PaidouBsis 



Fig. 4 The dimenslonless complex frequencies of the second and 

 third modes of a flexible cylinder with cc,^ = ecj = 1 , 

 f, = f2=l, c, -C2=0, A=l, X, =X2 = 0.01. (Theory 

 of [26]). 



5.2 Results Based on the Theory of [ 26] 



Typical results are shown In Figs. 3, 4 and 5, obtained by 

 using Eqs. (lOa), (11), (12) and (13). 



We first consider Figs, 3 and 4 applying to bodies with well 

 streamlined nose and tall, and A = 1. Figure 3 shows the behavior 

 (with Increasing towing speed) of the two modes which at zero towing 

 speed have frequencies u)q= w. = 0; these are the so-called zeroth 

 and first modes and, at low towing speeds, are associated with quasJ- 

 rlgld body nnotlons --a matter to be further discussed in §6, Figure 

 4 shows the loci of the so-called second and third modes of the system 

 as functions of towing speed. The frequencies of these modes at zero 

 towing speed correspond to the second- and third-mode frequencies 

 of the flexible body treated as a free-free beam; accordingly, these 

 (and all higher modes) are flexural In character. 



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