286 - " - 



Examination of these equations reveals the remarkacle result that the corresponding equations of I 

 can Be made identical with them, if we make the very same changes in the variables that wo have 

 already introduced when discussing the motion of the plate up to cavitation, and the propagation 

 of the cavitation front. For convenience, we recapitulate these changes here. 



t becomes t - '-^H^ 

 C 



p Becomes p cos <M 

 •^m '^m ^ 



p becomes p cos <p 



a becomes a cos 



2 



The other variables remaining unaltered, except that, consequent on the change in a, S becomes 



S^ cos 0. The corresponding changes in the non-dimensional units introduced in I are:- 

 Unit of X becomes C & sec i/i instead of C ^ 

 Unit of y becomes ^m cos xp instead of ^m 



the units of time and pressure Being unaltered. 



When we make the modifications in a and S, we can take over the information in Tables 1 

 and 2 of I without having to repeat the numerical work. The main result of this work is that 

 for a thin plate about \ of the total energy falling on the plate appears ai damage. The work 

 in I shows that this figure is not very sensitive to S, and for a small it almost certainly only 

 varies slowly with a, so_ we conclude that it is probably not very sensitive to v// either. We 

 thus conclude that, for a large plate, when cavitation occurs, the final damage corresponds to 



1 Pm^ ^ 



plastic energy of approximitEly - -2 cos i// per unit area of plate which. If w= assume a to 



3 p^Z 



to T ahd to be proportional to Vi, where W is charge weight and D is distance, leads to a 



formula of the type 



Central Deflection "° ^!LE21'1^) (4) 



D 



The Effect of Cavitation on Damaj^e , 



We now examine various models of a structure undergoing damage to see what valid 

 comparisons can Be made between the consequences of the assumption that water can stand no tension 

 at all, and of the assumption that water can stand unlimited tension. At first sight one would 

 think that the answer is obvious, and that if a plate is free to leave the water when the pressure 

 drops to zero it must always suffer more datrage than if tensions can occur. For a sufficiently 

 large plate this is certainly true, furthermore the work of I shows that if cavitation occurs, 

 a further contribution to damage is made by impact of cavitateo water with the plate. For a 

 finite plate, however, one has to consider the effect of diffraction from the edges. For a 

 very small plate, the effect of diffraction is to prevent tension occurring at all, and there 

 will be no difference between the consequences of the two assumptions. (Criteria for this 

 are worked out in ll). For a somewhat larger plate tension sets in before the arrival of the 

 diffraction wave from the edges, and the pressure alternates in time between positive and negative 

 values. It will be shown later that positive values predominate, so that the effect of 

 diffraction is always to increase damage. For a sufficiently small plate this contribution 

 is considerable, and it may well be that the effect of cavitation in preventing the diffraction 

 wave from acting all over the plate more than balances the gains in damage due to the non- 

 existence of tension at the plate and the effect of "follow-up". 



(1) 



