2. The first order motions obtained in paragraph 1 (c) 

 above are used to scale up the unit amplitude radia- 

 tion potentials to the radiation potentials. This is 

 done for each frequency as is the next step. 



3. These radiation potentials are combined with the 

 diffracted potentials obtained from 1 (a) to yield, 

 after some manipulation, the mean drift forces. The 

 main assumption underlying this procedure is the 

 far-field approximation (Newman, 1967). 



4. The mean drift forces corresponding to the various 

 frequency components are then combined using the 

 procedure outlined by Newman (1974) to yield the 

 time-varying drift (or second order) forces. This 

 procedure is a recognition of the weak contribution 

 from large frequency-difference combinations components. 

 In other words, the off-diagonal contributions are 

 neglected. 



5. The first order force time histories are generated 

 by superposition (either random phase or artibrarily 

 specified phase) and combined with the second order 

 force time histories to provide a set of synthetically 

 generated excitation time histories corresponding to 

 the input wave spectrum. 



6. Using the relations derived by Ogilvie (1964) the 

 constant inertia coefficients and the impulse response 

 functions are obtained from the added mass and damping 

 coefficients . 



7. From the above, the time-domain system of equations is 

 solved to yield the resulting motions and line loads 



in the form of time histories. The pertinent statistics 

 of interest are computed. To provide additional confi- 

 dence in the statistical results, steps 5 and 7 are 

 repeated for different phase angles between the components 

 of the wave spectrum and different phase relations be- 

 tween the first and second order time histories. Each 



21 



