Civil Engineering Reference
In-Depth Information
11.7
Applications
This section presents application examples of the transfer matrices to the prediction of
the absorption and transmission loss of sound packages. Further examples, taking into
account size effects, mechanical excitation and/or more complicated structures will be
discussed in Chapter 12. The predictions in the following examples are calculated using
a computer program implementing the method of the transfer matrices as detailed above.
All the examples of Chapters 5 and 6 can be easily reproduced using the transfer matrix
method and thus are not reproduced here.
11.7.1 Materials with porous screens
A porous screen is a thin layer of porous material, with a thickness of about 1 mm or less.
Measurements and predictions using the TMM of the surface impedance of two materials
with porous screens are compared in this section. Thin porous screens are frequently
used at the surface or inside sound absorbents. They can improve the absorption with
a small increase in the thickness of the sound absorbing material. If the screen is an
isotropic porous material, it can be modelled as a layer of isotropic porous material and
represented by a transfer matrix. If the screen is anisotropic, approximate descriptions of
sound propagation can be used.
In spite of possible simplifications, these descriptions remain complicated, with many
parameters that are not easily measurable. As for the case of the glass wool studied
in Section 6.5.4, it is generally possible, at normal incidence, to model the anisotropic
porous screen as an equivalent isotropic material. The examples herein are restricted to
normal incidence. Examples of prediction at oblique incidence are given in Rebillard
et al
. (1992) and Lauriks (1989).
The first material, represented in Figure 11.6, is a plastic foam covered by a sheet of
glass wool. The parameters for the foam and the sheet are given in Table 11.3.
Sheet
porous Foam
Figure 11.6
A porous material made up of a sheet of glass wool bonded onto a layer
of plastic foam. The material is bonded onto a rigid impervious wall.
Table 11.3
The parameters used to predict the surface impedance of the material in
Figure 11.6.
Material
Thickness,
φ
σ
α
∞
ρ
1
E
ν
s
(N s/m
4
)
(
µ
m) (
µ
m) (kg/m
3
)
h
(mm)
( a)
5
×
10
3
130
×
10
3
Foam
38
0.98
1.1
150
216
33
0.3 0.1
1
·
1
×
10
6
1 0 0 0
.
6
×
10
6
Glass wool
0.45
0.7
0.3 0.1
