Civil Engineering Reference
In-Depth Information
m
B
2
eff
B
=
ω
and
c
= ω
.
(8.37)
4
eff
B
4
B
m
k
Figure 8.20
shows a typical example of the frequency dependence of the bending
stiffness. In this example, the face sheets are 9 mm chipboard and the core has properties
corresponding to PVC foam (see
Table 8.1)
. The bending stiffness is shown for two
different thicknesses of the core, 50 mm and 100 mm. In the latter case, the dashed line
shows the result of reducing the E-modulus and thereby also the shear stiffness by a
factor of two.
500
200
100
100
50
50
20
10
5
2
1
0.5
10
20
50
100
200
500
1000
2000
5000
Figure 8.20
Bending stiffness of a sandwich element. Face sheets of 9 mm chipboard with foam core (PVC) of
thickness 50 and 100 mm. Dashed curve indicate 100 mm core with reduced shear stiffness.
Frequency (Hz)
Table 8.1
Material data used in
Figure 8.20
.
E-modulus
(Mpa)
Density
(kg/m
3
)
Thickness
(mm)
Poisson's ratio
Face sheets
4000
800
9
0.3
Core
50
60
50 - 100
0.3
Core (dashed curve)
25
60
100
0.3
What are then the consequences for the phase speed of the bending wave and
further on for the sound reduction index of a sandwich element? Using the second
calculation in Equation
(8.37)
, the corresponding phase speed will be as depicted in
Figure 8.21.
Keeping the same bending stiffness as present at low frequencies would
result in a very low critical frequency. However, depending on the core shear stiffness
