Civil Engineering Reference
In-Depth Information
60
50
40
30
20
10
Test
Prediction (FEM: Poroelastic)
Prediction (FTMM)
0
10
2
10
3
10
4
Frequency(Hz)
Figure 13.14
Transmission loss of a plate - foam system. Tests versus FTMM and FEM
predictions; 1/3 octave band comparison.
and expensive method: the FTMM and even the TMM does an excellent job. Finally,
it is worth mentioning that for this particular problem (unbonded foam) similar results
can be obtained using a limp model for the foam thus diminishing considerably the
computational effort (Figure 13.13).
13.9.5 Application to the modelling of double porosity materials
As discussed in Chapter 5, the concept of meso-perforations in appropriately chosen
porous media can help enhance their sound absorption performance. The meso-perforated
materials are also referred to as 'double porosity materials' since they are made up of
two interconnected networks of pores of different characteristic size. Several theoretical,
numerical and experimental studies have been done on this subject. Sgard
et al
. (2005)
give an excellent review of these studies and establish practical design rules to develop
optimized noise control solutions based on this concept. This section is limited to an
example explaining the use of finite element methods to simulate these materials.
The general configuration of the problem is depicted in Figure 13.15. It consists of
a meso-perforated porous material placed in a waveguide with rigid walls, acoustically
excited by a plane wave. The rear of the material is terminated by a rigid wall. Let
the porous material be characterized by its porosity
φ
m
, its static flow resistivity
σ
m
, its
geometric tortuosity
α
∞
m
, its viscous and thermal characteristic lengths
m
and
m
,and
its thermal permeability
m
(
0
)
. The perforations are assumed rectangular or cylindrical
and are characterized by a perforation rate (also named meso-porosity)
φ
p
, a radius
