69 
APPENDIX C 
Effects of pressure pulse normally inoident on a plane plate 
Ci. FigeCi shows the pressure 
pulse normally incident on unit 
area of an infinite plate. Let 
t+ = time measured from the first 
Onan arrival of the pulse at the 
INCIDENT PULSE plate 
x = displacement of the plate 
k resistance to motion for 
kx unit area per unit 
x displacement 
Pp, = pressure in incident pulse 
P. = pressure in reflected pulse 
P = pressure on plate 
ae P, = maximum pressure in pulse 
u, = particle velocity due to 
the incident pulse in 
water touching the plate 
particle velocity due to 
the reflected pulse in 
u 
Fig.C1 = Pressure pulse incident on water touching the plate 
unit area of infinite plate f mass density of water 
te) 
n 
velocity of sound in water 
mass of plate per unit 
area of surface 
The plate can reasonably be assumed thin enough to neglect elastic waves 
within it and can be treated as moving bodily with velocity dx/dt The 
particle velocities are taken in the direction of travel of the respective 
waves. The total particle velocity of the water in the x direction is 
therefore u,-u,- Assuming in the first instance that the plate and water 
move together, the continuity of velocity implies — 
x = u-u, coe eco eco eco eco eco eco (C1) 
Now equation A13 holds generally for a plane wave or pulse travelling in 
any direction, the particle velocity being taken as measured in the direction 
of travel of the wave. Hence 
P, = peu, 
mm & 
Substituting in equation Ci 
B50 | cod" noGe doa "dasa, sccae doo. (G2) 
pot = BP, eco coe eco eco coe eco eco (c3) 
The equation of motion for unit area of plate is ~~ 
2 
max = Pp +p ok coe eco eco eee eco coe (C4) 
at>  °2 
Substituting for p, from equation 33 
ax ax be 
mt * Poa +kxe = 2p, coo eve eee ° ° (C5) 
