Civil Engineering Reference
In-Depth Information
Figure 13.16
Normal incidence absorption coefficient. Comparison between analytical
fluid equivalent model, numerical Biot model and measurement for 5.75-cm-thick rock
wool (Sgard
et al
. 2005). Reprinted from Sgard, F., Olny, X., Atalla, N. & Castel, F.
On the use of perforations to improve the sound absorption of porous materials.
Applied
acoustics
66
, 625-651 (2005) with permission from Elsevier.
particular that the numerical model is able to capture the skeleton resonance occurring
around 1350 Hz. Also, this figure demonstrates the important increase in the absorption
coefficient of the perforated material compared with the corresponding single porosity
value. Another advantage of the numerical model is the illustration of the physics derived
from the homogenization theory, namely the pressure diffusion effect. Figure 13.17 shows
an example of the variation of the pressure at the mesoscale for the studied example.
It is seen that the wavelength in the microporous domain is of the same order as the
mesoscopic size.
The finite element approach avoids most of the hypothesis of the analytical model
and can be used to deal with more complex configurations. In particular, the modeling
at the mesoscopic scale does not require that the size of the hole be small with respect to
the dimensions of the microporous material. This assumption is however necessary for
the analytical model to be able to homogeneize the heterogeneous porous material. The
numerical model can thus account for the diffraction by the hole. Also the handling of
complex shaped holes can be implemented straightforwardly using appropriate meshing
tools contrary to the analytical model which is limited to simple shapes. Finally, the
numerical model allows for a mixture of arbitrary located microporous materials and gas
patches together with a coupling with other subdomains (vibrating structures, air gaps,
