Civil Engineering Reference
In-Depth Information
Table 12.4
The parameters of the plate - fibre system.
ρ
1
Material
Thickness,
φσ
∝
E
ν
s
(N s/m
4
)
m) (kg/m
3
)
(Pa)
h
(mm)
µ
µ
(
m) (
6
.
9
×
10
10
Panel
3
2742
0.3 0.01
0.99 10
.
9
×
10
3
Limp foam 30
1.02 100
130
8.8
The first example considers a 1 m
×
1 m 3 mm aluminium plate. The properties of
the plates are given in Table 12.4. A comparison of the space averaged quadratic velocity
and radiated power of the bare panel computed using the three presented approaches
and the FEM are given in Figures 12.9 and 12.10. An excellent agreement is observed
for the quadratic velocity using the three methods and the FEM. Both the FEM and
the modal approach depict modal fluctuations at lower frequencies (recall that data are
presented in one-third octave bands). The results of the classical TMM (infinite panel
radiation efficiency) and the FTMM (infinite panel expression with size correction of the
radiation efficiency) are shown in Figure 12.10 for the radiated power. As expected the
TMM mainly captures correctly the radiated power above the critical frequency. However,
using the FTMM, good agreement is observed over the whole frequency range. In this
simple case (bare panel), the good agreement observed between the three approaches and
the FEM is expected. Still the results corroborate the validity of the FTMM in estimating
the radiation efficiency of a flat plate compared with the classical Leppington asymptotic
method and Rayleigh integral methods.
Next, the same plate with an attached limp porous layer is investigated. The properties
of the layer are given in Table 12.4. In the FE predictions, the limp layer is modelled
using brick8 equivalent fluid elements (see Chapter 13 for the finite element modelling
of porous media). A comparison of the quadratic velocity and the power radiated into the
−
40
FTMM
SEA Approach
Modal Approach
FEM
−
45
−
50
−
55
−
60
−
65
10
2
10
3
Frequency(HZ)
Figure 12.9
Quadratic velocity of a panel excited by a point force.
