40 
104. The yielding plate BC of 
fig. 19 is represented in fig, 20 
by a rigid piston BC whose motion 
is resisted by a force proportional 
to displacement The baffle is 
considered to be effectively 
infinite in extent and completely 
Pixed and rigid. The pressure 
pulse is taken to be a plane pulse 
of small amplitude arriving at 
normal incidence to reach the 
target at time t = 0, the pressure 
in the pulse varying with 
time according to the expornntial 
form of equation 10 The problem 
can be considered in two stages:- 
PRESSURE PULSE 
FROM EXPLOSION 
(4) if the piston BC be held 
fixed then the whole 
Fig. 20 - Pressure pulse incident plane ABCD in fig. 20 is 
on yielding piston in fixed and rigid and the 
infinite unyielding wall pressure pulse undergoes 
complete reflection. In 
particular, the pressure on BC will then be twice that in the 
incidence pulse, namely - 
=n 
pressure with BC fixed = 2p,e” «+. see (42) 
(2) the effect of the motion of the piston must now be added and as 
an approximation the compressibility of the water can be 
neglected so far as this motion is concerned, The second 
stage of the problem is thus to consider the incompressible 
flow associated with the motion of a rigid piston in an aperture 
of a rigid wall So far as the piston motion is concerned, 
this flow results in an increase of the effective mass of the 
Piston by the addition of a virtual mass M', the magnitude of 
which depends on the size and shape of the aperture. 
405 For a circular piston of radius a in an aperture of a rigid wall in 
water of mass density , the virtual mass M' is given byt 
Mi os Spe ated Micicicytvesik WelesHemicis: | iMeace kei (43) 
This mass of water M' effectively moves with the piston of mass M and exerts 
a drag on the piston which decelerates it In addition, the resistance 
ke on the back of the piston also resists the movement of the piston caused 
by the incident pulse. The equation of motion® for the piston can, 
therefore, be formed from these three forces, The resistance kx is small 
in the initial stages, that is, when the force due to the incident pulse 
is not small. If the resistance kx is neglected, an approximate relation 
for the velocity v communicated by the pulse to the piston is given by 
2H ey 
(ers Ws) jertcniNhGa ste: hncutar res via Ken ale tsCatD) 
-at 
phe equation of motion is:- (cat ) 3 +kx = 2ifa'p e 
If the term kx is neglected the solution for the velocity v is- 
ax 2 a seh 278 Pp, 
ye ae: hie aT) a sas Gin 
