Beginning with large lengths, the cable assembly behaves as a fixed-ended 

 spring, and the role of damping, which is dependent on the input amplitudes, is to 

 provide an additional margin of safety. Thus higher frequencies for the same length 

 at constant input amplitudes can be tolerated without danger of breaking the cable. 



As the length decreases, a transition occurs and the cable assembly takes on 

 the characteristics of a free-ended spring. Again the role of damping is to provide 

 an additional margin of safety against failure. 



Finally at very short cable lengths, the cable appears to behave like a rigid 

 connection between source and load rather than as a "spring. " In this case, the 

 role of damping (drag) is reversed in that, for constant input amplitudes, smaller 

 frequencies can be tolerated than for the case when /S = 0. 0. 



All of the above trends are confirmed by the calculations for both the damped 

 and undamped cases as the length L approaches zero, as indicated by Figure 33. 

 For comparative purposes, a few results obtained by applying the method developed 

 by Whicker for a free-ended cable are included. The mathematical formulation by 

 Whicker does not include the damping term. Thus a direct comparison of the effect 

 of damping is available. 



It is recognized that the analysis used for this investigation — that given in 

 the report by A. D. Little, Inc. — does not accurately describe the prototype situ- 

 ation by virtue of the linearization required in the drag term |Su/Bt'| (3u/St'), which 

 is necessary in order to solve the basic equation of motion. In the present state of 

 the art concerning nonlinearly damped oscillations there appears to be no alternative 

 to the linearization. Further theoretical analysis is considered necessary and justified 

 in order to resolve the question of safety of lowering systems as the length of the 

 cable increases. Such an analysis would consider the use of analogue computations 

 to allow retention of the nonlinear | 9u/9t' | (Bu/St') term. 



Similar interpretations regarding the safety of a load-lowering operation may 

 well apply at greater depths for lower frequencies if the curves presented in Figure 33 

 were extended. From the general shape of the curve shown and for a given input 

 amplitude oscillation there is a limiting input frequency below which the operation 

 is safe (the maximum dynamic stress is not exceeded) down to a certain depth. For 

 a particular lowering operation it may be possible to use a working vessel which has 

 little or no response to excitations above this limiting frequency. Alternatively, the 

 operation may be carried out in a lower sea, but this does not necessarily imply a 

 maximum frequency of input oscillation, although it does imply a diminished ampli- 

 tude of oscillation which would render the operation safe. 



A similar discussion may also be applied to Figure 34 for the case of a steel 

 cable, although an unsafe condition is not likely to occur until depths of 20,000 feet 

 even with input amplitudes of 14 feet. In this case, however, an additional factor 

 must be considered, namely the very significant increase in static stress due to the 

 weight of the cable. As far as the dynamic stress is concerned, it may be concluded 

 that the operation may be safe for cable lengths greater than 100 feet when input 



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