Civil Engineering Reference
In-Depth Information
where
S
is the area of the aperture. The limit 0
.
48
(S)
1
/
2
=
0 can be obtained by
calculating the radiation impedance of a single square aperture in a plane. Both limits
for the circular and the square aperture are the same.
for
s
9.3
Impedance at normal incidence of a layered porous
material covered by a perforated facing - Helmoltz
resonator
9.3.1 Evaluation of the impedance for the case of circular holes
The material covered by the facing is represented in Figure 9.5. The surface impedance
in the free air close to the facing can be calculated in the following way. At first the
surface impedance is calculated at
B
, at the boundary surface between the porous layered
material and the facing. As in Section 9.2, due to the symmetry of the problem, a partition
of the material can be performed. The elementary cell, represented in Figure 9.6, is a
cylinder having a square cross-section and a circular aperture.
Two different cases were considered by Ingard (1954). For the simplest case
(Figure 9.6a), the facing is in contact with a layer of air. In this case, the modes of
higher order responsible for the added length are present only in the layer of air if
the frequency is much lower than the cutoff frequency
f
c
c
0
/D
. The effect of these
modes is the same as in the free air. Moreover, the acoustic field in the porous layer
is plane, homogeneous and propagates perpendicular to the layer. The value of the
=
A
B
Figure 9.5
A layered porous material covered by a perforated facing.
air
porous layer
(a)
(b)
Figure 9.6
The elementary cell of the partition compatible with the symmetry of the
problem. (a) The facing is in contact with air, (b) the facing is in contact with a porous
layer.
