E7) and Sarpkaya (E4) leads to the result 



2CsJ,""^(yydt = iTfji 



2 \.^iz)dz 



(Qf Y sm<t> — Cre y sin<t>i) 



J,\{z)c 



jyiz)dz 



where Ci£ and C^£ are "equivalent" force coefficients similar in form to those given by equation 

 (E.1.18). 



E.2 Random Vibration Models. Predictive models for vortex shedding-induced oscillations based 

 on a random vibration approach have been introduced by Blevins and Burton (E8) and by Kennedy and 

 Vandiver (E9) . The latter model is tailored specifically toward the prediction of cable strumming oscil- 

 lations which are not in complete resonance with the vortex shedding. The former model is a pure- 

 mode approach, based upon an assumption of resonant interaction between the body and the fluid. 

 Also, the model equations are derived for arbitrary flexible cylinders, of which the cable is but one 

 specific example. 



Blevins and Burton (E8) derive the equation of motion for a flexible cylinder in a manner similar 

 to that given in Section E.l. It is then assumed that 



■^2 c" f. L SFizi,Z2,oymzi)ilj(z2)dzidz2 



j)2 = J dSL^ ^—j. p do> (E.2.1) 



where y is the rms cross flow response and Sf{zi,Z2,<o) is the cross spectral density of the vortex- 

 induced lift force, and z(w) is the impedance of the system. This equation reduces to 



Y/D = 



{.lirStYks 



'0 



where the equivalent excitation force coefficient, Qf, is 



Jo ^'^' 



CrF. (E.2.2) 



^2 _ KlKl ^^ ^^ g{z{)g{z2)r{z, - Z2mz,mz2)dz,dz2 



l/o H 



In this equation KiK2g{z) is the rms lift coefficient at the spanwise location z and riz\ — z-^ is the 

 spanwise correlation coefficient. K\ and K2 are arbitrary constants. The correlation coefficient is 

 specified from experimental measurements on a cable or cylinder at resonance. 



167 



