Analyses of Multiple-Float- Supported Platforms in Waves 



The Importance of Damping 



The primary effect of an increase in the damping coefficient 

 on the heave transfer functions is to reduce the maximum heave re- 

 sponse, which occurs at a frequency slightly lesser than the resonant 

 frequency, and to increase the minimum value which occurs for the 

 frequency when the wave-induced force is due to the damping devices 

 alone . 



For design-analyses, the spectral response is most useful. 



Figure 34 shows effect on significant heave motion of damping 

 coefficient, c/c c , for a particular float geometry. It is evident that 

 damping is very useful to control motions in high sea states where 

 some wave energy exists at frequencies corresponding to heave natur- 

 al frequencies. 



The damping which is available due to wave radiation can be 

 obtained from the Kaskind-Newman relations [32] , which gives the 

 same result as Newman's slender-body analysis for the forces at re- 

 sonance (_3 6 J . These give 



,2 



Z. = -^ IZ.I (40) 



w 



thus, at resonance co = a> 

 damping can be obtained as 



, the ratio of wave -damping to critical 



u c 



Z. 

 z 



w 



2 ^ 1+C HH»"n 



w 



PgA 



w 



2 T 

 U> 1 



n 



A 



w 



(41) 



and the corresponding transfer function 



Z, /PgA I 

 tw' & w 1 



2(c/c c ) w 



(42) 

 contd , 



829 



