Analyses of Multiple-Float-Supported Platforms in Waves 



plate added mass, 

 depth z e = T-L a . 



is assumed to be 0.3 m' and its effective 



The results presented are typical : as frequency increases, 

 the vertical forces decreases at first until it reaches a minimum value 

 (which corresponds very closely to the "damping" component of the 

 wave-induced force, Eq.(34), and then increases again when the com- 

 ponents of force which are out-of-phase with wave elevation (due to 

 pressure gradient and added mass) become important, followed by 

 asymptotic attenuation to zero force for very short waves. Both R a /R Q 

 and L a /T are seen to have important effects on the wave-induced 

 force, T/R Q ; T/R Q is less important, in fact, the simplified theory 

 (Newman [36J ) neglecting added mass and damping indicates no de- 

 pendence on T/R . 



Transfer Functions 



The ratio of heave motion to wave elevation can be derived 

 from the solution of Eq. (30). This may be re- written in a form similar 

 to that for the familiar simple harmonic oscillator. 



Z r r/pgS(o)f 



V^'-te?-*) 



^n 



!38) 



where 



2 T 

 n 



C (1 + C ) 

 vp HH 



-1 



;39) 



Only one set of transfer functions, exhibiting the dependence 

 on R a /R Q for L & /T = 0.5 , T/R Q = 30 , c/c c = 0.07 , m' = 0.3m a 

 and z e = 0.5 (for damping plates), will be given in Figure 30. These 

 results are, again, typical : the trends of the variation of motions with 

 frequency follow the wave forces modified by the dynamic amplification 

 factor. Note that the damping coefficient assumed, c/c c = 0.07 , 

 results in values of the transfer function around 2.0 at resonance, and 

 that the maximum value depends on the float shape as well as the re- 

 lative damping. 



827 



