A History of Research and a Review of Recent Developments

Concentrated external loads on underwater structures 101
Figure 5.7 Underwater cylinder subjected to pressure pulse (from Haxton and
Haywood, ref. 5.9).
which the wave path length must be measured around the surface of the cylinder.
The following equations were derived for p 1:
(5.18)
T is the decay time constant, c is the velocity of sound in water, e n=2 when n=0
and e n=1 when n=1 where n is the circumferential modal index for the deflections
of the cylinder wall.
A long time before analytical work of the above type was attempted, the
problems of close-in explosions had been discussed by Christopherson [4.6].
In 1945 no satisfactory measurements had been made of the pressure inside
a gas bubble, and when an underwater target was very near the source of
the explosion there was no general theory of loading. There had been tests
during the Second World War at the UK Road Research Laboratory which
suggested that a charge of TNT of weight W lb in contact with a lightly
reinforced concrete slab of thickness t ft underwater would produce heavy