Blevins and Burton have applied their formulation to a number of specific cases. One such case is 

 plotted in Fig. El where the predicted peak displacement amplitude for a sine mode (taut cable) at 

 resonance is plotted. At the lower displacement amplitudes the cable response is dependent upon the 

 correlation length, but only a single prediction is the result at displacement amplitudes above Y ~ 0.3 

 D. The limiting value of Y/D (see Fig. 2.2) is 1.2 for the particular case of a cable as shown in Fig. 

 El. 



Kennedy and Vandiver (E9) have introduced a stochastic model for the cross flow strumming 

 response of marine cables. The lift coefficient Qg in the non-lock-on regime is assumed to be a nar- 

 row band random variable centered about a local Strouhal frequency that is characterized by its correla- 

 tion function or its power spectrum. Much the same approach as had been used by Blevins and Burton 

 is employed, except that the response of the cable is treated as a forced oscillation. A normal mode 

 response with mode shape 4ij and modal frequencies / is assumed, and the modal force spectrum is 

 given by 



^FjK^^ = ///(,%, (zi)0,(z2)5f(zi.Z2,/)^Z,^Z2. (E.2.4) 



In the analysis cross terms (j ^ k) are assumed to be small in relation to the modal response for which 

 j = k. The response and force spectra are then related by 



^(2i,Z2,/) = Y.^j(z,Hj{zj)\Hj{f)VSFj{f) (E.2.5) 



J 



where 



5f,(/) = /p Jo ^M^^M)SFiz,,Z2J)dz^dZ2 



The total displacement response spectrum then is the sum of the individual modal response spectra that 

 are included in the excitation bandwidth. Kennedy and Vandiver have applied their model to two prac- 

 tical problems: the response of a nonuniform cable in a uniform flow and the case of a uniform cable in 

 a nonuniform (shear) flow. These problems are discussed in detail in reference E9. 



Forced vibration models based upon random oscillations have been introduced by Howell (ElO) 

 and Kwok and Melbourne (Ell) for the purpose of predicting the cross flow response of aeroelastic 

 structures in turbulent shear flows. 



168 



