Civil Engineering Reference
In-Depth Information
1.6
FEM
TMM
FTMM
1.4
1.2
1
0.8
0.6
0.4
0.2
0
10
2
10
3
Frequency (Hz)
Figure 13.6
Absorption coefficient of 2-in-thick foam slab of dimensions 0
.
5
×
0
.
5m
excited by an oblique plane wave (Atalla
et al
. 2006).
curves asymptote towards the TMM result. The same results are obtained for an oblique
incidence plane wave, Figure 13.6.
Next, we consider the transmission loss of the same foam sample, which is now
between two semi-infinite media. The results are shown in Figure 13.7 for an oblique
incidence plane wave excitation (45
◦
,
0
◦
)
and compared to the TMM results. Once again,
and as expected, the two methods lead to similar results at high frequencies. At low
frequencies, the size effects lead to an increase in the transmission loss. Again, the finite
size correction of Chapter 12 is shown to lead to acceptable corrections at low frequencies
(within 1 dB). Again, for large samples, the results will asymptote towards the TMM
result.
13.9.2 Radiation effects of a plate - foam system
Usually, the effect of radiation damping of foam is neglected when the latter radiates
in free field. To check this assumption, the following example considers a plate - foam
system excited by a point force. The material properties and dimensions of the plate and
the foam are listed in Table 13.1. The frequency range of interest is the range below
800 Hz. The plate is meshed using 24
×
15 thin shell elements and the porous material
is meshed using 24
9 linear brick poroelastic elements. The plate is assumed
simply supported. The foam is bonded onto the plate, clamped (bonded to a hard baffle)
along its edges and has a free face which can radiate into a semi infinite space. The
space averaged quadratic velocity
×
15
×
v
2
of the plate is shown in Figure 13.8 for three
configurations of the free-face boundary condition: (i) using the radiation impedance
