73 
Work done by pressure 
Dhe If the motion is produced by some given pressure distribution 
p(t, x, y) which varies in a known manner with t, x, y, the work W done 
by this pressure is 
W = | \ DGber ps y) #( x,y) Stet) Gydxdtin tem nueciohn ieee (14) 
0 -a -b 
which may be written 
W = H+) | at ai) Bete dels hes a) ee eee (D15) 
oO 
a 
where Kt) = p(t, x,y) f( x, y) dydx Oi OCiee COC, OIC (116) 
-a -b 
D5. For a given pressure p and any assumed form for the deforming plate 
such as equation D1i0, the function Kt) is mown, Hence, equating the 
combined plastic and kinetic energy to the work done, that is 
We O p+ (ay 
gives from equations Di1, Di3 and D15 an equation of the form 
2 2 
su fede + £ew(t) = (x9 Saal at. Soo ect (D17) 
t dt 
Co) 
256 
where M = 3 f hab 
eee e@eo ooo eoe eee coe (m8) 
x = 128 (2 + 2) ayn 
The energy equation Di7 can be differentiated with respect to time to give 
2 
tel + kwy(t) = Kt) eb, obs. - aide: SOCOM (119) 
Thus the assumptions of proportional motion and a uniform membrane stress 
in the plate lead to a motion analogous to that of mass M on a spring of 
stiffness k subject to a dynamic load KX t). 
