Civil Engineering Reference
In-Depth Information
9
Porous materials with perforated
facings
9.1
Introduction
Sound absorbing porous materials with perforated facings have been used for many
years, because they can present a high absorption coefficient at low frequencies. Models
of predicting the surface impedance and the absorption coefficient have been carried out
and checked, at normal and oblique incidence, for different configurations (Bolt 1947,
Zwikker and Kosten 1949, Ingard and Bolt 1951, Brillouin 1949, Callaway and Ramer
1952, Ingard 1954, Velizhanina 1968, Davern 1977, Byrne 1980, Guignouard
et al
. 1991).
The effect of a perforated facing was described in an elegant and physical way by Ingard
(1954) at normal incidence. In this chapter, the results in Ingard (1954) are generalized
at oblique incidence, and for anisotropic stratified porous media. As in all the previous
modelling, the facing and the frames of the porous layers are supposed to be motionless.
Nonlinear effects are not studied in this chapter. Information about this subject can be
found in Ingard and Labate (1950), Ingard and Ising (1967) and Ingard (1968, 1970).
9.2
Inertial effect and flow resistance
9.2.1 Inertial effect
Let
R
be the radius of the perforations, and
d
the thickness of the facing represented in
Figure 9.1.
Let
s
be the fraction of perforated open area, also called the open area ratio, equal to
nπR
2
if
n
is the number of perforations per unit area. The radius
R
of the perforations
and the thickness
d
of the facing are supposed to be much smaller than the wavelength
λ
in the air:
d
λ, R
λ
