applicable at cross flow displacements less that Yl D = 0.2 and reduced dampings greater than l,Jfx = 

 2. This is somewhat beyond the range in Fig. 2.2 that is most applicable to marine structures and cable 

 systems. 



In order to specify the excitation component of the lift forces, Blevins and Burton fitted a qua- 

 dratic curve to the data of Vickery and Watkins (1964) and Hartlen, Haines and Currie (1968) that are 

 plotted in Fig. 2.7. The curve is given by 



Q£(z) = a +b\^M)\ Y^^x + c|.A,(z)P r^^ 

 with a = 0.35, b = 0.60 and c = — 0.93, and Qg is evaluated from the equation 



C,.^=-^ 



Jo CiE(z)^i(z)dz 



(4.3.5a) 



(4.3.5b) 



which is discussed in Appendix E.l. Blevins (71) has carried out the necessary integrations for a rigid 

 cylinder (i/;(z) = 1), a pivoted rod (t//(z) = z/L) and a sine (taut cable) mode (i//,(z) = sin(/i7-z/L)). 

 The results are listed in Table 4.2 for the case where the correlation length l^ is much larger than the 

 length L of the cylinder. The calculation of additional cases is straightforward. 



Table 4.2 Excitation Force Coefficient C^g for 



Three Cylindrical Structures; from 



reference 71. 



Structure 



Mode Shape i|/,(z) 



Cle He > L}- 



Rigid cylinder 



1 



a + b(Y/D) + ciYlD)^ 



Pivoted rod 



z/L 



a +^b{YlD) + ^(YlD)' 



Sine (taut cable) 







mode, / = 1 



sin (ttz/L) 



a +^ bif/D) + 4 ciY/D)' 

 4 3 



Qf is the average value calculated from equations (4.3,5a) and 

 (4.3.5b). Y/D is the peak displacement amplitude for a given mode. 

 a = 0.35, b = 0.60, c = - 0.93 



The coefficients for a cubic fit to the data in Fig. 2.7 have been computed and are based upon a fit 

 to all of the data points shown there. This cubic equation is given by 



Qf =01 + ^1 Y^fE^^x + ^1 Yeff.max + d] Yeff,max (4.3.6) 



94 



