Multilayer elements 295
wooden studs, CM is zero. However, common experience shows that steel studs may have
quite different elastic properties; the elasticity is not frequency independent. Estimating
this property must therefore be based on experience.
The transmission factor for the part being transmitted across the cavity is
0P 22 22
12 0 12
12 12
12 121
2
,
222
c
fS
mm c mm
aa aa
mm fS mmπ
τ
D D
π−
=
⎡⎤++⎡
⎢⎥++⎢
⎣⎦⎣
⎤
⎥
⎦
(8.28)
where
2
00 c,1i i 1.fm f
a
cfπ
U⎡⎤⎡ ⎛⎞⎤
=⋅−⎢⎥⎢ ⎜⎟⎥
⎣⎦⎢ ⎜⎟⎥
⎣ ⎝⎠⎦
As apparent from the expression, the influence of a finite area S is taken into account.
Further, a mean absorption factor Dfor the cavity is introduced. This may be put equal to
1.0 having a completely filled cavity but in other cases it may be difficult to estimate.
The sound reduction index which includes both contributions according to Equations
(8.27) and (8.28) is then
R=−10 lg(τB,line+τP) for f 0 < <ffc,1. (8.29)
Davy (1991) also gives an estimate for the frequency range above fc,1, applied to the case
of infinitely stiff studs but we shall not quote that here.
An example on the use of Equations (8.20) and (8.26) after Sharp and Equation
(8.29) after Davy is shown in Figure 8.16. The specimen is a double leaf partition of 13
mm plasterboards having a cavity depth of 70 mm, which was filled with mineral wool of
nominal thickness of 60 mm. The boards are mounted on common studs, either wooden
or steel. The predicted results are nearly identical when it comes to the case of wooden
studs and the frequency is sufficiently below the critical frequency. In this case, however,
none of the predictions fits the measured data particularly well.
Setting CM equal to 5.0⋅ 10 -6 m^2 ⋅N-1 as the compliance for the steel studs, the fit
between the prediction using Davy’s equation and the measured data is surprisingly
good. The crucial question remains however: How to estimate CM?
More recently, Hongisto et al. (2002) conducted a large experimental study on
double walls, although on small size specimens (1105 x 2250 mm). The set-up was thus
similar to the one used by Brekke (see Figure 8.5). However, here they used 2 mm thick
steel panels and altogether four types of steel stud plus wooden studs were tested. Other
variables were the cavity depth, the amount of absorber material filling the cavity and the
flow resistivity of the absorber. Altogether 54 tests were conducted where the cavity
conditions and the coupling between the panels were varied. No attempt to compare with
prediction models was made.
For uncoupled panels the results show, as discussed in section 8.2.1, that the
important parameters are the cavity thickness and the amount of filling. The flow
resistivity played a minor role. For the coupled case, the stiffness certainly was the
important factor, for wooden studs the spacing of the fastening screws also played an
important part. Wang et al. (2005) used one of these measurement results, one with
wooden studs and an empty cavity, to compare with their rather complex analytical
model treating the double wall as a periodic structure. The periodic model gives quite an