VL BUCKLING 



We assume that the cable buckles as soon as the total stress at some 

 point becomes compressive. Since, without any dynamic input, the cable is 

 under tension due to gravity, not all kinds of inputs will make the cable buckle. 

 In order to find whether a given input will cause buckling, step by step we must 

 trace in the cable the propagation of the input, as well as its interaction with 

 and reflection by the array and vessel. Here we will investigate only one as- 

 pect of this complex problem, namely, buckling within the time T = — after 

 the onset of the input. 



In the absence of any input, the static elongation of the cable, u 



is given by 



u = 



s 



L 

 SE 



- (w-b) + W " B 

 2 a a 



(31) 



Now the simplest input dynamic displacement, u , which satisfies the condi- 

 tion that at time t = the vessel is stationary is u = -r t^, where a is an 



2 



acceleration. Therefore, if buckling is to occur within the time T, u must 

 become greater than u in time equal to or less than T, i.e.: 



a > 



Lw 



- (w-b) + W 



(32) 



where g is the acceleration of gravity . Thus, the acceleration a necessary 

 for buckling decreases with increasing L and with decreasing net weight of the 

 array. For L = 20,000 ft, w = 10 lb/ft and W^ = 100 tons (and no buoyancy 

 anywhere), a> 3g. For W = 0, a > g regardless of L and w. Therefore, 

 it takes tremendous input accelerations to buckle the cable in this manner. 



Suppose, though, that the cable has buckled. Then, depending on the 

 degree of buckling, the cable may or may not form kinks. When the vessel now 

 moves upwards and stretches the cable, these kinks will make the failure of the 

 cable easier. In order to determine the degree of buckling, let us assume that 

 the array falls freely in the sea after buckling. 



29 



^nhnx JD.ILittlcJnc-. 



S-7001-0507 



