Evaluation of Motions of Marine Craft in Irregular Seas 



(34) 



The integrand is immediately recognized as the effective or lumped frequency 

 response function for the ship-sea system defined by Eq. (20). Hence the 

 c^-integral is the effective impulsive heave response function for the ship- sea 

 system: 



K,e(u;^, O = 2^J^1^ ^^ j g^^'^'^^ ^ d^ 



= ^ J *z.(-) e^"'^ do. (35) 



- 00 



so that for both heave and pitch 



where K^^ is the impulsive response of the ship-sea system in pitch with free- 

 dom in heave present. 



It is of interest to note that the same result for the response can be obtained 

 by normalizing the forcing functions with respect to the vertical fluid displace- 

 ment at depth. To illustrate this, consider the forcing function F(t) in this light 

 and one can write 



CO 00 io) ' I o) ' I ^ 



F(t) = ^ r 77(r',^, O J f'(^') e ^ gia,'(t-r') ^^,^^, (37) 



where it is to be noted that e''^ ^/^ ^as been suppressed and the motion at depth 

 v(r,^, O is used. Then the component response in heave is 



00 CO 



- CO - 00 ^ ' 



CO CO CO ico ' \ OJ ' \ ^ 



(277)2 J_^ J_^ J_^ 



CO 



J.. T(a;) 



doidr 



469 



