canceling the gravity forces completely. It is highly desirable to have the 

 cable in an appreciable static tension so that compressive dynamic stresses 

 will not buckle the cable. Buckling of the cable is not in itself dangerous, but 

 the formation of kinks, which can occur when the cable buckles appreciably, 

 is. Some consideration of this problem is given in Section VI . Perhaps, the 

 problem should be pursued further. 



The motions of the vessel in a rough sea (heave, roll, etc.) will 

 induce dynamic stresses in the cable. Due to its great length, the cable can- 

 not be considered nonflexible for the kind of inputs that exist in a realistic sea. 

 In fact, for sinusoidal inputs, resonance can occur at frequencies as small as 

 1.5 rad/sec. These frequencies correspond to periods as large as four sec- 

 onds, which are included in the spectrum of a disturbed sea. 



In order to obtain an accurate value of the maximum dynamic stress 

 induced in the cable by a regular (sinusoidal) surface wave, the dynamics of 

 the vessel, cable, and array must be analyzed simultaneously. The parame- 

 ters necessary for such an analysis are too many, and the problem can become 

 formidably long and difficult. However, it can be safely assumed that the dy- 

 namic loading of the vessel by the cable and array is negligible, except possi- 

 bly when the cable is attached to the vessel by a boom extended from the side. 

 Thus, the problem can be simplified by considering the dynamics of the vessel 

 and of the cable -array system separately. 



A theory is developed which takes into account the propagation of 

 longitudinal elastic waves in the cable and the complete dynamics of the array 

 in water. It is shown that friction on the cable by the surrounding water is 

 small and can be neglected, even near resonance, since friction on the array 

 is much larger. The drag on the array must be taken as quadratic because of 

 the large Reynolds number involved. This is the only nonlinear term in the 

 theory. It is linearized to a quasi -quadratic form. Thus, a formula is de- 

 rived for the maximum dynamic stress due to a sinusoidal input. It gives this 

 stress in a parametric form as a function of the input frequency and amplitude, 

 characteristics of the cable, and of the weight and shape of the array. This 

 formula is plotted in a dimensionless form with two parameters . 



It is shown that resonant frequencies as small as 1 .5 rad/sec can 

 induce very large stresses for input amplitudes of one or two feet; furthermore, 

 that dynamically heavy arrays increase the dynamic stresses a lot, especially 

 near resonance. Entraining or displacement of large amounts of water in- 

 creases the dynamic mass of the array. Therefore, the array should be a 

 trussed open structure. Also, the velocity of sound in the cable should be as 

 large as possible. This makes the resonant frequencies large so that they lie 

 on the cut-off edge of the spectrum of a given sea state . 



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S-7001-Q307 



