Appendix D 



THE "WAKE-OSCILLATOR" MODEL FOR PREDICTING 

 VORTEX-EXCITED OSCILLATIONS 



The periodic lift force F^, characterized by a Hft coefficient Qt which acts on a bluff structure as 

 a result of vortex shedding, is assumed to respond during lock-on or wake capture as would a modified 

 van der Pol oscillator (D1,D2). The governing equation for Q, in the form employed most recently 

 by Skop and Griffin (D3,D4), is 



Q + colQ - [do - Cl - \cji>>^\{o,sGCL - o^IHCl.) = (osF{Y/D). (Dl) 



Here, a dot denotes diflferentiation with respect to time /, Y is the transverse displacement amplitude of 

 the cylinder due to the incident flow of velocity V, and D is a. characteristic transverse dimension 

 (diameter) of the cylinder. The frequency coefficient ws (rad/sec) and the four dimensionless 

 coefficients Qo, G. H, and F represent parameters which are to be evaluated from experimental 

 results. It is interesting to note that Iwan and Blevins (D5) and Iwan (D6) have justified the introduc- 

 tion of models similar to equation (Dl) from a consideration of the momentum equation for the 

 fluid/ structure system. 



For flow over a stationary cylinder (that is, for Y = 0), equation (Dl) exhibits a self-excited, 

 self-limited solution given by 



Q = Clo sin (list. (D2) 



This result leads to the interpretations of Qo and ws as, respectively, the fluctuating lift amplitude and 



shedding frequency from a stationary cylinder. The shedding frequency w^ is determined from the 



Strouhal relation 



ojs = lirStVlD (D3) 



where St is the Strouhal number. 



tThe lifl force /"/ (per unit length along the structure) is normalized by Fi = 1/2 p V DC^. 



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