where 



X 2 = —^ , a = 0.525 iiTT, n= 1, 3, 5, etc. (B17b) 



a — tana 



Additional experimental results are discussed in a recent paper which deals with marine cable applica- 

 tions (B6). 



B.3. The Inclined Slack Cable. The linear theory just described has proven to be a valuable tool in 

 the analysis of marine cable vibrations. A shortcoming of the original analysis is a restriction to hor- 

 izontal cables or, more precisely, to cables with supports at the same elevation. The simplest way to 

 extend the theory to cables with inclined chords is to view the cable in a coordinate system inclined 

 with the cable (B7). In order to retain symmetry about the cable midpoint, an essential feature of the 

 linear analysis, one must ignore the effect of the chordwise component of gravity. The problem then 

 reduces to the previous analysis except that the weight per unit length is given by w = mg cos 6 where 

 9 is the chord inclination angle from the horizontal. 



According to the linear theory, the horizontal (or chordwise) component of tension H is constant 

 along the cable, 



H= mg cos 9 iVSs. (B18) 



However, the chordwise component of gravity produces a change in H from one end to the other of an 



inclined cable by an increment A// given by 



AH ^^ mg I sin 9. (B19) 



Thus the modified linear analysis for inclined slack cables is subject to 



^=¥«' 



or 



e = Sis/ 1) lane « 1. (B20) 



This condition places rather stringent limits on the sag-to-span ratio as the chord inclination angle 

 steepens. 



Experiments were conducted at NRL to examine the natural vibration of inclined slack cables. 

 Essentially, the earlier Double Armor Steel (DAS) cable experiments were repeated in the DTNSRDC 



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