Civil Engineering Reference
In-Depth Information
5.6
Prediction of the effective density and the bulk
modulus of open cell foams and fibrous materials
with the different models
5.6.1 Comparison of the performance of different models
A systematic comparison of the performance of the Wilson model and the Johnson
et al
.
model has been performed by Panneton and Olny (2006) in the following way. The
parameters that characterize the effective density have been evaluated as a function of
frequency from careful measurements of the effective density, with the impedance tube
technique of Utsono
et al
. (1989), and the method proposed by Iwase
et al
. (1998) to
minimize the vibrations of the frame which is motionless in the previous models. In a
second step, the effective density has been predicted with these parameters. The first
test concerns the variations of these parameters with frequency. The variations must be
negligible in the range of frequencies where the model can be used and the measure-
ments sufficiently precise. The second test concerns the agreement between the predicted
and the measured effective density when an optimal unique measured set of parameters
is chosen. The materials were a low-resistivity polyurethane foam, a medium-resistivity
metal foam, and a high-resistivity rock wool. The measured and the predicted effective
densities are close to each other for both models, with a slight difference at low frequen-
cies for the metal foam and the Wilson model. A similar comparison has been performed
by Olny and Panneton (2008) for the bulk modulus with the simplified Lafarge model,
the Wilson model and the Champoux - Allard model. The materials were a low-resistivity
polyurethane foam, a medium-resistivity glass wool, and a high-resistivity rock wool.
The simplified Lafarge model provides excellent predictions of the bulk modulus. For
the Wilson model, the measured and the predicted bulk moduli are close to each other
for the three materials. For the Champoux - Allard model, the predicted bulk modulus
and the measured bulk modulus are noticeably different for the rock wool, the thermal
permeability being very different from
φ
2
/
8. A noticeable difference between predic-
tion and measurement with the simplified Champoux - and Allard model was observed
previously in Lafarge
et al
. (1997).
5.6.2 Practical considerations
Simulations show that the Pride
et al
. model and the simplified Lafarge model can give
precise predictions of the effective density ad the bulk modulus in the whole audible
frequency range. The use of physical parameters in these models provides a link between
the acoustical and the physical domain. The improvement of the performances of sound
absorbing porous media can be carried out via the modifications of these parameters. A
problem for the use of the full models is that some parameters can be very difficult to
measure. The use of simple phenomenological parameters, such as the Wilson model,
can provide around normal temperature and pressure conditions a simple and precise
representation of the measurements over a large frequency range. Moreover, natural and
synthetic porous structures are to some extent nonhomogeneous, anisotropic, and not
