189 
29 IV. EFFECTS OF PRESSURE WAVES 
8. ELASTICALLY SUPPORTED PLATE 
The largest value, 2,,/x, = 4, occurs when n= 8 = 0, i.e., for no damping 
and for a steady pressure beginning suddenly at a given moment. The value of 1,,/z, 
decreases with decrease in the natural frequency of the plate (decrease inyu,), or 
with decrease in the length of the wave (increase ina); either of these changes 
makes the effective time of action of the wave less adequate for the production of 
a maximum effect. In an actual case the plate would probably be heavily overdamped 
by the radiation of waves into the water. Thus for a steel plate 1 inch thick in 
contact with sea water, y = 3900 (i.e., 68.2 x 144 x 12/2 x 7.8 x 1.94), so that for 
vy < 600 cycles per second 8 = y/u, = y/2mpy,>1 and overdamping exists. The plate is 
not loaded by the water, however; its frequency of oscillation v is modified by con- 
tact with the water only because of the damping action. 
For the conclusions of this section to be valid, the lateral dimensions of 
the plate must be large as compared with the wave length of the compressive waves 
emitted into the water. 
Ee EFFECTS OF PRESSURE WAVES 
9. EFFECTS ON A SHIP 
9. EFFECTS ON A SHIP 
Oscillations of the type just described might correspond roughly to oscil- 
lations of a ship in which one of its sides moves in and out as a whole, against the 
elasticity of the bulkheads. The natural frequency for such oscillations should be 
of the order of 100, corresponding to wy = 600; but, with a weight of 50 pounds per 
square foot in the skin, y = 3200 (i.e., 68.2 x 144 x 32.2/2 x 50), so that B= y/o 
= 5. Thus the oscillations should be heavily overdamped. For a pressure wave with 
oa = 1200, as in practical cases, n = @/y,) = 2. A glance at Figure 13 shows that 
x,,/%, is small, the maximum displacement being much less than the static displacement 
due to the maximum pressure in the wave. 
The same mathematical theory should be applicable to all modes of oscilla- 
tion of a ship's side. It is only necessary to substitute in the formulas suitable 
values of the damping constant y and of the undamped frequency vy). In all other 
cases than that of the infinite plane plate, however, v, is altered as if the vibrat- 
ing body were loaded to a certain extent by the water. As a rough rule, it may be 
said that damping by emission of compressive waves will be large or small according 
as the lateral dimensions of the vibrating segment of the ship are large or small as 
compared with the wave length in the water. Thus, the commonly studied oscillations 
of a single panel, st a frequency of perhaps 10, corresponding to a wave length of 
500 feet, should be only slightly damped, as observed, 
It should be remarked, however, that the time required for the propagation 
of elastic impulses along the bulkheads should also be taken into consideration. 
