are considered in the general procedure, but emphasis is placed here on the case of a single flexible 

 cylinder or cable. The reader should consult references 2 and 68 for further discussions of arrays of 

 structural members. A second flowchart that describes the steps necessary to compute the amplified 

 drag forces and steady deflections is given in Fig. 4.2. 



All of the methods developed thus far are in agreement that the following parameters determine 

 whether large-amplitude, vortex-excited oscillations will occur (3): 



• the logarithmic decrement of structural damping, 5 



• the reduced velocity, V/f„D 



• the mass ratio, mJpD^. 



Here m^ is the effective mass of the structure which is defined as 



XL 

 m (x) y^(x) dx 



Wj, = ■ ' ^z. — — 



Jo >''(^) dx 

 where mix) is the mass per unit length including contributions due to internal water, fluid added mass, 



joints, sections of different material, etc., 



y{x) is the modal shape of the structure or cable along its length, 



L is the overall length of the structure or cable, measured from its termination. 



The eff"ective mass m^. defines an equivalent structure whose vibrational kinetic energy is equal to that 

 of the real structure. In the context of cable strumming, this equation is generally applicable to bare 

 cables and to cables with attached masses. 



As described in the previous sections the mass parameter and the structural damping can be com- 

 bined as 



2m fb l,^ 



/c, = ;- or — = Itt St k, , 



(4.2.1) 



89 



