364 



.t-tf 



o o 



The diaphragm has a radius Rq. thickness a^, and is constructed of material 

 of density D and yield stress 0^ , At time "t the diaphragn is deflected an 

 amount z at a distance r from the center, p^ is the density of water, R^a?^ 

 is the velocity of transverse plastic waves in the free (unloaded) plate. 



In solving Eqo (22) we replace the operator by unity as a first 

 approximation. If the diaphragm moves as a piston^this replacement gives 

 the correct water loading at the center, but gives too large a water loading 

 some distance from the center. We now have 



Taking the Laplace trans foirm of both sides we get 



(23) 



u,Hl^:^)L-u,/i^f^(^A_.L.). )^^, (24) 



where L = Sq x Cx,tr; e"*^^ d t^ 



andLp = Sr^oCt)e-'*'^at , 



The solution of Eq, (24) is 



I ^ -L. Jr£ fi- iZkCiii2L)N (25) 



where k = (»+>)'* to /(t>o • Inverting the Laplace transform we obtain immedi 



ately the solution of Eq, (23) 



C-cao 



51 



