which are called the reduced damping. As noted by Hallam, et al. (68), the reduced damping /c, is the 

 ratio of the actual damping /o/re (per unit length) and pf„D^, which may be considered as an inertial 



force (per unit length). The results in the preceding sections also suggest criteria for determining the 



critical incident flow velocities for the onset of vortex-excited motions. They are: 



where Fr„,( = 1.2 for in-line oscillations and K^^.,,, = 3.5 for cross flow oscillations at Reynolds numbers 

 greater than about 5(10^). For Reynolds numbers below 10'', Vr^n = 5, which is a typical value for 

 cable strumming applications. 



An increase in the reduced damping will result in smaller amplitudes of oscillation and at large 

 enough values ofCs/t^ or l^s the vibratory motion becomes negligible. Reference to Fig. 2.2 suggests 

 that oscillations are eff"ectively suppressed at ^s//x > 4 (or /c^ > 16), but cylindrical marine structures 

 and marine cables fall well toward the left-hand portion of the figure. The measurements of in-line 

 oscillations by King (46) have shown that vortex-excited motions in that direction are eff"ectively negli- 

 gible for k^ > 1.2. The results obtained by Dean, Milligan and Wootton (5) and others shown on Fig. 

 2.2 indicate that the reduced damping can increase from Cs/f^ = 0.01 to 0.5 (a factor of fifty) and the 

 peak-to-peak displacement amplitude is decreased only from 2 to 3 diameters to 1 diameter (a nominal 

 factor of only two or three). At the small mass ratios and structural damping ratios that are typical of 

 light, flexible structures in water, the hydrodynamic forces predominate; it is difficult to reduce or 

 suppress the oscillations by means of mass and damping control in that range of parameters. Typical 

 values of k^ for marine cables are given in Fig. 3.10. 



Step-by-step procedures for determining the deflections that result from vortex-excited oscillations 

 have been developed by Skop, Griffin and Ramberg (59,69), by King (2), by Hallam, et al. (68) and by 

 Griffin (3). The steps to be taken are explained in detail in these references and generally should follow 

 the sequence given most recently in reference (3): 



• Compute/measure vibration properties of the structure or cable system (natural frequencies or 

 periods, normal modes, modal scaling factors, etc.) 



90 



