On the other hand, as Figure 3 shows, certain resonant frequencies 



can induce very large dynamic stresses o The frequencies of these resonances 



are close to ud' = tt, and their peaks are very high for small values of \j. . 



For the above cable and U = 1 ft, we have (at resonance) tw' = 3.2 and 

 o 



Is' I s: 90 , Therefore, E = 90, 000 psi and O) = 2.2 rad/sec, corre- 



' max max 



sponding to a period of about three seconds . If we take | U | = 3 ft, then 



I E 1 = 195, 000 psi at UD = 2.2 rad/sec. Clearly then, resonant frequencies 

 max! 



with rather small amplitudes can break the present cable easily. Depending on 

 the state of the sea, the above resonant frequency with the corresponding am- 

 plitudes can be found in a realistic sea. However, the input amplitude to the 

 cable at this frequency can be much less than the amplitude of the sea, depend- 

 ing on the stability of the vessel (or lowering platform) and the method used to 

 attach the cable to the vessel. These aspects will be treated in the following 

 Section, but the following two general conclusions must be emphasized here . 



TTC 



First, since the resonant frequency is given by tA) = — — • , it is de- 

 sirable to have as high values of c as possible so that this frequency can fall 

 in the region of the input spectrum which is characterized by small amplitudes . 



Second, it is highly desirable to have a large value of u . This means 

 that the dynamic mass of the array must be small. The present cylindrical 

 array is poorly designed with regard to this aspect, because of the large quan- 

 tities of displaced and entrained water. 



A linear array made of aluminum trusses can serve the same pur- 

 pose as the 50 -ton cylindrical array. The aluminum array does not entrain any 

 water, it displaces a very small amount of water, and it weighs only about 15 

 tons . It appears that a reasonable value for the dynamic mass of this array in 

 water is about 20 tons. (Compare this with the 300-ton dynamic mass of the 

 50-ton cylindrical array.) Let us consider with this array a 6 x 37 Special 

 Flexible Hoisting wire rope (USS) with a diameter of 1-5/8 inches, which has 

 the following characteristics: 



E = 11 X 10^ psi S = 1.1 in2 



c = 10, 000 ft/sec OJ = 4.1 lb/ft 



Notice that, for L = 20,000 ft, u is now equal to 2. 



21 



artbur Sl.HittlcJinr. 



S-7001-0307 



