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APPENDIX D 
Deformation of reotangular plastic panel by suddenly applied pressure 
In fig..Di & rectangular panel of 
plating of sides 2a, 2b with axis 
Ox, Oy parallel to the sides and 
having origin at 0, the plate centre, 
: is subjected to a suddenly ace 
F* pacos 2 cos ty pressure distribution p,cos Fa cos Lg 
If now 
h = plate thickness 
8, = uniform membrane stress 
J? = mass density of plate 
t = time 
Wt) = deflection of point (x,y) in 
plate at time t 
W(t) = central deflection at time t 
Fig. 1 - Rectangular plate subjected 
to impulsive pressure 
distribution 
then for deflections which are relatively small compared with the small span 
(one sixth or less), the equation of motion of the plate is 
2 2 2 
t Uz... 4Y dw t) Pa t) 
pa ome . p,cos 5 cos st + 8,h | et eiye Bp 60g. ada. (044) 
If the plate is fixed around the periphery the solution of equation i is 
wt) = w,(t) cos iL cos Le coe coe coe ooo coe coe coo (D2) 
2. 8 ~* 
viore ph dim(id - », . thi f1., thee We ke 
Subject to the initial conditions that the plate is flat end at rest, the 
solution of equation D3 is 
Wot) mR 2\(1) = comet)” aes Lees jmeny, pe occ) «ccm gumae einen 
where K = we abe (D5) 
= Te.h a+b= coo coe coe ooo eee ere eee 
ote] £3} dae! See) bee) Jee) ea URE een! 
The final solution given by equations D2, Dh, D5 and Dé Will be valid so long 
as the plate is stretching, which is true up to t =fifx. At this instant, 
Wo(t) = Wo = K and the plate is at rest everywhere with no velocity and has 
a deflected shape given by 
weiK cos ‘= cos LY eco eco coo eee eee eee eee (D7) 
