velocity potentials, and £ k0 , k = 2, . . . , 

 6 are the complex amplitudes of the displacement of the body from 

 its mean position in sway, heave, roll, pitch, and yaw modes, res- 

 pectively. The pressure at any point of the hull is obtained from 

 Bernoulli's equation by 



p= -fu 2 - »($ t + g z(t)+ i ! v< £ |2 ) (64) 



At this point, we will establish the following conditions : 

 (1) the motion of the body is small, so that the pressure at a point 

 on the body surface at any instant can be obtained via Taylor's expan- 

 sion of the pressure at the mean position of the body; (2) the terms 

 of <|> (<J>J , S (j> o , <|>! , S ko b , £ ko <) D , £ kQ ) will be discarded in the 

 evaluation of the pressure; (3) only those components of the pressure 

 which have harmonic time dependence will be considered, and (4) 

 the static-pressure component and the component which contributes 

 to the static restoring force or moment of the body will not be inclu- 

 ded in evaluation of the pressure. 



With the foregoing conditions, the complex amplitude of the 

 pressure at a point on the body surface can be expressed by 



P = P ( j w + U -A- ) Cj> 

 ox o 



evaluated at the mean position of the body. 



(65) 



6 



6 These conditions are also applied to monohull ships by Salvesen, 

 Tuck and Faltinsen (1970). 



528 



