339 



The elimination of )? between Eqs, (1) and (2) with the introduc- 

 tion of the dimensionless variable % ~ y R© yields the result 



L^^'^^j ^*- -7^ s>x^'' j^y = -"^^^^ (3) 



where 



and O is an integral operator defined hj 



The quantity uJ^ is equal to the reciprocal of the time required for a 

 transverse plastic wave to travel the radius of the plate. The parameter 

 determines the magnitude of the inertial effect of the surrounding water* 



Eq. (3) is an integro-differential equation whose solution is sub- 

 ject to the follo%dng initial and boundary conditions: 



In solving Eq, (3) under the conditions (4), it is convenient to 



expand z in a series of Bessel functions 



CO 



^(x,t)= 2: xtCt? J«(k,'x), (5) 



where J^^u.) is the zero order Bessel function of u and kj,'is the i-th zero 

 of 3^C^) • The details of the solution are given in Appaidis B. The solu- 

 tion in the case of an e Jtponential wave 



pe Ce)= ^^e.-*"/** ,6^0, (6) 



is 



30 



