498 - '' 



We thus have six equations given by (49), (50), (5t) and (52) for the six unknowns T, T*, 



'0 



W S S and S . The equations are only valid so long as the conditions (48) are satisfied. 

 ' ' 1 



From (30), (39) and (49) we note that: 



A^w^ ^ 



*3 * 



4> * *3 ^ 



so that during Type II motion we have by virtue of (no) that: 



T > 

 Also from (51) and (52): 



^? '^° - ^' = r-s" 



so that (48) may be replaced by: 

 Sj > 

 S S Y 

 For future use wo also note, from (5l), (52), (53) and (39), that 



pt\ S 



1 + 





A W 

 ph A^ i^ ♦ -i— (A^ P(t) - T^ A W) 



*2 



(53) 



(54) 



(55) 



(56) 



(57) 



TYPE II I. Plate at rest. 



The physical conditions are: 



(58) 



(59) 



Thus we have six equations for the six unknowns T, T', W, S , S and 5 . Also from (58), 

 (32) and (33) the state of rest will only be possible so long as: 



T- ,< T^ 



T ^ T 







whence from (59) and (34) the plate can remain at rest provided: 



"0 ''(') ■? ^ '1 ** 



(60) 



(61) 



A,q The cne rgy equation . 



Having shown that, with our assumptions of initial rest and pressure always positive, the motion 

 is compounded of stages of Type l. Type 11 or rest in which S and S are either constant or increasing, 

 it follows that the energy absorbed in the plate at any stage is: 



T d 



