Appendix C 



ADDED MASS AND DAMPING COEFFICIENTS 



C.l Structural Damping of Marine Cables. In order to quantify the coefficients in the equation for 

 the resonant vibrations of marine cables, both the structural and the hydrodynamic damping coefficients 

 must be specified. These damping coefficients have been measured for a variety of marine cables as 

 part of the NAVFAC research program in cable dynamics. Some typical, but limited, measurements of 

 the structural damping, from experiments conducted at NRL, are now discussed. Free vibration experi- 

 ments with the DTNSRDC test cables (CI) and the CEL-supplied small diameter cables were con- 

 ducted and the results are summarized here. The characteristics of the DTNSRDC cables are listed in 

 Table CI. 



The measured in-air natural frequencies for two representative test cables are plotted in Figs. CI 

 and C2. In the DTNSRDC test apparatus that was employed in the experiments discussed here (see 

 Fig. 3.6), the cable span was maintained while the length was varied to accommodate changes in the 

 tension. The differences between the various test spans and cable lengths were small, but they did 

 account for some of the apparent discrepancies between the two sets of experiments. Another 

 difference between the two sets of experiments was due to changes in the rigidity of the cable supports. 

 The stiffness of the DTNSRDC cable mounting struts (see reference CI for a detailed description of 

 the test apparatus), as seen by the cable, depends on the relative orientation of the two struts. Strut 

 motions were quite evident during the tests when the DTNSRDC test apparatus was configured for the 

 cable axis normal to the towing direction. The stiffness of the struts was increased by rotating them 

 until their longest dimension was nearly aligned with the cable axis. As indicated in the accompanying 

 figures, an increase in the support rigidity raised the measured cable natural frequency at a given 

 tension. This effect diminishes with increasing tension as the vibration-induced tension fluctuations 



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