Kim and Mevciev 



where 



{—) is the vertical force due to waves on the j float as 



j, o though it were isolated, 



th 

 and W expresses the interaction effect of the k float on the 



vertical force due to waves on the j float. 



The interaction is expressed simply as a function of the distance be- 

 tween the two floats, which would be valid under the assumptions stat- 

 ed of negligible free surface and viscous wake effects. This repre- 

 sentation indicates that the interaction effect should be symmetrical, 

 fore-and-aft. It is not possible, at this time, to say whether the asym- 

 metrical characteristic of the force is due to free-surface or viscous 

 wake influence. An investigation of the effect of wave diffraction ac- 

 cording to a simplified slender body analysis is presently being plann- 

 ed. 



Dynamic Motions Analysis 



The response of multi-degree-of-freedom dynamic systems to 

 constant frequency exciting forces can, in general, be expressed as a 

 sum of normal mode components (cf . , Biggs 66 or Timoshenko 61 ), 

 which can be expressed for a beam in the form 



n 



z(x,t) = E A n . (DLF) <p (x) (48) 



n st n *n 



where 



ip (x) = is the normalized model shape of the n mode of 



n 



A "st 



o scillation of the structure 



_ y pi(x) yfo(x)dx 



co /m <p (x)dx 

 n J n 



p..(x) = distributed exciting force 

 m = mass per unit length of beam 



co = (natural frequency) of n normal mode 



DLF = s ; for simple harmonic exciting force with 



l-(co/co ) frequency co , neglecting damping 



Normal mode shapes, <p n , may be characterized as symmetrical and 

 asymmetrical about the midlength of the deck (beam). 



844 



