Civil Engineering Reference
In-Depth Information
Table 13.1
The parameters of the foam.
Porosity,
Flow
Tortuosity,
Viscous
Thermal
Density
Young's
Poisson
Structural
φ
α
∞
resistivity,
charact.
charact.
of frame,
Modulus,
coefficient,
damping,
σ
ρ
1
ν
η
dim. (m)
dim. (m)
(Pa)
(N m
−
4
s)
(kg m
−
3
)
0.99
12569
1.02
0.000078
0.000192
8.85
93348
0.44
0.064
1.4
FEM
TMM
FTMM
1.2
1
0.8
0.6
0.4
0.2
0
10
2
10
3
10
4
Frequency (Hz)
Figure 13.5
Absorption coefficient of 2-in-thick foam slab of dimensions 0
.
5
×
0
.
5m
excited by a normal incidence plane wave (Atalla
et al
. 2006.)
Figures 13.5 and 13.6 show the corresponding absorption coefficients. The latter are
calculated using a power balance method:
diss
inc
α(θ,ϕ,ω)
=
(13.72)
In this expression
diss
denotes the power dissipated in the foam and
inc
denotes
the incident power. The results obtained using the transfer matrix method (TMM) are
also shown for comparison. As expected, it is clearly seen that, at higher frequencies, the
finite element (FEM) calculation asymptotes to the infinite extent configuration since the
normalized radiation impedance reduces to 1. The finite size correction of chapter 12 is
also used here to compute the curve referred to as FTMM in Figures 13.5 and 13.6. As
expected it captures the initial slope of the absorption curve which is governed by the
size of the tested sample. Note that as the sample becomes larger, the FEM and FTMM
