Civil Engineering Reference
In-Depth Information
5.4.1.6
Membrane absorbers
These absorbers are, as the name suggests, ideally, an impervious membrane stretched at
a certain distance from a hard surface making up an airtight cavity. In common speech
the notion has a wider use, also including cases where one is not using membranes but
stiff materials such as metal or plastics. This means one is using materials giving bending
forces and bending displacements, not only tensional ones. Modelling these absorbers,
taking the bending stiffness into account, is relatively complicated. We shall therefore
give an approximate model where we assume that the bending stiffness is negligible in
comparison with the stiffness of the cavity. This implies that we return to the ideal
membrane case. Assuming normal sound incidence, the input impedance may be written
as
ZR
=+ −
j
ω
m
j
ρ
c
cotg (
k
A
)
g
m
0
0
2
00
(5.41)
⎛
⎞
ρ
c
or
Z
≈
R
+
j
ω
m
−
,
⎜
⎟
g
m
⎜
⎟
ω
A
k
A
<<
1
⎝
⎠
where
m
is the mass per unit area of the membrane, and where
R
m
represents the
resistance component in the system. By using the approximation shown in the last
equation, where we assume that the depth
A
of the cavity is small compared with the
wavelength, we have returned to the simple mass-spring system having a resonance
frequency
f
0
given by
2
ω ρ
ππ
1
c
60
0
0
0
f
==
≈
.
(5.42)
0
22
m
A
m
A
In the approximation shown by the last term we have used ρ
0
= 1.21 kg/m
3
and
c
0
= 340
m/s.
The absorption factor at resonance and the width of this resonance are certainly
wholly dependent on the resistance. Estimating this quantity poses the real practical
problem when designing membrane absorbers. Normally, thin metal panels are applied
where the resistance is partly due to internal energy losses in the material itself, partly to
frictional losses in the mechanical coupling between elements and partly to acoustic
radiation. As pointed out above one also havs to take the possible influence of plate
resonances into account, i.e. the eigenmodes of the single plates. This may give an
absorption factor varying quite irregularly with frequency. This type of “membrane”
absorber normally ends up having a badly adjusted resistance, which seldom gives a
absorption factor in excess of 0.5. This also applies even when the cavity is filled, wholly
or partly with a porous material. The simple model treated here does, however, not cover
that case.
A quite different kind of membrane absorber is a collection of small, completely
closed plastic “boxes” having wall thickness of some tenth of a millimetre (see e.g.
Mechel and Kiesewetter (1981)). This gives a distributed resonant system where the
effective resistance of each box is more optimal for the system than in the case of metal
panels described above.
Another development, which deserves mention here, even if the membrane effect is
not the primary concern, is absorbers using different types of flexible, microperforated
sheets. These are, in fact, MPAs where the normal hole-perforated plates are replaced by
flexible plastic sheets with holes made by heated spikes, a process much cheaper than
making such holes in panels of hard materials as metal, glass etc. However, as these
sheets are very light one cannot neglect the mass of the sheet itself and the calculation
