Civil Engineering Reference
In-Depth Information
pressure radiated by the smart foam. The comparison is excellent. The pressure in the
back cavity is constant up to 1250 Hz (Figure 13.19a) where the second resonance mode
of the foam - PVDF system begins to affect the displacement field. At the other end of
the tube (Figure 13.19b), the radiated pressure is controlled by the modal behaviour of
the tube. All the peaks correspond to tube resonances. Note that the pressure level is
around 100 dB which is quite important. In the back cavity, it is around 103 dB.
Figure 13.20a, b presents the comparison for the displacement at the centre of the
free surface of the foam and the centre of the PVDF film, respectively. It is observed that
the model follows closely the trends in the measured displacement data (Figure 13.20a).
However, there are few discrepancies. For the foam displacement, the model seems to
slightly overestimate the amplitude (Figure 13.20a). The peak of the experimental data is
well represented by the numerical model, but it is located at a slightly higher frequency.
For the PVDF displacement, the FE model predicts the amplitude very well, but does not
clearly capture the shape of the peak (Figure 13.20b); this may be due to the uncertainty
on either the measurement position or the properties of the film.
In the passive absorption configuration, the measured absorption coefficient of the
smart foam is compared with predictions in Figure 13.21. Overall, the comparison is
very good. The main differences are observed at frequencies lower than 200 Hz and
higher than 1000 Hz. At low frequencies, possible leaks in the tube may have disturbed
the measurements. Moreover, at these low frequencies, the relative influence of the other
dissipation mechanisms in the tube (speaker suspension, join, wall
...
) is important. At
frequencies higher than 1000 Hz, the uncertainties on the microphone position become
important. Moreover, the modal behaviour of the foam - PVDF system is significant and
affects the absorption. And since the structural behaviour above 1000 Hz is not perfectly
predicted by the model, the predicted absorption coefficient is slightly different from
measurement.
Despite various uncertainties on: (i) the properties of the foam, the PVDF film and
the bonding layer (glue) between the two; and (ii) the fabrication of the smart foam
prototype, the comparison between the model and the measurements is very good. The
results clearly demonstrate the validity of the model. It constitutes a useful platform to
simulate and optimize various configurations of smart foams. A thorough discussion is
given by Leroy (2008).
13.9.7 An industrial application
Finally, an example of an industrial application, courtesy of Faurecia (Duval
et al
. 2008),
is shown. The vibroacoustic response of a car floor module, excited by a shaker was mea-
sured at Faurecia labs. The module was fixed in the separation wall of a reverberant room
coupled to a movable absorbing concrete-walled receiver cavity. The floor was excited
by a shaker positioned at a front reinforcement beam location and its radiation measured
using microphones in the receiver movable concrete cavity. To achieve a clamped bound-
ary condition, 3-mm-thick plates were used to connect through continuous welding, the
floor perimeter to a 100
100 mm
2
metal frame filled with concrete and fixed to the
horizontal separation wall of the coupled reverberant rooms. These additional plates have
been 3D modelled and integrated in the FEM model.
The simulations, conducted at Faurecia, use a sub-structuring based implementa-
tion of the
(
u
s
,p)
formulation. This implementation, described in Hamdi
et al
. (2000)
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