Civil Engineering Reference
In-Depth Information
1
0.8
0.6
0.4
0.2
no gap
gap
0
0
0.5
1
1.5
Frequency (kHz)
2
2.5
3
3.5
4
Figure 3.9
The absorption coefficient at oblique incident (
θ
=
π/
4
)
for both configu-
rations of Figure 3.6.
Z(M
1
)
is the impedance of the air gap. This impedance may be evaluated by the use of
Equation (3.39), where
k,k
3
and
Z
c
are given by
k
o
k
3
=
k
o
1
−
sin
2
π
k
=
4
1
/
2
=
k
o
/
√
2
(3.47)
Z
c
=
Z
o
where
Z
c
is the characteristic impedance in air.
The impedance is represented in Figure 3.7 for the first configuration while Figure 3.8
shows the result for the second configuration.
The absorption coefficients in air for both configurations of Figure 3.6, evaluated
from the calculated impedances by using Equations (3.44) and (3.45), are represented in
Figure 3.9. It may be noted that as in the case for normal incidence, pressures, velocities
and impedances are individually equal at either side of the boundary between air and the
fluid equivalent to the porous material; however, due to the variation of the characteristic
impedance, the reflection and absorption coefficients are different.
3.7
Plane waves in fluids equivalent to transversely
isotropic porous media
As indicated in Section 2.5, fibrous materials such as fibreglass are anisotropic (Nicolas
and Berry 1984, Allard
et al
. 1987, Tarnow 2005) because generally most of the fibres lie
in planes parallel to the surface. A panel of fibrous material is represented in Figure 3.10.
The normal direction is parallel to
x
3
and the planar directions are parallel to the plane
