76 62 



values of z, and also smaller values of v^, are obtained if cavitation is 

 assumed to set in at a pressure below hydrostatic pressure. 



Hence, as was pointed out In the original report (21 ), an addi- 

 tional source of energy must be found. The water will in fact, overtake the 

 diaphragm and may do additional plastic work upon it. According to the ana- 

 lytical results, the water should acquire considerable velocity even if the 

 Incident wave has entirely ceased; but, actually, at t = T„ = 0.037 milli- 

 second, the Incident pressure has decreased only to a fraction g-87oox37xio 

 or 0.73 of its initial value. An attempt to allow for the additional plastic 

 work was made in Equation [84], and values of 2 calculated from this equation 

 and [80a] are shown in Table 2 as z^^i^. These values are In good agreement 

 with the observed deflections. 



The assumptions underlying Equation [8U] are certainly wide of the 

 mark in certain details, but it may be that in their broad outlines these as- 

 sumptions reproduce roughly the process that actually occurred. If this is 

 so, about three-fourths of the plastic energy was delivered to the diaphragms 

 by the water as it impinged upon them after closure of the cavitation. 



The final result will presumably not be very different if cavita- 

 tion occurs first in the water, or if, beginning at the diaphragm, it then 

 spreads back into the water. 



REFERENCES 



(1) "Damage to Ship's Plates by Underwater Explosions," by 



S. Butterworth, Admiralty Research Laboratory Report ARL/S/lO, July 1924. 



(2) "Note on the Motion of a Finite Plate Due to an Underwater 

 Explosion," by S. Butterworth, Admiralty Research Laboratory Report 

 ARL/N1/H4, August 194-2. 



(3) "The Distortion under Pressure of a Diaphragm Which Is 

 Clamped along Its Edge and Stressed beyond the Elastic Limit," by 

 Professor G. I. Taylor, F.R.S., Ministry of Home Sec\irity, S.W. 



24 September 1942. 



(4) Professor G. I. Taylor, F.R.S., Ministry of Home Security, 

 R.C. 21'}, July 1941. 



1,3) "Memorandum on the Plastic Deformation of Marine Structures 

 by an Underwater Explosion to August 1, 1942," by John G. Kirkwood, 

 NDRC 308, OSRD 793, August 1942. 



