37 



51 



0.25 



1.4 1.6 1.8 2.0 2.2 



Figure 21 - Curves for a Diaphragm Loaded Impulsively 



For further explanation, see the text and the note under Figure 20. 



^^ M +M, 



JF.dt = 



M 



M + Ml 



[53] 



Thus the Initial velocity soon becomes reduced In the ratio M/(M + Mi) as the 

 loading by the liquid comes Into play. 



The corresponding curves for the velocity dzg/dt and for z^ as ob- 

 tained from the approximate difference-differential equation, for v^ = ^ and 

 pa/m= 12.5, are shown In Figure 21; the horizontal line represents Vf. The 

 curves and lines happen to be exact copies of those In Figure 20. The rapid 

 approach to the non-compresslve velocity is again evident. 



Solutions for either of these two simple cases could be utilized to 

 construct by addition the general solution of Equation [48], provided * Is 

 known as well as F,. The case first discussed corresponds to Heavlslde's 

 unit function. 



MOTION OF A PLATE OR DIAPHRAGM CONSTRAINED ONLY AT THE EDGE 



The accurate treatment of a plate that is not constrained as to 

 shape presents a very difficult problem even on the hydrodynamlc side, apart 

 from all the difficulties that arise from the varying elastic and plastic 



