Civil Engineering Reference
In-Depth Information
imaginary part of the impedance does not depend at low frequencies on the radii of the
apertures and the flow resistivity close to the facing. It increases when the open area ratio
decreases. In order to increase the absorption coefficient at low frequencies, the imaginary
part of the impedance, which is too large and negative, can be set close to zero by using
a small value of the open area ratio and a porous layer of high flow resistivity. A value
of the real part of the impedance close to the characteristic impedance of air can be
obtained with a small value of
R
and by inserting between the porous layer of high flow
resistivity and the facing a thin layer of material with a low flow resistivity. The thin
layer of low flow resistivity and the small value of
R
are necessary for the real part of
impedance not to be too large.
The predicted surface impedance and absorption coefficient of a layered material
covered by a perforated facing is represented at normal and at oblique incidence in
Figures 9.17 and 9.18. The material is made up of two layers, a thin layer
M
1
of low
flow resistivity in contact with the facing, and a thicker material
M
2
having a large flow
resistivity in contact with the impervious rigid backing. The parameters that characterize
both layers are given in Table 9.1. The thickness of the facing is
d
=
1 mm, the radius
of each hole is
R
0
.
005.
The absorption coefficient
A
0
reaches a maximum close to 1 around 500 Hz. The
counterpart of this performance is a low value of
A
0
at high frequencies. It may be
noticed that Bolt (1947) designed a material having a large absorption at low frequencies
which presented similar characteristics, i.e. small holes, a small open area ratio, and a
flow resistivity lower than for the configuration designed for sound absorption at higher
frequencies without facing.
=
0
.
5 mm, and the perforation ratio is
s
=
9.3.5 Helmholtz resonators
The cell of Figure 9.6 is called a Helmholtz resonator if its lateral boundaries are imper-
vious rigid surfaces. The Helmholtz resonator is a volume with an aperture. Different
shapes for the volume and the aperture can be used; the acoustical properties of these
resonators were studied by Ingard (1953). In practical cases, the viscous forces in the
empty volume can be neglected since the lateral dimension of the volume is much larger
than the viscous skin depth, and the effect of the viscous forces can be taken into account
only at the neck of the resonator. It may be pointed out that the term
(
4
+
2
d/R)R
s
in
Equation (9.21) is generally much smaller than the real part of
Z(B)
when porous media
are present in the resonator. If there is no porous material in the resonator, this term
cannot be neglected. Helmholtz resonators generally are designed to absorb sound at low
frequencies. An array of resonators is represented in Figure 9.15.
Ta b l e 9 . 1
The parameters that characterize the two layers M
1
and M
2
. The layer M
1
is in contact with the facing and the layer M
2
with the rigid impervious backing.
Material
Flow
Viscous
Thermal
Tortuosity
Porosity
Thickness
resistivity
dimension
dimension
α
∞
φ
e
(cm)
σ
(N m
−
4
s)
(mm)
(mm)
M
1
5000
0.12
0.27
1.1
0.99
0.1
M
2
50000
0.034
0.13
1.5
0.98
1.9
