Civil Engineering Reference
In-Depth Information
Note that for large samples and/or at high frequencies (see Figure 12.1),
Z
R,avg
(θ)
=
1
cos
θ
, and the classical field incidence absorption formula is again recovered
π/
2
0
4Re
Z
A
cos
θ
2
cos
θ
sin
θ
d
θ
|
Z
A
cos
θ
+
1
|
α
inf,st
=
(12.40)
π/
2
0
cos
θ
sin
θ
d
θ
Note: A 'true' absorption coefficient can also be obtained by accounting for the size
effect in the incident power. 'True' is used here in the sense that its value is always less
than one. The idea is to replace the incident power by the input power accounting for
the geometric impedance seen by the incident wave
2
π
0
π/
2
0
4Re
Z
A
sin
θ
d
θ
d
φ
abs,f
inc,f
=
|
Z
A
+
Z
R
|
2
α
f,true
=
(12.41)
2
π
0
π/
2
0
4cos
θ
|
1
+
Z
R
cos
θ
|
sin
θ
d
θ
d
φ
2
Compared with the statistical coefficient, we obtain the following correction factor
2
π
0
π/
2
0
α
f,true
α
f,st
=
cos
θ
sin
θ
d
θ
d
φ
π
sin
θ
d
θ
d
φ
=
2
π
0
π/
2
0
2
π
0
π/
2
0
4cos
θ
|
1
+
Z
R
cos
θ
|
4cos
θ
|
1
+
Z
R
cos
θ
|
sin
θ
d
θ
d
φ
(12.42)
2
2
In terms of the heading averaged radiation impedance, it reads
α
f,true
α
f,st
=
1
(12.43)
π
2
8cos
θ
sin
θ
d
θ
0
|
1
+
Z
R,avg
cos
θ
|
2
12.3.3 Examples
Transmission loss of a plate - foam system
The first example considers an aluminium panel with attached foam excited by a dif-
fuse field in a reverberant room. The panel is 1
.
37
×
1
.
64 m and 1 mm thick. The
5.08-cm-thick foam was bonded along its edges to the panel using a double-sided tape.
The properties of the materials used are shown in Table 12.1. First, the TL of the bare
panel is compared in Figure 12.3 with simulations using the classical TMM and the finite
size correction (FTMM). It is clearly seen that the FTMM significantly improves the
predictions at low frequencies. Next, Figure 12.4 shows the comparison for the case with
the added foam. Again, the comparison is good at low frequencies where size governs
the TL. Note that, for much smaller panels, the stiffness of the panel will control its TL
at low frequencies (up to the first resonance of the panel) and this is not accounted for
in the presented size correction.
