Analyses of Multtple-Float-Supported Platforms in Waves 



acceleration for this component of force should be the depth correspond- 

 ing to the damping source. 



The total added mass, m" , is the sum of that associated with 

 the attenuator shape plus that due to damping devices. 



The heave damping force rate, Z. , is partly due to generation 

 of radiated surface waves and partly to viscous influence associated 

 with turbulent eddies around the float and damping plates and skin 

 friction drag. It will be shown in the following section that the damping 

 due to wave generation, which is strongly dependent on frequency, is 

 quite small for slender vertical floats and, therefore, it is advantageous 

 to provide additional viscous damping, which is likely to be independent 

 of frequency. The damping coefficient will be expressed in terms of 

 the ratio of the damping to the critical damping coefficient, (c/c c ), in 

 the form 



Z. = (— ) x (2p V + m")a> (37a) 



z c n 



c 



where 



= (— )x2 P A VgTC (1+C ) (37b) 



c c w vp HH 



V 



C = vertical prismatic coefficient, — r — =r 

 vd AT 



vp 



m' 

 C = added mass coefficient, 



w 



HR _„„, ^ 



The viscous drag due to external damping devices will not, in 

 general, be simply linearly proportional to velocity (although for 

 small waves and motions it will be approximately so). The use of a 

 linear coefficient may be justified on the bases that calculations based 

 on such a simplification are instructive and that "equivalent" lineariz- 

 ed coefficients may be derived for drag which is proportional to some 

 other power of velocity in the way that Blagoveshchensky [42] and others 

 have dealt with square -law damping. 



Particular values of drag coefficients may be estimated for 

 plates oscillating in a direction normal to their surfaces from results 

 of significant investigations by Keulegan and Carpenter [43] , McNown 

 [44] , McNown and Keulegan [45] , Paape and Breusers [46] , Martin 

 [47] , Ridjanovic [48] , Brown [49] , Henry [50] , Woolam [5l] and 

 Tseng and Altman [52] . Additional investigations of the oscillating 

 drag of ring-type damping collars around bodies of revolution will be 



825 



