343 



The nondiagonal terms Q^,Cc "t j) in the secular determinant^^ 

 have a small effect on the fiindamental frequency and the first overtone. 

 This point is discussed in Appendix C. Also C|^and C^, are much smaller 

 than C|, or C^x. • These results mean that the hydrodynamic interac- 

 tion between the two principal modes of vibration is small, and that the 

 nondiagonal terms Sj' • could have been neglected without large error (at 

 least in the two-mode treatment). 



The maxLmimi central deflection x,^ is found by methods desciribed 

 at the end of Sec, 2, It is found mathematically that the part of the dia- 

 phragn midway between the center and the periphery reaches its msiximum at a 

 time about 20% greater than tJ^y^ , the time of maximum central deflection. 

 This is not important because of reasons mentioned in Sec, 2» 



In the presentation of numerical results, appropriate dimensionless 

 variables are chosen. Accordingly, in Tables I-A, II-A, UI-A, and IV-A, 



^o'^H^ and \Z TTS ST^ *r® presented as functions of iAj,0 for four 



values of X = Rof«»/a<,j? • These tables allow us to find the time of deflec- 

 tion 't ^ and the maximxm central deflection Zu» if the diaphragm jjarameters, 

 ^p t ^o » f » ^'^^ ^o * *^® shock-wave characteristics, p^ and O , and the 

 density f^ of water sure given. 



The diaphragn profiles, z/r^^ vs, r/Rp , are given as functions 

 of the reduced time t/t^ for several values of */<Og& and A in Tables 

 I-B, I-C, I-D, II-B, Il-C, II-D, III-B, III-G, III-D, IV-B, IV-C, and IV-D, 

 The appropriate values of z^^ and -b^ are found by consulting the tables 

 mentioned in the previous paragraph. The tables considered thus far are 

 grouped according to values of X , the tables having a Roman numeral I 



3k 



