559 

 This may be represented by the analytical equation: 



r -I 0«T3 



W = K (D,o6j, i„^) (27) 



H 



represents the difference in damage between thin and thick diaphragms. 

 K is a constant, D q^ ^^ is the damage of the thick diaphragm. 



No significant difference was observed in the weight exponents fotmd 

 for the thin and thick diaphragms. 



(b) The baffle effect . The Kirkwood Damage Theory predicts greater 

 damage for a diaphragm held in a rigid "infinite" plane disc (which will 

 reflect the shock wave and momentarily double the pressure) than for a 

 diaphragm held in the center of a disc of finite radius because of the 

 lower pressiire wave moving in from the edge. Actually, the "infinite" 

 disc is one whose radius is larger than a limiting value; this limit is 

 such that for a longer radii damage is complete before the diffracted 

 shock wave can reach the diaphragm. The "infinite" disc must also be 

 thick enough that reflections from the back surface will be so late in 

 occurring that they can have no effect on the deformation of the diaphragm. 

 The limiting radius can be found by multiplying the velocity of soxind by 

 damage timeiZ/ and is about 1-1/2 ft. for regiolar UERL small charge work 

 with steel diaphragms in the standard gatige. The effect of size of baffle 

 on damsige is predicted by the theory, and comparison of predicted and 

 actual results provides a test of the theory. 



(i) Theoretical predictions . The following analysis is based on 

 the assinnption that the baffle is not fixed but is able to move almost 

 freely during the time interval required for the deflection of the 

 diaphragm. This assumption conforms with the conditions of the experi- 

 ments discussed below. The assumption Is further made that the baffle 

 is of infinite radius. 



Consider an initially flat circvilaT diaphragm of thickness a^, 

 radius Rq, density / , and yield stress (Tq mounted in an 

 infinit^T)affle of mass m per unit area. Suppose that the baffle is 

 surrounded on both sides by water and that the diaphragm is in contact 

 with water in front but is backed by air. During an interval of time t 

 after the front of an exponential pressure wave of the form 



P(t) = Pm e ' t > o; 



p(t) = o, t ^ o; 



(28) 



has struck the system, the diaphragm undergoes a displacement ZQ(t) with 

 reference to the baffle, which in turn \mdergoes a displacement z-,(t). 

 At low pressures the soiond velocity in water is c and the density of 

 water is ^o' '^^ differential equations of motion of the center of the 



17/ Ct J. G. Kirkwood, OSRD 1115, Eq. (S-H) December 19i^2. 



