Civil Engineering Reference
In-Depth Information
3
ReZ - Measurements
ReZ - Prediction
ImZ - Measurements
ImZ - Prediction
2
1
0
−
1
−
2
−
3
0
0.5
1
1.5
2
2.5
3
3.5
Frequncy (Hz)
Figure 11.7
Surface impedance
Z
at normal incidence of the foam described in
Table 11.3. Measurements reproduced from Rebillard
et al
. (1992).
The Johnson - Champoux - Allard model, summarized in Section 5.8, is used for the
two materials. The characteristic lengths for the glass wool verify
=
2
as predicted
by the model of Section 5.3.4. The static bulk modulus of the frame of the sheet is large,
about 1 MPa and at normal incidence the sheet can be considered as a rigid framed
material, due to its small thickness. The dynamic Young's modulus
E
has not been
measured, but has been chosen sufficiently large for the sheet to behave as a rigid framed
material at normal incidence.
The surface impedance is presented in Figure 11.7 for the foam and in Figure 11.8 for
the sheet bonded on to the foam. The measured surface impedances have been presented
in Rebillard
et al
. (1992). The absorption coefficient of the foam and of the foam plus
the facing, are presented in Figure 11.9. The increase in absorption due to the facing is
very large at low frequencies for the material considered. The main effect of the facing
at medium frequencies is an increase in the real part of the impedance of the foam that is
close to the flow resistance
σh
of the facing. This effect is easily explained. The density of
the sheet is very large, and the inertial force almost immobilizes the screen. The velocity
of the air does not vary noticeably from one face to the other in the sheet, because of its
small thickness; consequently, the pressure difference
p
between both sides of the sheet
is equal to
p
σhυ
,
υ
being the velocity of the air above the sheet. The increase in
the impedance is
p/υ
and is equal to the flow resistance
σh
of the sheet. However, in
the case of porous screens with lower density, the screen is not motionless, and a porous
elastic or limp model must be used for the screen to predict the surface impedance.
=
