284 



W = Weight of charge. 



= Distance from charge. 



* (^r'' = ^--s '='" ^* ^' 



Cf 

 7T! 



t = Time variable. 



f = A variable of integration. 



Introduction , 



In two previous reports, referred to as l(l) and I I (2) we have considered some of the 

 modifications that have to De made in the theory of the motion of a clamped plate when subjected 

 to an underwater explosion pulse, if we assume that water is incapable of standing any finite 

 tension. Taylor (3) made a start on this problem for an infinite plate, considered as a mass 

 backed by a spring, (tlie spring representing the elastic and plastic forces in the structure). He 

 calculated the energy that was imparted to the plate up to the instant at which the pressure 

 dropped to zero at the plate. In I we obtained explicit formula'- governing the propagation of 

 cavitation- into the water subsequent to this instant, and formulated the equations governing the 

 subsequent motion of the plate, as it is gradually brought to rest by the spring, but is subjected 

 to the impact of the cavitated water which is thus given an opportunity to catch up. Solution 

 of these equations showed that, for thin plates, the major portion of the dairege would be caused 

 by this "follow-up" mechanism, t(.; final damage corresponding to about two-thirds of the energy 

 brought up by the explosion pulse, the remaining third being partly reflected away before cavitation, 

 and partly lost in the collision between water and plate. In II we investigated some of the 

 modifications that would be needed for a finite plate. In particular, we found that Kirkwood's (u) 

 suggested criterion for the occurrence of cavitation was probably correct, and also that it did not 

 differ very much from the criterion that, in the absence of cavitation, incompressible theory 

 would be a valid approximation for determining damage. 



We have so far not attempted two of our main problems: 



(a) To determine whether damage is greater if cavitation occurs at zero pressure than it 

 would be if water could stand tension. 



(b) The effect of a pressure-pulse at oblique incidence. 



In this report, we shall attempt both of these problems for a large plate. For small plates 

 neither question arises, because we havc shown in II that, e.g. for diaphragm gauges, cavitation 

 probahly does not occur and that Incompressible theory is probably a fair approximation. Further 

 if incomprrsslble theory does apply, the damage would be practically independent of the angle of 

 Incidence, (-S Is, In fact, observed experimentally for diaphragm gauges)* 



The Effect of Oblique incidence, if Cavitation occurs . 



Taylor (3) was able to generalise his work to oblique incidence on the following two 

 assumptions: 



(a) Conditions are not too near those of glancing Incidence. 



(b) The motion of each eUment of the plate is independent of that of neighbouring elements, 

 i.e. effects propagated through the plate may be neglected In comparison with effects 

 propagated through the water. 



Assumption 



