491 



Dots are used to denote differentiation with respect to time t, while the four subsidiary 

 symbols 8, y, e, and 9', which are used only temporarily, are defined where they occur. 



A. 2 



Exp ressions /or surface increases . 



The forms assumed for the displacements are: 

 w ? W(t) fj (x,y) 



U(t) f^ (x,y) 



V = V(t) fj (x,y) 



(1) 

 (2) 

 (3) 



where U, v and W are to be determined, while specific forms for f , f, and f, will be assumed later. 



We note for present use that f^, f^. f ^ must satisfy the following boundary conditions: 



(u) 



f, = along edges x = ± a 

 and y = ± b 



f, = along edges y = ± b 

 f, -? along edge x = a 



f, ^ C along efge x = -a 



f, = along edges x = + a 



t ^ 4 along edge y = b 



f, ^ along edge y = -b 



(5) 



(6) 



The inequalities in (5) and (6) merely specify without loss of generality the signs of U and 

 V (namely positive) In the light of the physical condition that the plate is pulling-ln at edges. 

 Also without loss of generality we can specify: 



1 

 uab 



a A) 



f dx dy = 1 



(7) 



so that W Is identified with the mean deflection. 



To 



