4. STRUMMING CALCULATION METHODS 



4.1 Analytical Models. A number of analytical models have been developed to predict the vortex- 

 excited oscillations of general bluff, cylindrical structures. Application to cable strumming problems is 

 but one specific example of the utility of the various methods. In general the models that have been 

 developed fall into these categories: 



• Nonlinear, or wake, oscillator models. 



• Empirical models, which are based upon measured fluid dynamic force coefficients. 



• Random vibration models. 



• Discrete vortex models, which are based upon the insertion of arrays of small vortices to 

 represent the overall features of the vortex shedding. 



• Numerical models, which are based upon numerical integration of the governing equations of 

 fluid motion. 



The wake oscillator models have been developed because many features of the resonant interac- 

 tion between the vibrations and the vortex shedding exhibit the characteristics of a nonlinear oscilla- 

 tion. This observation was first made by Bishop and Hassan (61) and the idea since has been developed 

 by Skop and Griffin (9,62), Iwan and Blevins (8,63) and Hartlen and Currie (64), among others. The 

 wake oscillator model most recently has been applied to marine riser vibration problems. Some limited 

 success has been achieved as discussed by Fischer, Jones and King (40). The wake oscillator concept is 

 discussed in further detail in Appendix D. 



Random vibration models to predict vortex excited oscillations in general and cable strumming in 

 particular have been developed by Blevins and Burton (21) and Kennedy and Vandiver (55), respec- 

 tively. Some limited success has been achieved. A general model for employing measured force 

 coefficients in an empirical formulation has been developed by Griffin (3,6) and Chen (65). Measured 



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