measured for the three cables at NRL and are discussed in Appendix C. The measured displacements 

 at the cable antinodes contain components in-line with the tow direction as well as in the transverse 

 direction. These in-line components in all cases have a frequency equal to the transverse cable vibra- 

 tion frequency. For most of the tests conducted at the second harmonic of the fundamental frequency, 

 however the in-line component of the displacement signal at the cable antinode is equal to or greater 

 than the transverse component. 



If the two components of the cable motion at the frequency w = Itt/ are 



a: = A' sin (w t) in— line (3.3a) 



y = F sin (w / + (ji^y) transverse, (3.3b) 



then the results show that (}>xy = for most of the Double-Armored Steel and Uniline cable experi- 

 ments. This suggests that the cable strumming waveform at the antinode takes the form 



r = VFTF sin {(ot) = R sin (w t) (3.4) 



where R = v X^ + Y^ is the resultant displacement. When the phase angle (jt^y is non-zero as in a 



number of cases, i.e., the slack cable conditions, a complex strumming waveform shape with time- 

 varying displacement is obtained. 



The displacements for several runs are plotted in Fig. 3.10 as a function of the reduced velocity 

 V^ = K sin 6/f„D, where the normal velocity component incident to the cable is given by F sin 6. 

 (The legend on the figure lists the tension, inclination angle, structural log decrement, and the reduced 

 damping k^ for the three cables.) Each run corresponds to a resonant, vortex-excited response over the 

 lock-on regime between the vortex shedding and cable vibration frequencies. In the first mode in = 1) 

 results shown in Fig. 3.10, all three cables exhibit nearly the same maximum strumming displacement 

 at Vr = 6, which is typical of vortex-excited oscillations of cables and bluff structures as shown by the 

 results in Fig. 2.1 and Table 2. The peak displacement amplitude for the yawed DAS cable is higher by 

 about 20% from the unyawed cable even though the yawed cable damping is apparently higher. The 

 structural damping of the cable was dependent upon the orientation of the mounting struts (see 

 Appendix C) as they were rotated to align with the tow direction. Thus there is some variation in the 



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