The value of the Strouhal number varies somewhat in different regimes of the Reynolds number and 

 with the shape of the cylinder (circular, D-section, etc.). For the ranges of the Reynolds number when 

 the Strouhal number remains constant the relation between the shedding frequency and the velocity is 

 linear for a given cylinder, i.e. 



fs = KV. 

 where K = St/ D. When a cylinder immersed in a flowing fluid is free to oscillate in the cross-flow 



direction, the latter relation does not hold in the vicinity of the natural frequency of the cylinder. This 

 complex resonance phenomenon— called "lock-on" or wake capture — is discussed in detail in this sec- 

 tion of the report. 



If the Reynolds number is lower than about 10^, then the vortex shedding is predominantly 

 periodic and the value of the Strouhal number can be assumed to be roughly 0.2 for a circular cylinder 

 or cable. The Strouhal number — Reynolds number dependence is discussed further in Section 2.4. 

 Measurements of the frequencies, displacement amplitudes and forces which result from vortex-excited 

 oscillations have been obtained by many investigators from experiments both in air and in water. In 

 this section of the report, some of the most recent of these experiments and related studies are sum- 

 marized in order to provide a background for the cable strumming problem. A detailed review of the 

 basic aspects of the problem of vortex-excited oscillations in general has been made recently by Sarp- 

 kaya (1). King (2) and Griffin (3) have reviewed the subject in the context of ocean engineering appli- 

 cations. 



A typical structure used for experimental strumming tests consists of a cylinder positioned nor- 

 mally to the flow and flexibly supported at each end. Representative measurements for such a cylinder 

 in air have been reported by Griffin and Koopmann (4) and in water by Dean, Milligan and Wootton 

 (5). The results obtained are generally the same in both media; as the incident flow velocity F, or the 

 "reduced velocity" V, as in Fig. 2.1, is increased, the unsteady displacement amplitude first builds up to 

 a maximum, after which it begins to decrease as the upper limit of the locking-on range between the 

 vortex and vibration frequencies is approached. For one example shown in the figure, the lock-on lim- 



