493 



., J-t, 



1 ,b 



-D 

 ,a ^6 



^2 - 



t ax fly 



f / dx dy 



f,"^ dx dy 



(13) 



J-. J-b 



Using the concept of a jeneralised mean strtss(3) to cover the case when the plate is not 



ing 

 stretching, then the potential "nergy of plate stretching is given Dy use of (8) as: 



,S ^w rU '■^ 



T d S„ 



T Aj^ d W 



T B d U - 



T C 3 V 



(11) 



in which T may he regardei as i function of time and is oqu:;l to T at any time when the plate is 

 stretchi ng. 



Similarly, the potential energy of puU-ln is by use of (ll) : 



T' d S, 



T' B d U + 



Jo 



T- C^ d V 



(15) 



where T' may be regarded as a function of tire and is eqjal to T at any time when pull-in is occurring. 

 Fuller consideration of T and T' is given later (paragraph A. 5). 

 Finally, if the anplied impulsive pressure is of the form: 



p(t, X, y) = P(t) f^(x, y) 

 then the potential energy of this pressure can be written as: 



r 



-b Jo 



p -- dt dx dy = - A 

 dt ° 



r 



p(t) d w 



(16) 



(17) 



whe re : 



fo(x. y) fi(x> y) dx dy 



(18) 



Hence, we havo finally from (l2j^ (l.H)_, (15) and (l7) that: 

 Total K.E. = -^ ph [ A^ i^ + B^ U^ + C, V2 ] 



Total P.E. = A 



U 

 TW dW - B^ I (T - T') d U 

 -'0 



(T - T') d V - A I P(t) d W 



(19) 



(20) 



A.U 



