Civil Engineering Reference
In-Depth Information
Carpet (1)
Carpet (2)
Screen
Fibrous layer
Figure 11.16
A porous material made up of several porous layers with an inner imper-
vious screen and bonded onto a rigid impervious wall.
Table 11.7
The parameters used to predict the surface impedance of the material
represented in Figure 11.6.
Material
Thickness,
φ
σ
α
∞
ρ
1
E
ν
s
(N s/m
4
)
(kg/m
3
)
h
(mm)
(
µ
m)
(
µ
m)
E( )
10
3
10
3
×
×
Carpet (1)
3.5
0.99
5
1
23
28
60
20
00.5
5
×
10
3
20
×
10
3
Carpet (2)
3.5
0.99
1
23
28
60
00.5
Screen
3
2000
33
×
10
3
100
×
10
3
Fibrous layer
1.25
0.98
1.1
50
110
60
00.88
it is modelled by a thin plate with negligible stiffness. Material parameters are given in
Table 11.7.
Figure 11.17 shows the comparison between measurements, taken from Brouard
et al
.
(1994), and predictions for the surface impedance at normal incidence. Predictions using
the finite element method (FEM) are also shown. The FEM model is based on the mixed
pressure formulation described in Chapter 13. To model an infinite extent material, one
quad 4 element with sliding boundary conditions was used in the plane of the materials.
The numbers of elements through the thickness were chosen to achieve convergence. For
the TMM and the FE predictions, the poroelastic model was used for the carpets and
the fibrous layer while a septum model (mass layer) was used for the impervious screen.
Good agreement is observed between the two models and the measurements.
11.7.3 Normal incidence sound transmission through
a plate - porous system
A layer of the glass wool studied in Section 6.5.4, of thickness 5 cm, is bonded on
to a plate of aluminium, of thickness 1 mm. As indicated in Section 6.5.4, the glass
wool is anisotropic, and the transmission is calculated only at normal incidence using
the properties of Table 11.8. At normal incidence, there is no flexural deformation of the
plate, and one only needs the values of the thickness and the density to characterize
the plate (the transmission is governed by mass law). The transmission coefficient
τ
at
normal incidence is represented in Figure 11.18, and compared with the transmission
through the plate, with the glass wool removed. It appears that the transmission is larger
in two intervals of frequencies when the glass wool is present. The frame of the glass
