Page 270 - Dynamic Loading and Design of Structures

Page 241

Figure 6.7 Weak blast wave reflection.

6.2.5 Interaction of shock waves with plane surfaces

(a) Reflection of weak shocks
Spherical shock waves of low overpressure reflect from a plane surface as if the reflected
shock waves (Figure 6.7) came from an imaginary source equidistant, and on the same
perpendicular, from the surface as the real source but on the opposite side of the surface. The
reflected waves propagate with the same velocity as the incident waves.
Influence of surface properties:

1. If the plane surface is a rigid protective wall, then at (0, t1), the particle velocity v=0 and
the peak pressure p is larger than p . At t the real shock covers a circular area of the
2
s0
r
surface, radius OA. Peak pressure p (t ) is increased around the circumference of the circle
s0 2
of effect by reflection. Providing AXO≤35°, p has the same magnification by reflection as
s0
when AXO=0°.
2. If the plane surface is the external wall of a normal building, it is less than rigid and at (0,
t ) the surface is accelerated and has a velocity and a displacement. The surface continues
1
to accelerate as long as an overpressure p exists on one side. The reflected pressure is of
s
lower amplitude than for the rigid surface.
The surface may not exceed the limiting elastic deflection if the reflected overpressure is low
or +ve duration is short. For greater overpressure or longer +ve duration, plastic deformation
and possibly collapse may occur.
If the +ve duration of the shock wave is much longer than the natural period of the surface
then surface response is similar to that of a spring instantaneously loaded with a constant load.