Building Acoustics

Multilayer elements 303

63 125 250 500 1000 2000 4000

Frequency (Hz)

0

10

20

30

40

50

Sound

reduction index (dB)

Core thickness

50 mm

75 mm

100 mm

Mass law

Figure 8.22 Sound reduction index of a sandwich element. Material data from Table 8.1.

8.3.2 Sandwich element with compressible core

Excluding sandwich cores of the honeycomb variety, we cannot in general neglect
movements normal to the plane of the sandwich panel, i.e. there will be a transverse or
dilatational movement where the face sheets move in opposite phase. There will be
symmetric movements, dilatational modes, which may be considered as a generalized
kind of double wall resonance, in addition to the anti-symmetric modes due to the
bending waves as illustrated in Figure 8.23.
Moore and Lyon (1991) give analytical expression to calculate the sound reduction
index of infinite size sandwich panels, for cases with isotropic as well as with orthotropic
core materials. Concerning orthotropic materials, see Chapter 3 (section 3.7.3.3) and
Chapter 6 (section 6.5.3). An interesting spin-off from their work is that a panel with an
orthotropic core may in certain frequency ranges give a higher sound reduction index
than predicted by the mass law.
The derivation of their expression is rather involved, and we shall not repeat it here.
We shall look at the case of an isotropic core and show some calculated results where
comparison with measured results is possible. Moore and Lyon’s work is based on the
transmission factor for plane wave incidence expressed by the wall impedances Zs and Za
for symmetric and anti-symmetric wave motion, respectively: