170 



total effect is simply to bring about a simple radial velocity distribution 

 and to afford a means of transferring the kinetic energy lost at the bending 

 wave into kinetic energy of radial motion in the flat central region. 

 Kinetic energy of thinning is supposedly very tiny and is neglected. 



As regards the properties of the metal of which the diaphragm is 

 composed, we shall suppose the following. Because we are here dealing with 

 finite deformations and strains, all purely elastic effects, other than those 

 of the initial stress wave which have already been mentioned, would seem to 

 be negligible. Consequently we shall suppose that except for the initial 

 elastic action, we are dealing with an ideal incompressible plastic material, 

 with a zero elastic strain range. This is consistent of course with the 

 surmise of the initial very high speed elastic stress wave and the "freezing " 

 of the material when it unloads as the bending vrave passes by. Furthermore, 

 we shall suppose that there are no strain rate effects affecting the plastic 

 flow. \'}e shall suppose, therefore, that the data obtained from a tensile 

 test of the diaphragm material in which the tensile stress is exhibited as 

 a definite function of the natural elongational strain, are, in combination 

 with general laws of plastic flow, sufficient to specify the plastic properties 

 of the material. 



Naturally the mathematical statement of the problem depends to a 

 certain extent upon the choice of the type of plasticity theorv. although 

 in any case an apparently consistent loi luxation may result. As a matter 

 of fact, for the type of motion herein investigated, no differences arise 

 whether one applies the plastic deformation type of theory, or the plastic 

 flow theory of plasticity.* The point of view of the latter is taken in this article. 



*For a discussion of these basically different theories see W. Prager, 

 "Theory of Plastic Flow vs. Theory of Plastic Deformation", J. App. Phys., 12 

 540 (June, 1948). 



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