19 



1.0 



0.9 



0.8 



0.7 



0.6 

 yi,2 

 0.5 



0.4 



0.3 



0.2 



0.1 



10 20 30 40 50 



Figure ^ - Parameters Relating to the Incidence 

 of an Exponential Wave on a Plate 



d}z 



2mp 



'■^Vm. I -at 



pc — am \ 



+ ^e 



pet • 



[4: 



df pc 



where e is the Napierian base; see TMB Report U80 (10), page 25. 



From this equation it is found that the load pressure vanishes at 

 the time 



1 Inx 



t = r„ = 



x = ^ 

 a X — 1 ' am 



[5a. b] 



where In denotes the natural logarlthim. At this time the Incident pressure 

 as given by Equation [2], which would be the actual pressure in the water if 

 the plate were not present, has decreased to 



J 



1 -I 



Pi = Pm^' ' [6] 



and the velocity of the plate has attained its maximum value of magnitude 



v„ = 2 



^ olii 



1 -X 



pc 



[?] 



See TMB Report U89 (n ), page 7. 



In Figure U there are shown plots of aT^or In x/(x - 1 ), and of 

 the factor x ^ ' " or pcv„/2p^ as functions of i. 



The parameter x defined by Equation [5b] can be interpreted as the 

 ratio of two time constants, as follows: 



