397 



The maximviin value of h^-'' ' (x, t*) occurs at x = and T = 



tC5/2) = Oo513 and has a value h^^/S) = h^5/2)/o ^(5/2)1 . 0.1253. 

 m m I m / 



(^) 

 It is perhaps interesting to note that the function y {x, "V) 



giving the plate profile as a function of time approaches a nonvanishing 



constant value for V = 1/2 as the tin-e becomes infinite/ but approaches 



zero for 3^ = 3/2, 5/2. This behavior is presumably related to the fact 



(V) p.-z^ 



that the velocity distribution given by g = (1 + x*^) corresponds 



to an infinite kinetic energy for 7/= 1/2 ana to a finite kinetic energy 



for V>l/2. Also it may be noted that the central part of the plate 



remains concave dovmward for all time in the case of V= 1/2 whereas it 



becomes convex dovmward after some time in the case of V = 3/2, 5/2. 



These remarks apply only to a membrane under constant tension and are 



perhaps somev/hat acadanic on that account. A real material is subject 



to stress relief when the rate of strain changes sign; consequently, the 



behavior of the functions y (x, Y) and h^ ' {:x.,^) is significant 



only in the interval < -^^y of the reduced time where Tf^^ ^ 



is the value of the reduced ti/ne at which the rate of strfdn first changes 



sign at any point on the plate. At a r iven point x on the plate, the rate 



of strain changes sign at a value of 2!gi"ven by ^ h^ ' (x>'£')/«' '^ = 0, 



It will be stated but not proved here that the rate of strain changes sign 



first at the center x = (this behavior is illustrated in the tables); 



consequently ti^^^ is given by d h^"*^^ (O, Y)/^ T = 0. Thus the time 

 c 



of j-aximum central strain is equal to the time at which the rate of strain 

 first changes sign anin^here, or, in short, t ^ '^ i * 



80 



