)»-,''> ,i.^ f rv_C.) 





321 



(27) 



(28) 



It is now apparent that in the first approximation the constant t = ■\)o'^/p 

 is the velocity of transverse plastic waves. 



If the solution of Eq, (2?) be known, the solution of Eq, (28) 



can be given in terms of it as follows 



where r (t) is a nonzero value of r at which the radial displacement van- 

 ishes. In the case of an infinite plate r*(j:)^eo . The first approxima- 

 tion to the strains is given as an immediate corollary of Eq, (29) by 



-^-1:'r'(«..^-p'. 



Since the integrand of Eq, (30) is always positive for every real solution 

 of Eq, (27)» the strains must always be greatest at rs o , the center. 



It should be noted that in this approximation the time enters ex- 

 plicitly only into Eq, (27)^givir^ the profile z*'^ , This fact means that 

 the membrane at a given instant of time t has the same radial-displacement 

 distribution as a raanbrane statically constrained to the profile z. * C'^t); 

 with no tangential traction. An equivalent statement would be that tangen- 

 tial propagation effects occur with essentially infinite velocity. 



12 



