used are listed in Table 4.1. The prediction curve developed by Griffin, Skop and Ramberg (69) is a 

 least-squares fit to those data points in Fig. 2.2 that were available in 1976 (about two-thirds of the 

 points now appearing in the figure). The Iwan and Blevins curve was developed during a study of one 

 wake-oscillator formulation (8) and Sarpkaya's result is based upon a modeling study (1) similar to the 

 one described in Appendix E. The dimensionless mode shape factor y is given by 



r,= I«/',(z)ImW/,'^'. (4.3.1) 



Representative maximum values of y, for different end conditions and mode shapes can be calculated 

 from the results in Table El in Appendix E. 



All of the equations in Table 4.1 correctly model the self-limiting displacement amplitude that is 

 shown at small values of reduced damping in Fig. 2.2. It is also important to note that all of these 

 models are based upon the structural damping ratio, typically the still air value, for whatever mode of the 

 structure is excited (see Appendix E). The models in Tables 4.1 tend to overpredict the cross flow dis- 

 placement ampHtude at Y/D < 0.05 to 0.1 where the vortex shedding is not fully correlated over the 

 length of the cylinder, but these small-amplitude cross flow oscillations are of more concern in gas flows 

 rather than in water. 



Table 4.1. Predictions of Cross Flow Displacement 



Amplitude Due to Resonant Vortex-Excited Oscillations 



as a Function of the Reduced Damping 



Investigator 

 Griffin, Skop and Ramberg (69) 



Blevins (71) 



Sarpkaya (1) 



Predicted Displacement Amplitude 

 y,n 1.29r 





[1 +0A3{2itS 



lo 3 1 ^-^2 1 



1/2 



"^ (1.9 + k,)St' 

 y,r, 0-32r 



^•^ ' il.9 + k,)St 



' [0.06 + (In St' k,)'V'' 





Legend: Y = displacement amplitude; D = cylinder diameter; m = mass or 

 equivalent mass (equation (4.2.1)) per unit length; Si = Strouhal number; k^ = 

 reduced damping (equation 2.2)); y = dimensionless mode shape factor (equation 

 (4.3.1)), y = 1 for a spring-mounted rigid cylinder, y = 1.3 for the first mode of a 

 cantilever, and y = 1.16 for a sinusoidal mode shape (cable). 



92 



