384 



where 



MCk,tO« P»l(,c,^03- CKx^xJ^-x. 



(15) 



This result is obvious if the pressure is regarded as a superposition of 

 impulses . 



The first approximations to the meridional and circumferential 

 strains, C.-^ and i^, respectively, are given as a function of position and 

 time by 



«. = t^ ' -^^WCx.l:), (16) 



where 





(17) 



These are notliing laore than Eq. 3^ "f ^"■'rl' T , recast in nondijnensicnal fcrra. 



The case of interest here, impiilsive loading of the plate by an 

 underwater explosion wave, involves an initial velocity distribution of 

 the form 



0^ (WtcV 



(18) 



the particular value of 3/4 for _x^ being of greatest interest. Here, x is 

 equal to the radius r divided by the distance H between the plate and the 

 center of the explosive charge. In Sec. n of this Fart the deter.nination 

 of the values of £^and_^on a physical basis vill tie discussed. In the 



67 



