6 -6- 



These differences are not very considerable, and considering the tendency of the plate to 

 present a convex surface to the blow (see section 2) in the absence of forces of restitution it is 

 considered that the 'piston' equation may be taken as fairly representing the energy produced by the 

 blow. 



Using equations (24) and (u), and inserting the values of p for water and a for steel viz. 

 pg = 62.5 lbs. per cubic foot cr/p = 7.7 we find for the kinetic energy produced by the explosion 

 of a weight w lb. of T.N.T. when acting on a steel plate of radius a feet and thickness t inches 

 fixed in a rigid w^ll at distance feet from the charge 



4/3 



E (in foot lbs.) = J-^"** ^ (29) 



D"^ (l + 0.78 t/a) 



This energy is the kinetic energy residing partly in the plate but mainly in the surrounding water 

 just after the pressure wave has died away. The energy in the water is due to the water following 

 up the plate in its inward motion and is derived not merely from that portion of the wave which 

 impinges on the plate area but also from surrounding portions. The fact that the establishment of 

 this flow produces a relief pressure over the wnole of the wall is sufficient to show that this Is 

 the case. We need not therefore be alarmed if it turns out that equation (29) gives greater energy 

 than that calculated from the energy content of the charge radiating outwards in all directions. 



Modification due to finite duration of blow. 



It has been shown previously that if a wave of the form e"" is to act upon a vibrating system 

 of natural period t the maximum deflection obtained depends upon the value of mT. For a wave of 

 given momentum the greatest deflection is obtained when mr is very large. For finite values of nrr 

 the relative values of the deflection are given by the following table 



1.5 



0.640 



5.0 

 0.310 



Since the strain energy developed in the system is proportional to the square of the maximum 

 deflection this table may he used to find the proportion of the energy given by (29) which it is 

 possible to convert to strain energy in the absence of Jissipative forces. Thus if the natural 

 period of the plate is 0.011 second and the weight of the shot is 300 lbs., 



m = 1122^,, = 1100 

 (30C)''3 



so that 2 n/m T = 0.5. Hence from the table the modifying factor is (0.896) = 0.8 or 801 

 of the energy given by (29) will be converted to strain energy in the plate if dissipatlve forces 

 are absent. The real difficulty in applying this correction is in estimating the natural period of 

 the plate. If the plate is to be ultimately stretched beyond its elastic limit then initially the 

 plate behaves as a clamped pUte having no slope at its edges. This condition alone imposes the 

 maximum strees at the edge and in addition the loss of reli.'f pressure at the edges will cause a 

 further stress to be developed there. it is probable tn.'.t under ^ heavy blow the elastic limit at 

 the edges is reached at an early stage and thereafter the plate will more probably behave as a 

 stretched membrane the tension of this membrane being of the order of the mean tension load between 

 elastic limit and breaking point. If the platt had no watsr load the period would then be given by 



T = 2.6 a /o-Zl. (30) 



where L is the- tonsion loa3 and for steel is of the ord'^r 22 tons per square inch. 



