The hydrodynamic contributions to changes in the natural frequency (added mass) and in the 

 damping also can be determined for slack cables. The method is approximate, but it demonstrates the 

 applicability of the data in Figs. C5 and C6 to slack cable vibrations in water. Computations were car- 

 ried out for the Double Armor Steel (DAS) cable because a range of EA was available only for that 

 particular cable construction. A single value of EA was chosen for the computations despite the likeli- 

 hood that it was tension-dependent. This value of EA was selected to give a good representation of the 

 measured frequencies in air and of the observed modal crossover (see Appendix B) in particular. 



The natural frequencies were predicted from equations (B4) and (86) for two equilibrium posi- 

 tions corresponding to the in-air and in-water tests. Thus, the difference between the predictions 

 shown by the dashed lines in Fig. C7 represents a change in the natural frequency due to a reduction in 

 the linear weight of the cable. Subtracting this buoyancy contribution from the total difference between 

 the frequency measurements yields the added mass effect of the water. From the computations, this 

 correction disappears, as it should, when the cable becomes taut (A.^ — » 0). The predictions are about 5 

 percent below the in-air measurements at large tensions, most likely due to the neglected bending 

 stiffness of the cable. At the lowest tensions there is a large discrepancy between the predictions and 

 the measured points that raised some doubt as to the validity of the measurements represented by those 

 data points; it was later determined that this anomaly was probably a result of the particular cable 

 configuration (see Appendix B, Section B5). The added mass coefficients nevertheless were computed 

 from the data and with the exception of the results obtained at the lowest two tensions, the coefficients 

 in Table C3 are comparable to the added mass results in Fig. C5. 



Estimates of the fluid damping involved additional approximations but good results were obtained. 

 After calculating the approximate in-air and in-water values of 8, the fluid damping contribution was 

 estimated by taking the difference between the log decrements measured in the two media at the same 

 sag-to-span (s//) ratios. In this way the significant contribution of the structural damping for slack 

 cables was discounted from the measured total damping in water, and the fluid damping was compared 



145 



