490 - * - 



Mathematical theory of pull-in at edges. 

 A.1 Nomenclature. 



t = time 



x,y = rectangular co-ordinates in plane of plate. 



2a, 2> = lengths of sides of unsupported plate area. 



w = w(t) f, (x,y) = deflection at point of plate. 



U(t) f^ (x.y) 

 v(t) fj (x,y) 



displacement in plane of plate. 



h = thickness of plate. 



p = mass density of plate. 



S = increase of plate area due to stretching, 

 c 



5 = increase of plate area due to pull-in. 



S. = final maximu'n V5\ue of S. 

 m 



S' = final maximum value cf S 

 m 1 



W = final mean deflection = maximum value cf W. 

 m 



W , IK = borderline values of W for nc strstching in the two loading cases consiosred 



p(t,x,y) = P(t) f (x,y) = applied impulsive pressure. 



V = initial mean velocity due to instantaneous impulse. 



p = magnitude of P(t) when load is suddenly applied and maintained constant. 



T = generalised uniform membrane tensior> ptr unit length in pl.<te. 



T" = generalises uniform tension c^r unit l:-ruth rem: eages of unsupported 

 Plate area.- 



T = constant value of T when plat-, is stretching. 



T = constant value cf T" wr.en ejges are puUing-in. 



A = areal strain at centre of slate. 







(AJ = final strain at centre cf plate. 



e = at 



, \ = Valuer of'' and t at cmr:;ncemcnt o' pl-.te ctretching. 



c 



6 . t = values at 9 and t at cessation of plate stretching. 

 A is defined oy equation (18). 



