its, defined by vibration displacements greater than the resonant threshold i2Y/D = 0.1), are given by 

 reduced velocities Vr = 4.5 and 7.5 in air, with the maximum displacement amplitude occuring at V^ ~ 

 6. For the in-water experiments the resonance band is somewhat wider, from K, = 4 to nearly 8, but 

 the peak displacement amplitude again is excited at V, ~ 6. The narrow resonance band in air is 

 typical of lightly-damped systems while the broad resonance in water is typical of systems with relatively 

 higher structural damping. From the table in the figure it can be seen that even though the damping 

 and mass ratios of the two systems differ by factors of ten, the reduced damping is very nearly the same 

 and so are the peak displacement amplitudes Ymax for the two cylinders. Typical values of V^ 

 corresponding to Y^ax are listed in Table 2.1. 



When Reynolds and Froude number eflfects are neglected, the maximum cross flow displacement 

 amplitude can be expressed from dimensional analysis as being dependent on three quantities, viz.. 



Cs' M 



(2.1) 



^MAX ^ ^MAXl D = / 



Here Ws/w„ is the ratio of the Strouhal and structural frequencies Wj = Itt St VI D and w„, respectively; 

 and ^5 is the srrac/wra/ damping ratio. The parameter /u, is a mass ratio, defined by ix = p D^liiT^St^m, 

 where p is the fluid density and m is the structure's or cable's effective mass. St is the Strouhal number 

 and D is the cylinder diameter. This parameter also results from the normalization of the force 

 coefficients in the governing equation of structural motion as shown, for example, by Griffin (6), Sarp- 

 kaya (1), and Vickery and Watkins (7). 



It has been demonstrated experimentally (2,3,7) that the peak displacement amplitude Kmax of 

 vortex-excited oscillation for any given structure is a function of a "reduced damping parameter" of the 

 form: 



k = ^^, (2.2a) 



' pD'' 



or equivalently 



U^ = 2nSt'k„ St = ^, (2.2b) 



