out-of-phase with the cyHnder's velocity. It is possible to deduce the reaction effect of the fluid from 

 the measured force coefficients by means of the equations developed in Appendix E (see also refer- 

 ences 3 and 6) as 



Cr£- = Cr sin0i = — C„/, sin e. (2.5) 



As a further step in comparing the two approaches some typical results are plotted in Fig. 2.8. All of 

 the measurements show the same general pattern of behavior even though some were made with freely 

 vibrating cylinders in a wind tunnel and some were made with cylinders that were forced to vibrate in 

 water. 



The remaining force components, the added mass and the fluid inertia, can be obtained from the 

 equations given in references 3 and 6 and Appendix E when the force coefficients and the structural 

 parameters of a cylindrical structure and its mountings (i.e., internal damping, natural frequency) are 

 known. Detailed and related discussions of the forces and displacements that result from lock-on are 

 given by Sarpkaya (1) and Griffin (3). 



Not only are the unsteady forces amplified as shown in the preceding figures but the steady drag 

 loads also are increased substantially as a result of vortex-excited oscillations. Sarpkaya (12) has meas- 

 ured steady drag coefficients as high as Co = 3.1 for a cylinder vibrating in water at a displacement of 

 2 Ymax = l-^- This represents an increase of nearly a factor of 300 percent from the drag on a station- 

 ary cylinder, i.e. Cdo= 11 in this case. Griffin, Skop and Koopmann (15) found that the drag 

 coefficient was increased by as much as a factor of 1.8 from the stationary cylinder case (Coo = 0-9) for 

 their experiments plotted in Figs. 2.2 and 2.7. The steady drag amplification on circular cross-section 

 cylinders due to vortex-excited oscillations is plotted in Fig. 2.9. The solid line on the figure is a least- 

 squares fit to the data points (see Section 4.1). 



The static deflection at the tip of a flexible cantilever that experienced resonant cross flow oscilla- 

 tions in water (16) is plotted in Fig. 2.10. The drag coefficient on the vibrating flexible cylinder was 



13 



