256 - 1 - 



to ' Zn K plait ie pseudo-frequency of plate " 



tr • yield stress of plate. 



/^ 



R > radius of plate. 



S • ii)6 a • ratio of time constant of pulse to that of plate. 



N means that the special non-ainenslonal units defined in sub. paragraph S(b) 



must be used. 



y , t , X ' values of y, t and x oihen plate comes to rest. 



Introduction . 



The behaviour of a steel plate when subjected to an underwater explosion pulse has been 

 treated theoretically by quite a nunber of workers. Butterworth sjimarised the earlier work on the 

 subject and considered both an infinite plate backed by a sprinj and a piston moving in a circular 

 aperture in i rigid wall. Taylor(l) considers the former model and shows that one jets Increased 

 damaje if one supposes that the plate leaves the water as soon as the pressure in the water touching 

 the plate falls below zero. He also su^jests(2) that. In this case, the plate ray jain still more 

 energy if cavitation spreads outwards from the plate into the water. The resulting spray will be 

 projected towards the plate and must eventually catch up and Boffibard it. This suggestion was partly 

 explored by Fox and Rollo, who showed that such cavitation and follow-up of water would imply that, 

 for a thin plate, virtually all the incident energy was trapped in the neighbourhood of the plate, 

 and might conceivably contribute to damage. *n actual mechanism of reloading has been considered 

 by Kirkvpod(3) who concludes that, in practical cases, almost all the energy expended in producing 

 cavitation in water eventually contributes to damage. Unfortunately, only an abstract of this work 

 is at present available. The general theory of the propagation of cavitation in water tes been 

 given by Kennard(*) who h.3S applied it to a discussion of the effect on structures (5), and has given 

 an account of the present position of the theory of the distortion of a plate by an explosion(6). 

 It is the purpose of this report to obtain a definite numerical assessment of the extra energy 

 communiccited to an infinite ol "te by this process of cavitation and subsequent 'follow-up' or 

 bombardment with spray. *ork is now proceeding on the similar problem for the piston in rigid wall, 

 in order to assess the effect of the finite size of the plate, the importance of which Is fully 

 realised. It is hoped to deal with this in detail in a later report, but, in the meantime, a short 

 discussion of the relaWon between the two types of theory seems appropriate. 



Relation be tw een the. "Infinite Plate" and the "Piston in Rxgid Vail" theories . 



It is probable that the infinite plate on a spring is a reasoreole representation of the 

 behaviour of a ship, provided that one may assume that the effect of stiffeners, etc., is spread 

 evenly all over the plates. If, however, the stiffeners are strong, it is necessary to know how 

 the theory must be modified to 2II0W for the fact that the parts of the plate near the stiffeners are 

 practically Inmobile. This problem has been considered by Friedlander, who has obtained an estimate 

 of the effect of stiffeners in delaying the onset of cavitation, and also of the effect of a slight 

 curvature of an infinite plate on the time of onset of cavitation. Infomation on the effect of 

 clamped edges is also wanted for the discussion of box models or diaphragm gauges, particularly when 

 a baffle is fitted. For such cases the 'piston in rigid wall' seems a definitely better 

 approximation thsin the infinite plate. 



Let us suppose, for the moment, that water is capable of stanoinj tension. For ships' plates 

 of the thicknesses used in practice, the reflected wave set up when they are acted upon by an 

 explosion is almost entirely one'of tension for a large plate so that the pressure at the plate quickly 

 drops to zero and then to negative values. However, the pressure at the immobile wall remains 

 positive, and a diffracted wave travels towards the centre of the plate, and thus enhances the damage. 

 It is, in fact, shown by Butterworth that the effect of the diffracted wave may in a typical case be 

 so gre-il as to prevent the occurrence of tension at all, and that even when tension does occur, the 

 diffracted wave eventually wioes it out, \nd urges the plate forwards ai^ain. In the infinite plate 



