ment with calculations based on linear theory is good as indicat- 

 ed in Figures 1 and 2. 



However, the measured heave damping is substantially greater 

 than the predictions of linear theory. In cases such as this, 

 where a rather large difference occurs between experiment and 

 calculated results, the cause can generally be traced to viscous 

 effects. In the present instance, the bottom surface of the 

 barge acts as the wave generating surface in heave but since it 

 is rather deeply submerged its wave-making ability is diminished. 

 In this connection it may be noted that the damping coefficient 

 in heave is about one-fifth that of surge. Since the wave-making 

 damping in heave is very small the importance of viscosity is rel- 

 latively large and this presumably accounts for the experiment- 

 al values being considerably above the values based on the linear, 

 inviscid theory. 



Faltinsen and Michelson (1974) present no pitch data but 

 since motion of the barge in pitch typically produces a very 

 small radiated wave, the damping coefficient predicted by linear 

 theory is normally very small, except in the case of very shallow- 

 draft bodies where the wave-making surfaces are very near the 

 free surfaces. Thus, a similar situation to the above may be ex- 

 pected. In view of the small radiation damping in pitch, theory 

 generally predicts a very large resonance peak which is not ob- 

 served in reality. However, it is well-known that damping is 

 only important near resonance and, therefore, the motion response 

 is generally in error on this account only near resonance. 



Pinkster and van Oortmersen (1977) have also presented ex- 

 perimental results and comparisons with linear theory for excitation 

 loads and response motions of a barge of 150m length, 50m breadth 

 and 10m draft. In general, the linear theory agreed very well 

 with the experimental results. The only significant discrepancy 

 was the rather large resonance peak in roll which is to be expect- 

 ed in view of the above comments regarding roll damping. 



3. VESSEL MOTION 



There are two rather well-known and commonly applied methods 

 for treating the motion of a vessel in a seaway. These are refer- 

 red to as frequency-domain and time-domain analyses. 



The frequency domain analysis is based strictly on the 

 assumption that all forces acting on the floating body are linear 

 functions of displacement, velocity or acceleration, and as a re- 

 sult the response is directly proportional to the amplitude of 

 the incident wave. For a given frequency, the equations of mot- 

 tion for the floating body would appear as follows: 



(pn^i-Mi^('r))j:j(.±) tN^/^)^jW -^ K^jJTjW^ FT Co-) (1) 



in which fy^ii denotes the mass matrix of the body, McjCO') den- 

 notes the added mass matrix, N^^^ denotes the damping matrix, 

 Ki'i denotes the restoration force matrix due to buoyancy and ela- 

 astic forces, and F^ denotes the wave excitation force. 



To examine the difficulty in application of Eq.(l) to random 

 waves it is enough to consider two frequencies, cr, and OV • It 

 is generally assumed that the response associated with the two 



47 



