Civil Engineering Reference
In-Depth Information
−
30
FTMM
SEA Approach
Modal Approach
FEM
−
35
−
40
−
45
−
50
−
55
−
60
10
2
10
3
Frequency (HZ)
Figure 12.12
Radiated power of a plate - limp foam system excited by a point force.
The final example considers a 0
.
9
×
0
.
6 m double plate system made up of foam
sandwiched between a steel panel and a limp heavy layer. Two cases are considered:
limp foam and elastic foam. The first configuration depicts light coupling between the
two panels while the second involves a stronger coupling. The properties and thicknesses
of the three layers are given in Table 12.5. The three methods are compared with the finite
element method. In the latter, the foam is modelled using the formulations described in
Chapter 13. Figures 12.13 and 12.14 show the comparison between FEM and the FTMM
for the quadratic velocity and power radiated by the two plates, for the limp foam and
the elastic foam, respectively. Note that the SEA and the modal approaches, as presented,
cannot be used to estimate the velocity and radiated power at the receiver side. Their
results are not shown, but they have been found to correctly capture the vibration response
and radiated power of the excited panel for both the limp and elastic foams. The modal
method leads to the best correlation with FEM (both assume simply supported panels).
On the receiver side, the comparison is found acceptable between the FTMM and the
FEM in both cases, especially at higher frequencies. More discrepancies are observed for
the foam case; still the main tendencies are well captured.
Table 12.5
The parameters of the plate - fibre system.
∝
ρ
1
Material
Thickness,
φσ
E
ν
s
(N s/m
4
)
(
µ
m) (
µ
m) (kg/m
3
)
(Pa)
h
(mm)
2
.
1
×
10
10
Panel 1
1
7800
0.3
0.007
Limp foam
25.4
0.9
20000
1.6
12
24
30
1300
0
0.4
10
3
10
3
0.99 10
.
9
×
×
Foam
25.4
1.02 100
130
8.8
80
0.35 0.14
Heavy layer 1
1000
(PVC)
