492 



To the first order in u and v and to the second order in w the increase in area of the orijinal 

 unsupported plate area is: 

 a b 



3 u + 



|l . ifl^l . if|j«l dxdy 



■J "1 



A. W"^ - B, U - C, V 



(8) 



Where 



[3x j 



3 '. 



y J 



dx dy 



-b 

 ■a 



[ fj (- a.y) - fj (a.y) ] dy 



[ fj (x.- B) - f^ (x,b) ] dx 



(9) 



■We may note that: 



A^ ^ 



Bj >. 



C^ 5- 



(10) 



the first being obvious from the expression for A , while the latter two follow from the boundary 

 conditions (5) and (6), 



The total area of pull-in ;t edges is given by integration round the edges as: 

 ,b rb 



. _D -I -a 



i-a 



U fj (-a,y) dy 



- V f (x,b) dx + 



V f (x, -b) dx 



whence from (9): 



Sj = B^ U + C^ V 



(11) 



J. 3 En e rgy exprei 



The originally unsupported area of plats nay Be regarded as a closed system subjected to a 

 lateral loao and a tensile fores round its eJoes. 



The tctal kinetic energy of the system is then, using (1), (2) ana (3), 

 (-b 



i*^ ♦ u^ + C^) dx dy = -J ph (AjW^ + Bjil^ + C^V^) (12) 



J -a J-b 



I /Oh 



where 



