and if the cable parameter AEImgL is adjusted to reflect the change in the body force. This was the 

 case in the NRL experiments shown in Fig. B6 and this finding justified the simplified approach for that 

 range of conditions. In order to search for the limits to the theoretical approach implied by equation 

 (B20) a number of numerical cases were run for different sag-to-span ratios at several inclination angles 

 up to = 75 degrees from the horizontal. The results are plotted in Fig. B8 in the appropriate coordi- 

 nates, but with the numerical code parameter AE/mgl held constant. The frequencies collapse onto the 

 proper curves everywhere except at crossover. This behavior is correct since X^ (or AE/mgl) also must 

 be adjusted to reflect the cable inclination. Several runs were made which verified that the use of 

 AE/mgl cos 6 will collapse the crossover data up to inclination angles of 9 = 75°. The point to be 

 made here is that the limitations imposed by equation (B20) are far less stringent than they appear and, 

 within a numerical accuracy of a few percent, the horizontal cable limitation of s/l < 1/8 holds equally 

 well for inclination angles up to = 75°. This range of angles includes virtually all structural applica- 

 tions and most mooring cases as well. 



References 



Bl. S.R. Heller and B.S. Chung, "On the Transverse Vibrations of Wire Rope," Catholic University 

 Report 72-7, 1972. 



B2. S.E. Ramberg and O.M. Griffin, "Some Transverse Vibration Properties of Wire Rope with Appli- 

 cation to Flow-Induced Cable Vibrations," Naval Research Laboratory Report 7821, 1974. 



B3. D.S. Saxon and A.E. Cahn, "Modes of Vibration of a Suspended Cable," Quarterly Journal of 

 Mechanics and Applied Mathematics, Vol. 6, pp. 273-285, 1953. 



B4. H.M. Irvine and T.K. Caughey, "The Linear Theory of Free Vibrations of a Suspended Cable," 

 Proceedings of the Royal Society of London, Series A, Vol. 341, pp. 299-315, 1974; See also Cah- 

 fornia Institute of Technology Dynamics Lab Report DYNL-108, 1974. 



131 



