Dynamics of Submerged Towed Cylinders 



60 70 



Fig. 11 The dlmensionless coraplex frequencies of the second and 

 third modes of a flexible cylinder with f| = 1 - C| = 1, 

 f2= 1 - cg = 1, eC|^ =ecy=l,A=l, X| =X2 = 0.01. (New 

 theory) . 



This system is unstable in its first mode for < u < 3.43 and loses 

 stability in its second and third modes at u = 3.04 and u = 5.14, 

 respectively. As we may regard the smaller values of ec^ and 

 ecy to represent a smaller e = L/D, we may conclude that reducing 

 the slenderness of the system renders it less stable. 



Other similar complex frequency calculations establish that 

 the general conclusions regarding optimal stability are essentially 

 identical to those given by the old theory, in spite of quantitative 

 differences in the thresholds of instability. The main difference 

 appears to be that the first-mode instability is less extensive, in 

 terms of the range of parameters over which it is possible, than 

 predicted by the old theory. (Here it should be mentioned that these 

 calculations are still in progress and that stability maps of the type 

 of Figs. 6 and 7 are not yet available.) 



The question now remains on how well this theory Is capable 

 of predicting the experlnnentally observed dynannlcal behavior of the 



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