Remarks. A brief description of the program is 

 given along with information concernmg assumptions, 

 computer-time requirements, and where a program 

 listing may be found. 



Survey Results 



It is evident, after surveying the literature on 

 moored-cable-system analysis in general and 

 dynamic-cable analysis in particular, that two major 

 deficiencies exist. First, experimental data to validate 

 the programs are lacking; without this data, the pre- 

 cision and reliability of the programs are in doubt 

 and, thus, the programs are of limited usefulness. 

 Second, the dynamic programs must be generalized 

 and streamlined so that complex, three-dimensional, 

 moored structures can be analyzed using reasonable 

 amounts of computer time. 



CABLE-STRUMMING ANALYSIS AND DESIGN 

 CONSIDERATIONS 



When a cable is exposed to crossflow and the 

 resulting Reynold's number lies between 90 and 

 approximately 1 x 10 vortices spring from the sides 

 of the cable, producing a fluctuating fluid pressure. 

 The resulting forces cause the cable to vibrate in a 

 plane normal to the directional fluid flow. This trans- 

 verse vibration is cable strumming (see References 42, 

 69, 70, and 71 for descriptions of vortex-shedding, 

 cable strumming phenomenon). Cable strumming in 

 moored-cable SN'stems produces cable fatigue, high 

 acoustic noise levels, and increased drag. These fac- 

 tors all work to the detriment of the mooring and can 

 cause failure or unacceptable performance. Thus, 

 reliable methods for predicting when cable strumming 

 will occur and ways to suppress strumming must be 

 developed. 



One way to predict and describe the cable- 

 strumming phenomenon would be to solve the time- 

 dependent Navier-Stokes equations for the three- 

 dimensional separated flow that is characteristic of 

 cable strumming. Unfortunately, such a solution at 

 this time is not possible because the strumming 

 phenomenon still needs to be lietter understood. 

 What is required is some "tool" that permits reliable 

 prediction and description of cable strumming with- 



out being dependent on a complete numerical solu- 

 tion to the Navier-Stokes equations. 



Below, information is presented to aid in the 

 analysis and design of moored-cable systems that may 

 be subjected to cable strumming. 



Mathematical Oscillator Models 



The oscillator models, presented in Table 3, 

 attempt to duplicate the experimentally observed 

 behavior of cables and other bluff bodies in cross- 

 flow. None of the models given in Table 3 is capable 

 of predicting or describing cable strumming, but these 

 models form a base of information that, with further 

 development, may result in a predictive tool. 



Flow Field Models 



Table 4 presents the flow field models which 

 attempt to describe the flow fields near bluff bodies 

 in crossflow. Advanced versions of these models may 

 directly result in predictive and descriptive informa- 

 tion for cable strumming; or they may produce new 

 insight into the strumming phenomenon that, in turn, 

 can be applied to the development of predictive or 

 descriptive tools. 



Cable-Strumming Design Considerations 



This section presents currently available infor- 

 mation pertaining to strumming prediction, increased 

 drag due to strumming, and strumming suppression. 

 Though this design information yields only rough 

 approximations, it will show a design engineer how to 

 determine if strumming is probable, what can be done 

 to estimate the resultant increase in drag for short 

 smooth cables, and what methods are available to 

 eliminate strumming. 



Strumming Prediction. Experimental studies 

 have shown that flexible cylinders and cables are 

 induced to vibrate by vortex shedding at frequencies 

 approximated by the String Equation [103, 104). 

 The string equation for vibration in water is: 



f„ = (n/2L)(T/M..)"2 



(1) 



