_ 9 _ 263 



respectively, together with the pressure-time curves in the water at the "reloading front", (the 

 surface of the reconstituted layer) and at the surface of the plate. The method of obtaining 

 these curves is fairly straightforward, the qu-jntity p v. 35 represents the rate at which momentum 



''c " 3T 3T '^''^'■^'o'''' represents the pressure at the reloading 

 . _ um). The pressure at the plate Is obtained from this simply 



by subtracting x '^-X (to correct for the" pressure drop in the column of water of length x which Is 



dt^ J. 



being accelerated). Actually -^ is nejative so that the pressure at the plate is higher then that 



df^ 

 at the reloading front. For a = the pressure at the plate must be nearly equal to the pressure 



of the spring = p o} y. Since the plate Is stretching plastically, we have to stop the integration 

 as soon as y reaches a maximum; thereafter, instead of equstlon (19) we have y = constant, v^ and x 

 being still related to t by equations (8) and (18). By equation (s) v^. is given as a function of x, 

 and by equation (13) t cin then be found in terms of x. Wc can thus calculate the further grcwth 

 of the reloading front and the pressure at it is given by the expression p^j v^ ^ . After the 

 plate comes to rest, the pressure at it and at the reloading front must be equal, so that we get a 

 discontinuous drop in the pressure at the plate at the maximum of y. The pressure at the reloading 

 front remains continuous but there is a jump in its time-derivative. Such discontinuities are 

 common In plastic plate theory, and need not cause any alarm. In^hls case they have been caused 

 by the fact that while ^^f is zero at the m3< imum of y, there Is a finite jump in dy to zero, 



dr 



In any case, these discont inutles would be "rounded off" by the elastic recovery that always occurs, 



so that 2j! would change continuously, 

 dt^ 



TABLE 2. 



Final deflections of plate, and energy balance, 

 for various val ues of S. 



y™ " Maximum deflection of plate. 



t_ = Tiro at which maximum occurs, 

 in - 



X = Thicknc-ss of reconstituted layer at this instant. 



(a) 



Ener gy bal.incc. 



The fractions of ihs tctal snergy filling on the plate, that appears as kinetic energy 

 and that is reflected away into the witer before cavitation follow at once from Taylor's work(l). 

 The remaininj energy is ccnscrtsd into kinetic energy of the water. The energy absorbed by the 

 plate can be Inferred from th-- st-fi-by-step solution, in non-d imf.-nsional jnits this as a fraction 



of the .. 



