Building Acoustics

Multilayer elements 301

(^) eff^24 B^4 eff
B
and.
m B
Bc
k m
==ωω (8.37)
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.

10 20 50 100 200 500 1000 2000 5000

Frequency (Hz)

1

10

100

2

5

20

50

200

500

0.5

Bending sti

ff

ness (kN.m)

50

100

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.

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