resonantly vibrating cylinders, the proper selections for circular cylinders were related to the response 

 parameter Sq through the equations 



logioG = 0.25 - 0.21 Sg, (D9a) 



// = {/;, (D9b) 



\o%whS^ = -0.83 + 0.98 Sg, (D9c) 



F = AGSalh. (D9d) 



When the above relation for F is specified, the stable entrained responses are associated with the solu- 

 tions of equation (D7) for which S ^ 0. The above relations are valid within the nominal Reynolds 

 number range 400 to 10^ for which St and Qo are generally constant.* One consequence of equations 

 (D9) is that the maximum cylinder response amplitude A^ax in the entrainment region becomes a 

 function of only Sq. An example of the results that have been obtained with the wake-oscillator model 

 is given in Fig. Dl. 



The vortex shedding process is strongly dependent on the local amplitude of vibration, but only 

 weakly, or not at all, dependent on the behavior of nearby cable elements. This provides an initial 

 justification for extending the model to elastic cylinders— namely, the equation (Dl), without the intro- 

 duction of any spatial derivatives, should be applicable for describing the vortex-excited oscillating lift 

 force on an elastic, cylindrical structure. 



To develop the model for the vortex-excited oscillation of an elastic cylinder, it is useful to adopt 

 a normal mode formulation. Let the vortex-induced displacement Y{x,t) of an elastic cylinder by 

 expressed as 



Y{x.t) = Y^q^UHiM (DIO) 



where the ^,(/) are the modal response factors and the (//,(x) are the normal modes of the response. 

 The dynamical equations for the ^,(r) are then obtained as 



Qi + ICiMnjQi + OiiiQi = 1^ r , (DID 



''o 2w, 



'Available experimental results indicate a lack of coherence in the data for C^q, but the value chosen is reasonable. Different 

 values of Qq require different values of G, //, and F to yield accurate predictions of resonant vibrations. However, changing 

 the value C'iq affects only the numerical coefficients F, C, and //and not the functional dependence on Sq. 



155 



