13 - 



497 



We have therefore to consider the rotion as compoundea of successive stages In which the 

 plate may be either (i) stretching and pulling in at edges, or (2) inextensional but pulling in at 

 edges, or (3) at rest. We have throughout considered the condition of rest as a type of motion 

 because, while trivial if it forms the final stage, it could in fact be an intermediate stage between 

 stages of actual motion in the case where the applied load is of oscillating magnitude, i.e., the 

 plate could cease moving when the load was decreasing and then commence to move again when the lead 

 had subsequently increased t: a sufficient magnitude. We can now write down the relevant equations 

 which hold in the aifferent stages. 



A. 8 Equations governing each type of motio n . 



TYPE I.. Plate stretching and pjlling-in at edges . 

 The physical conditions are: 



=0 > ° 



Sj > 



Whence from (32) and (33): 



T = T 

 T- = T 



(43) 



M 



1 

 Thence from (21) and (27): 



ph A^ w + A^ T^ w = A^ P(t) (»5) 



(*«) 



1 ph 



defining a new parameter Y. 



We thus have four equations for tne four unl<nowns T, T", w and S and thence S and S are 

 given by (29). It mhy be noted for future use from (29) nnd (46) that: 



S^ = (5 - Y) (U7) 



during this type of motion. The solution of the preceding equations will be invalid if it violates 

 the condit ions (13). 



TYPE 1 1 . Plate inextensional but pulling-in at edg ss. 



The physical conditions imply in view of (32) and (33) that: 



> 



1 

 T < T. 



^0 " ° 



T- . T^ 



(«8) 



(M) 



whence the equations of motion (21) and (27) become: 



ph Aj W + A^ T W = A^ P(t) (50) 



Ph '\ = Aj (T - T^; (51) 



and equations (29) and (1*9) give: 



S = A^ W W = S^ (52) 



We thus . 



