Civil Engineering Reference
In-Depth Information
⎡
⎤
l
ij
KD
=+⋅
10 lg
⎢
⎥
,
(9.41)
ij
v ij
,
aa
⎢
⎥
⎣
ij
⎦
where
l
ij
is the length of the junction between elements
i
and
j
. The relationship between
reverberation time
T
and absorption length
a
is
2
2.2
π
S
f
i
ref
a
=
⋅
.
(9.42)
i
cT
f
0
i
The reference frequency
f
ref
is chosen to be 1000 Hz.
It should be mentioned that one may establish a relationship between
K
ij
and a
transmission factor (or reduction index) based on bending wave power in conformity
with Cremer's definition. However, maybe of more interest due to recent work by
Nightingale and Bosmans (2003) (see below) a similar relationship between the vibration
reduction index
K
ij
and the coupling loss factor η
ij
according to a SEA model may be
established.
50
40
K
13
30
20
K
12
=
K
23
10
0
0.1
0.2
0.5
1
2
5
10
20
50
100
Mass ratio (
m
2
/
m
1
)
Figure 9.20
Vibration reduction index
K
ij
as a function of the mass ratio of elements at an intersection involving
four plates. After EN 12354-1.
Altogether seven types of structural joints are considered in EN 12354 Part 1, for
which we shall reproduce data for one type only: an intersection involving four
homogeneous slabs. These data are shown in
Figure 9.20,
calculated using the following
equations
