Civil Engineering Reference
In-Depth Information
(a) (b)
Figure 13.9
Experimental set-up used to illustrate the damping added by the foam. (a)
Excitation system; (b) plate with foam attached using a double-sided tape (shown before
assembly).
condition of Section 13.8 (exact approach), (ii) pressure release condition (i.e.
p
=
0
on the free face) and (iii) assuming a plane wave radiation condition (
Z
R
ρ
0
c)
.Itis
clearly seen that the three results are similar except at the resonances where the effect
of radiation damping is noticeable, especially for low-frequency modes. Moreover, it is
seen that the exact approach and the plane wave approximation lead to similar results
at higher frequencies. However, the plane wave approximation clearly overestimates the
radiation damping at low frequencies. This result highlights the small effects of the
radiation efficiency of the foam. Calculations using other foam materials with different
properties (especially several ranges of flow resistivity) lead to similar conclusions.
=
13.9.3 Damping effects of a plate - foam system
The vibration of a plate - foam system is studied both numerically and experimentally.
Figure 13.9 shows the experimental set-up. It consists of a 0
.
480 m
×
0
.
420 m
×
3
.
175 mm aluminium panel glued to a thin frame to simulate a simple support.
The mechanical properties of the panel are: Young's modulus 7
.
0
×
10
10
N/m
2
;
density
=
2742 kg/m
3
; Poisson's ratio 0.33; loss factor 0.01. The panel is excited
mechanically using a shaker. The normal velocity of the panel is measured using
accelerometers positioned on a grid made up of 56 points uniformly distributed over
the surface of the panel. A 7.62-cm (3-inch) foam is added to one side of the panel.
The foam is attached to the panel along its edges using a double-sided tape, (see
Figure 13.9b). The foam is thus not perfectly bonded onto the panel since the double
tape creates a thin air space between the panel and the foam. Figure 13.10 shows the
measured space averaged quadratic velocity of the panel with and without the attached
foam. Significant reduction of the vibration level is observed, in particular at high
frequencies. This behaviour is typical of panels with attached noise control treatments.
To investigate the nature of this damping, numerical simulations are used. To achieve
confidence in the code, predictions are compared to simulation in Figure 13.11. The
acoustical and mechanical properties of the melamine foam used in the model are given
in Table 13.1. Good agreement is observed, keeping in mind that: (i) no attempt has been
made to select the modal damping of the first plate's modes in the predictions, (ii) in the
simulations the foam is assumed perfectly bonded onto the panel and (iii) the mechanical
properties of the foam have been measured at low frequencies using a quasi-static method
(Langlois
et al
. 2001) and are assumed constant over the whole frequency range.
