Civil Engineering Reference
In-Depth Information
Table 11.4
The parameters used to predict the surface impedance of the material
represented in Figure 11.10.
Material
Thickness,
φ
σ
α
∞
ρ
1
E
ν
s
(N s/m
4
)
(kg/m
3
)
h
(mm)
µ
µ
(
m)
(
m)
( a)
10
3
10
3
Blanket (1)
4
0.98
34
×
1.18
60
86
41
286
×
0.3
0.015
3
·
2
×
10
6
2
.
6
×
10
6
Screen (2)
0.8
0.8
2.56
6
24
125
0.3
0.1
87
×
10
3
143
×
10
6
Foam (3)
5
0.97
2.52
36
118
31
0.3
0.055
65
×
10
3
46
.
8
×
10
6
Foam (4)
16
0.99
1.98
37
120
16
0.3
0.1
8
6
4
2
0
−
2
ReZ - Measurements, with screen
ReZ - Prediction, with screen
ReZ - Prediction, screen removed
ImZ - Measurements, with screen
ImZ - Prediction, with screen
ImZ - Prediction, screen removed
−
4
−
6
8
−
0.5
1
1.5
2
Frequency (kHz)
Figure 11.11
The surface impedance
Z
at normal incidence of the layered material
represented in Figure 11.10. Measurements reproduced from Allard
et al
. (1987).
modelled as porous limp materials. The screen was modelled using a rigid porous mate-
rial following the model of Johnson, Champoux and Allard. As explained by Atalla and
Sgard (2007), the characteristic lengths of the screen were derived from the measured
flow resistance following
=
=
r
=
√
8
η/φσ
. The air flow resistivity and the poros-
ity (or percentage open area) of the screen were measured. The tortuosity was taken equal
to
α
∞
(ω)
=
1
+
(ε
e
/d)(α
Felt
+
α
Foam
)
where
α
Felt
and
α
Foam
are the dynamic tortuosity
of the foam and the felt, respectively,
d
, the thickness of the screen and
ε
e
is taken
equal to 0
.
48
√
πr
2
(
1
0
.
47
φ
3
)
. It is shown in Atalla and Sgard (2007)
that this model captures well the behaviour of perforated screens and plates in contact
with porous materials. Because of its small thickness, the stiffness and mass of the screen
were ignored. The results of Figure 11.13 confirm the validity of this assumption and the
used model for the characteristic lengths and tortuosity. Note in passing that the approach
1
.
47
√
φ
−
+
