294 Lecture 15 
SQ 0-1 Roughness steps 
0-05 ” 
Smooth 
uw 
o 
Maximum sound level db rel “0002 dynes/cm? 
50 00 
Velocity ft/sec 
Fig. 15.17. Radiated sound from typical rigid submarine measured at 100 yards for various surface 
roughnesses. 
over-all dilatory mode, i.e., that mode in which the whole shell either expands 
or contracts at the same time. Simple calculations, however, indicate that the 
damping in this mode would be overcritical and it cannot therefore be excited. 
The localized panel vibrations must now be considered, and since the pos- 
sible modes of vibration are difficult to define, a panel 30 by 24 by 11 in., as- 
sumed to be flat and vibrating in a fundamental mode, is used to give some 
indication of the possible radiation. The undamped natural frequency of such a 
panel is 398 cps if simple supports are assumed at the four edges and 760 cps 
if full fixation is assumed. As mentioned earlier, Mangiarotty [10] has both 
calculated and measured the damping ratio on one side of such a panel in air 
and, if his figures are used, the damping ratio of the panel in water is of the 
order of 0.13. If the submarine is assumedto be traveling at 45 ft/sec (25 knots) 
and the boundary-layer thickness to be 1 ft, the power spectral density at 400 
cps is, at the most, 4.8: i@=8 (psi)’/cps, and the correlation area of fluctuating 
pressures of this frequency is approximately 0.25 in? When subjected to this 
field, the panel will vibrate with an rms amplitude of 4.3- 10~° in. in the funda- 
mental mode simply supported at four edges. Ifthe energy from such a vibration 
is assumed to be radiated evenly over one hemisphere, the sound pressure level 
at 100 yards is approximately 70 db (re 0.0002 d/cm?). 
If all such panels vibrate randomly with respect to each other, then for a 
typical submarine the radiated level from the whole structure could be 90 to 100 
db (re 0.0002 d/cm’) in the case considered and is of the order of level actually 
observed. 
In practice, the panels will be neither fully fixed nor simply supported and 
their disposition will in any case depend on the details of attachment to frames, 
