187 



The solution of (30) nay nov; be written as 



R = a - ^ V t = a - i^ Z (^) 



H = h(i) '-^ (b) 



U = Xv (c) 



3""^ « 2 .4 .2 



S = 44 =^i_L2K_L^>3 (d) 



2X2 ^-^ 



vfhere, it will be remembered, C = 



V? 



For )<.= 1> ^= 3, and v = j=4=r °» ^'^'^ ^^® deformed diaphragm is 

 cylindrical, i.e., it ruptures completely, (Possibly in practice, rupture 

 Would occur before this, due to excessive thinning at the center, or shearing 

 at the edge; experiments indicated the central failure to occur first with 

 properly designed edge restraint's. 1'he above value of v might be regarded 

 as an upper limit.) 



For other allowed values of >^(=u.), this solutionis quite 

 similar to the elementary approximation presented earlier, even quantitatively 

 so, for large values. For then 



and (33) reduces to (29). 



B, Still another case, perhaps even the most important one for 



purposes of this paper, arises if we suppose that \ may have any desired 

 positive value, within reason, and that 5 is very large, so that x^ is 



small and 3^ is large. Vfe shall assume further that -ii- <«' 1, as is 



Hl (since M. varies from X to X|). Under these simplifying conditions 

 ^1 

 it is possible to derive an approxi.(nation to the integral (31) (c) but in a 



somewhat indirect way, much too long to reproduce here in detail. Ue find 



that: 



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