Civil Engineering Reference
In-Depth Information
(a) (b)
Figure 13.18
Photos of the active cell with smart foam; (a) active cell; (b) cell mounted
in the measurement tube (LeRoy 2008).
displacement of the film with its efficiently radiating radial displacement. The PVDF is
bonded onto the foam and mounted in a small cavity (interior dimensions: height 55 mm;
width 85 mm; depth 110 mm) equipped with electric connections in order to feed the
PVDF. Plexiglass flanges are placed on the foam of the back cavity that is not covered
with PVDF to ensure tightness with the back cavity. The smart foam and the cavity
form a so-called active cell (Figure 13.18a). The cell is placed in a rectangular tube
(Figure 13.18b) with a cutoff frequency of 2200 Hz. The frequency range of interest is
[100 - 1500 Hz]. In the radiation configuration, the tube is closed by a rigid plexiglass plate
and a voltage is applied to the PVDF film. Plexiglass is used to allow for measurement of
the displacement of the foam and PVDF surfaces using a Doppler laser vibrometer. On the
other hand, the acoustic pressures at both ends of the tube are measured. For absorption
measurements, a loudspeaker is installed in place of the plexiglass plate. The absorption
measurement is done using the Chung and Blaser (1980) method with several microphone
pairs in the tube. This measurement gives information on the passive behaviour of the
cell.
Finite element model
The model uses quadratic poroelastic elements with
(
u
s
,p)
formulation, as well as elastic,
fluid and piezoelectric elements. The weak integral formulation of the porous media is
given in Equation (13.7). However, since the measurement of the foam properties revealed
anisotropy, a simplified orthotropic model was assumed for the mechanical properties of
the foams. Because of the difficulty of measuring the anisotropy of the acoustic parameters
(flow resistivity, porosity, tortuosity, viscous and thermal characteristic lengths) they are
assumed the same for all three directions. The Young's moduli for the three directions
have been obtained by measuring the absorption coefficients of a cubic foam sample
oriented along the orthotropic directions. The three Young's moduli have then been
adjusted in order to fit the resonance peak of the absorption coefficient with the measured
resonance peak of the absorption. Special care was given to the mounting of the foam
in the tube since it is known to affect the absorption resonance (a controlled air gap was
left around the foam lateral surface).
The used PVDF film (made by Measurement Specialties Inc.) has 28-
m thickness
and Cu - Ni electrodes. Its properties were taken from published data. Since the melamine
is highly porous, its surface was conditioned with a heat-reactivatable membrane before
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