331 



motion and Eq, (5) is approached in the latter phase. A theory based upon 

 Eq. (4) will give final deflections which in general are too s;iiall, since 

 the damping term /o^o ^^/dt fades away for times greater than ©^ and 

 the second term of iq, (5), by increasing the effective inertia of the 

 plate, retards its deceleration in the later phase of the motion. 



The ccraplete deflection e quation, obtained by substituting 

 £q. (3) into Eq, (2), has the form 



dt* ©, At ®i '- <*• »j. 



This is an integro-differential difference equation, which can be solved 



by the method of Laplace transforms. The initial condition subject to which 



Eq, (6) is to be solved is 2.^6tj«o for 6 4o , 



3. Deflection of Circular Diaphragn by an Exponential Wave . 



It has been found that the initial pressure pulse im;riediately fol- 

 lowing the shock front of an underwater explosion wave has a pressure-time 

 curve >rtiich is closely approximated by the exponential formula 



it)* V'w.e-'/** , (7) 



where p^ is the peak pressure. It is therefore a matter of interest to in- 

 vestigate the solution of Eq, (6) for an aoqponential wave. In discussing 

 the solution of Eq, (6), we shall neglect the change in phase of the ex- 

 plosion wave due to the plate deflection. We will f irst consider the case 

 of an infinite baffle. 



22 



