Civil Engineering Reference
In-Depth Information
Table 10.1
Acoustical and mechanical parameters
for a typical glass wool. The tortuosity is identical
in directions
x
and
z
,and
F
=
A
=
0 (the Poisson
coefficients are equal to 0).
Flow resistivity
σ
x
(N m
−
4
s)
4000
Flow resistivity
σ
z
(N m
−
4
s)
8000
Porosity
φ
0.98
Tortuosity
α
∞
1.1
Thermal permeability
q
0
(m
2
)
6
.
10
−
9
Viscous dimension
x
(
µ
m)
200
Viscous dimension
z
(
µ
m)
140
Thermal dimension
(
µ
m)
500
Density
ρ
1
(kg/m
3
)
32
Rigidity parameter
G
(kPa)
260 (1
+
0.1j)
Rigidity parameter
G
(kPa)
125 (1
+
0.1j)
Rigidity parameter
C
(kPa)
46 (1
+
0.1j)
Equations (10.46) and (10.A.1) - (10.A.4) lead to
s
6
[
T
0
cos
6
θ
T
12
sin
2
θ
cos
4
θ
T
23
sin
4
θ
cos
2
θ
T
34
sin
6
θ
]
+
+
+
s
4
[
T
11
cos
4
θ
T
22
cos
2
θ
sin
2
θ
T
33
sin
4
θ
]
+
+
+
(10.55)
s
2
[
T
21
cos
2
θ
T
32
sin
2
θ
]
+
+
+
T
31
=
0
Equation (10.51) leads to
ρ
0
C
1
s
2
[
B
5
cos
2
θ
B
1
sin
2
θ
]
+
=
ρ
−
(10.56)
For the three waves polarized in the meridian plane, the real part of the slowness
s
,
which is the inverse of the phase speed, is presented in Figure 10.1 as a function of
θ
.
The imaginary part of
s
is presented in Figure 10.2. For the wave polarized perpendicular
to the meridian plane, the real and the imaginary parts of
s
are presented in Figure 10.3.
10.5
Sound source in air above a layer of finite thickness
10.5.1 Description of the problems
Glass wools and rockwools can be transversally isotropic and the normal to the large
faces of these materials is generally parallel to the symmetry axis. For a sufficient lateral
extension, the layer can be replaced in the calculations by a layer of infinite lateral
dimensions. If a plane wave impinges on the layer at an angle of incidence
θ
(see
Figure 10.4), the incidence plane can be denoted as the plane
XZ
and the slowness in the
direction
x
is 1
/c
k
0
sin
θ/ω
,where
k
0
is the wave number in the free air.
Due to the symmetry of the problem, only the waves polarized in the meridian plane
exist in the layer. In a first step, the frame displacement created by the plane wave and
the reflection coefficient of the layer are predicted. If the source in air is a point source,
=
