342 



the position it occupied at the time t,^ when the center point reached its 



maJcLmum. 



We remark here that an accxorate description of the early stage 



of the motion requires the retention of a large number of terms in the 



series (5). The approximate solution to be used in Sec. 3, in which only 



two terms are retained, while adequate for the later phase of the motion, 



is not very accurate for times less than, say, '.3 of the total time of 



deflection, 



3. Solution of Equation of Motion Using Two Terms in Bessel Function Expan - 

 sion of the Deflection. Presentation of Nvunerical Results 



When the Bessel function series (8) is approximated by the first 



two terms, the deflection of the diaphragm takes the form, 



:z:= p^& fC>,-t^, (20) 



vrtiere x « r/Ro ^ 



and ^ 



■* ^ C%- ^>.')t %i.j;Cw>;<)]9U*), 



pa-o «- uJ,* " ■ ' ' u?: 



'« "^x 



when the free field pressure of the explosion wave is given by 



^o6fc)= t'-e-*/* (21) 



Supplementary data concerning Eq, (20) are presented in Appendix C. The fre- 

 quency cOj is the i-th frequency of the free diaphragn and uX is the ^ -th 

 frequency of the water loaded diaphragm; A^, is the thickness and p is the 

 density of the diaphragm. 



33 



