Kim and Mevoiev 



needed to provide information on the type of configuration being con- 

 sidered for these floats, as shown in Figure 26, where damping plate- 

 body interaction effects may be significant. 



The wave-exciting force associated with the damping devices, 



Z . — — , may be estimated by taking Z . = Z. , and ==- is the wave 

 f ot c z at 



motion evaluated at the depth corresponding to the damping plate. Of 



course, since the oscillatory drag force on the damping devices is, in 



general, nonlinearly related to the relative velocity between the fluid 



and the plate, the detailed analysis of the motions would be rather 



more complicated than the simplified treatment given here. The effects 



of the nonlinearity of the drag may be expected to be important only for 



frequencies near the resonant frequency. 



Responses 



Although analyses have been presented by Newman [36] and 

 others for wave-induced forces and motions of isolated spar-type 

 floats, no results of systematic evaluations of the dependence of the 

 forces and motions on geometric characteristics of floats are known 

 to be available in published literature. Some results for the special 

 case of floats like that shown in the sketch accompanying Eq.(34) will 

 be presented here. 



The influence of the ratio fo the diameters of the lower and up- 

 per cylindrical parts R a /R , the ratio of the length of the lower 

 cylinder to the overall draft, L a /T > anc * the ratio of the draft to 

 waterplane radius (slenderness ratio), T/R Q , will be shown. Wave 

 forces and motions due to regular waves will be presented as a function 

 of frequency, and spectral response information will be given as a 

 function of significant wave height. The influence of the degree of damp- 

 ing on the responses will be described in a subsequent section. 



Wave-Induced Force 



The wave-induced vertical force, Z^ , expressed as a function 

 of the buoyant force, PgS(o)f , is exhibited in Fig. 27 as a function of 

 the dimensionless frequency parameter oi^T/g g showing the influence 

 of R a /R Q . Other geometric parameters were held fixed for these 

 results, viz., L a /T = 0.5 , T/R Q = 30 ; the assumed damping coef- 

 ficient corresponds to a value of c/c c = 0.07 . Figure 28 shows the 

 influence of L a /T for R a /R Q = 1.8 , T/R Q = 30 ; again, c/c c = 0.07. 

 The influence of T/R Q is presented in Figure 29 for R a /R Q = 1.8, 

 L /T = 0.5 and c/c c = 0.07 . For all cases presented the damping 



826 



