Civil Engineering Reference
In-Depth Information
There is certainly a need for performing simple estimations of the sound reduction
index of double constructions on common studs. We shall therefore include the
prediction model by Sharp (1978), a commonly cited reference. The model that assumes
infinitely stiff connections, either point or line connections, again uses Equation
(8.11)
as
a base. We may write it in the following way
⎛
⎞
W
W
W
i
2.P
R
=⋅
10 lg
=⋅
10 lg
⋅
⎜
⎟
⎜
⎟
W
W
+
W
W
⎝
⎠
2
2,P
2,B
2,P
(8.19)
⎛
⎞
⎛
⎞
⎛
⎞
⎠
W
W
W
2,B
2,B
i
or
R
=⋅
10 lg
−⋅
10 lg 1
+
=
R
−⋅
10 lg 1
+
.
⎜
⎟
⎜
⎟
⎜
⎜
⎟
⎜
⎟
without
⎜
W
W
W
⎝
⎠
⎝
⎠
⎝
2,P
2,P
2,P
We have then got an expression for the sound reduction index as a difference between
the reduction index for the partition
without
the structural connections and a term due to
these connections. Assuming that the sound radiation caused by these connections or
bridges is dominant, i.e.
W
2,B
>>
W
2,P
, Sharp shows that in the frequency range
f
0
<
f
<
f
d
,
where
R
without
increases by 18 dB per octave the last term will increase by 12 dB per
octave. Similarly, this term will increase by 6 dB per octave where
R
without
increases by
12 dB per octave, that is to say when
f
>
f
d
. Without going into detail, the resulting
reduction index will in effect have a shape as sketched in
Figure 8.14.
We end up with a
term Δ
R
added to the reduction index
R
, the latter determined by the total mass
M = m
1
+
m
2
of the partition:
RR
= Δ
R
,
M
⎡
ZZ
+
⎤
(8.20)
m
(
)
1
2
1
where
Δ=− ⋅ ⋅ + ⋅
R
10 lg
n
σ
20 lg
⋅
.
⎢
⎥
B
mm
+
Z
⎣
⎦
1
2
1
R
(dB)
R
(dB)
12 dB/oct
12 dB/oct
Δ
R
Δ
R
18 dB/oct
18 dB/oct
R
M
R
M
f
0
f
0
f
d
f
d
Frequency (log-scale)
Frequency (log-scale)
Figure 8.14
Principal shape of the sound reduction index of a lightweight double leaf partition with and with
and without infinitely stiff structural connections. Sketch according to Sharp (1978).
