186 
IV. EFFECTS OF PRESSURE WAVES 26 
7. ON A FREE PLATE 
3. the target is elastically connected throughout and does not break loose 
from the water. 
The point of the last proviso lies in the fact that, since the target must 
be negatively accelerated during the later stages, negative pressures may occur in 
the water and cavitation may result. 
It appears to follow from this analysis that if the skin of a ship were 
plane and held in place only by air pressure, the explosion of 300 pounds of TNT 20 
feet from the ship would merely shift its skin inward an inch or so and leave it at 
rest. That damage actually results from such an explosion must be due either to the 
presence of stiff bracing or, perhaps, to cavitation in the water, so that the nega- 
tive pressure during later stages fails to arrest the rapid inward motion of the skin. 
The case of oblique incidence of the waves is much more complicated than 
that of normal incidence and will not be considered here. It involves questions as 
to bending of the plate. 
The next case studied will be designed to throw light on the effect to be 
expected from bracing. 
IV. EFFECTS OF PRESSURE WAVES 
8. ELASTICALLY SUPPORTED PLATE 
8. TARGET, A THIN UNIFORM PLATE WITH ELASTIC SUPPORT 
Let the thin plate just described be held in position by springs or an 
equivalent support, with water on one side and vacuum or air on the other. The 
strength of the springs cen most conveniently be specified by assigning the value 
of the frequency 4, with which the plate would vibrate, moving one-dimensionally 
in a direction perpendicular to its faces, if the water were absent. As before, we 
assume a plene pressure wave to fall at normal incidence upon the plete. Then, as 
the equation of motion of the plete, we may write in place of [9] or [10], 
mig + 4n2y2 mz = p + p" 
a + pe 52 + 4n? v2 mx = 2p (11] 
Thus, if pc = O and p = 0, the solution is Asin(27v,t +a), representing an oscil- 
lation at frequency %. 
The left-hand member of Equation [11] is of the type encountered in deal- 
ing with linearly damped harmonic oscillations. The equation mey be rewritten in a 
convenient generalized form thus: 
dx dz 
— + —+ ur 
dees eae Oe 
2p 
= 12] 
