Evaluation of Motions of Marine Craft in Irregular Seas 



The forcing functions F^ and M^ for the case of bodies in regular waves 

 are in general complicated functions of incident wave frequency. Conceptually 

 they are secured by considering the in- and out-of-phase pressure distributions 

 developed on the body when restrained from moving in the wave system. Thus, 

 in general, they take the form 



F.e^-* = a'(-)0.ib'(a,)^.c'r, (11) 



Moe'"* = A'(.)0.iB'(.)|j.C'^ (12) 



where 77 is the wave or vertical fluid displacement at the body (which may be 

 submerged) referenced to some arbitrary point on the body (often to the center 

 of mass or amidships as a convention). For any regular progressive wave the 

 vertical motion at any point I, is 



va,Lt) = hje'~"^ ^e^-* 



= hoi gC'^.^-Oe^"* (13) 



where 1 17^ | is the amplitude of the wave at the surface and 



The complex exciting force and moment (11) and (12) become, after use of (13), 



Fo(^^'^'^) " (-^^a'(a)) + iwb'(aj) + c') h^|g(c^,^, O 



(15) 



M^Co;,^, O = (-co^A'Coj) + ia;B'(a;) + c') h^|g(a;,^, O • 



Thus it is seen that the force and moment acting on a body are both proportional 

 to the wave amplitude on the surface and are arbitrarily phased to the body 

 through the coordinates i, i. For sake of brevity let the force and moment per 

 unit of wave amplitude be written 



r-n- = f'C'^) g(^.^.0 (16) 



and 



M 

 —^ = m'(co) g(^,^, O (17) 



hoi 

 where f and m' are the complex polynomials 



465 



221-249 O - 66 - 31 . 



