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■without doubt be so unwieldy as to necessitate the introduction of radical 

 simplifying approximations. Hence it seems desirable to attack the 

 theoretical problem of analysis of this motion by the artifice of replacing 

 the actual mechanical system by a fictitious one in which are incorporated 

 certain constraints which do no work and which operate to simplify the 

 equations of motion. At the same tLme this idealized model must be so chosen 

 that i.TDst of the main qualitative features of the actual diaphragm motiOTi, as 

 described or surmiaed in the foregoing, are preserved. In this way it is 

 hoped that the motion of the model when found agrees closely enough with 

 that of the real system so that certain quantities, such as thickness 

 distribution, central deflection, total strain, and tine of deformation do 

 not differ too much in magnitude from their actually observed values « 



Consider, therefore, an ideal thin metal circular diaphragm of 

 uniform thickness h, and radius a, held rigidly at its periphery. Initially, 

 suppose that the diaphragm material has a uniform velocity component v normal 

 to its initial plane. Because in the actual diaphragm, an elastic wave may 

 then quicld.y set the .-.laterial in motion radially, we shall suppose in 

 addition that in the ideal diaphragm, there may be an initial linear radial 

 velocity distribution superimposed on the uniform normal velocity v.* 

 Estimates of the magnitude of this effect will be made in a later section. 



At any later instant, the situation is considered to be as follows. 

 A plastic bending wave has traveled inward some distance from the edge. In 

 connection with this vfave, vte shall suppose that its shape is as shown in 

 Figure 2j that is, the bending Wave represents a true discontinuity in the 



^Tl-iis initial elastic stress phase has been investigated, but not published 

 to the writer's knowledge, by F. 3ohinenblust . He indicated orally some years 

 ago to the -/n-iter that the circumferential stress component rises very 

 quickly behind the elastic-stress wave in which the only non-vanishing stress 

 component is the principal radial stress, 



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