The drag coefficient Cg for a structure vibrating due to vortex shedding is increased as shown in 

 Fig. 2.9. The ratio of Cp and Cpo (the latter is the drag coefficient for a cyHnder, cable or other flexi- 

 ble bluff structure that is restrained from oscillating) is a function of the displacement amplitude and 

 frequency as given by the response parameter (59) 



w, = (1 + 2Y/D){V,St)-K (4.3.2) 



Here again 2 K is the double amplitude of the displacement, K, is the reduced velocity and St is the 



Strouhal number. The ratio of the drag coefficients is given by 



Cd/Cdo= 1 . w, < 1 (4.3.3a) 



Cd/Cdo = 1 + 1.16(h', - 1)°", w, ^ 1 (4.3.3b) 



which is a least-squares fit to the data in Fig. 2.9. The equation 



- 1 29y 



''--/^= [1+ 0.43(2. Sr^^.)]"5 ^'-'-'^ 



can be combined with equations (4.3.2) and (4.3.3) to compute the unsteady displacements, the drag 

 amplification and the amplified static deflection that is due to the vortex excited oscillations. The local 

 displacement amplitude along a flexible cylindrical structure (in the ith normal mode) is given by 



y(z) = Ti(z)sin(27r/f). 

 where 



These equations are employed as outlined in Fig. 4.2 to iteratively compute the static deflection of a 

 structure or cable due to vortex-excited drag amplification (the drag coefficient C^o for the stationary 

 cylinder or cable is assumed to be known). , 



Blevins and Burton (21) have developed a random vibration model for predicting vortex-excited 

 cross flow displacement amplitudes. As noted in Section 4.1 and Appendix E, the model is based upon 

 random vibration theory in order to incorporate the effects of varying correlation length on the resonant 

 response of the structure and the flow-induced forces. The details of the model are given by Blevins 

 and Burton (21,71), and will not be repeated here since the variable correlation length effects are more 



93 



