Civil Engineering Reference
In-Depth Information
(a)
Z
′
b
c
Figure 10.8
The line source (thick line) on a free surface perpendicular to
Z
(a) and
on a free surface parallel to
Z
(b and c). The arrow indicates the direction of propagation
on the free surface.
If the rigidity coefficients are real, the slowness component
q
R
is real and is located
in the following intervals:
Case (a)
F
2
C
0
<q
−
R
<G
,(
2
G
+
A)
−
(10.123)
Case (b)
A
2
2
G
0
<q
−
R
<G,(
2
G
+
A)
−
(10.124)
+
A
Case (c)
F
2
2
G
0
<q
−
R
<G
,C
−
(10.125)
+
A
10.8.1 Example
The material is the glass wool described with the parameters of Table 10.1. A similar
material was studied by Tarnow (2005). Predictions of the phase speed 1
/
Re
q
R
and the
damping Im
q
R
of the Rayleigh wave are given in Table 10.2 for the three cases defined
in Figure 10.8 with Equations (10.120) - (10.122) for the frame in vacuum
The phase speed and the damping are represented in Figures 10.9 and 10.10 as a
function of frequency for the porous medium and the frame in vacuum.
Table 10.2
Phase speed 1
/
Re
q
R
and damping Im
q
R
for the
Rayleigh wave for the frame in vacuum in the geometries a, b, c of
Figure 10.8.
Geometry
Frame in vacuum Phase
Frame in vacuum Damping:
speed: 1/Re
q
R
(m/s)
Im
q
R
(s/m)
−
0
.
97
×
10
−
3
a
51
10
−
3
−
0
.
63
×
b
79
10
−
3
c
36
−
1
.
4
×
