Building Acoustics

348 Building acoustics

(^) , 10 lg S ,
2
ij
ij v ij
ij

RR S

RD

SS

+ ⎛⎞

=++⋅⎜

⎜

⎝⎠

⎟

⎟

(9.33)

where we have introduced the direction averaged velocity level difference

(^) ,,

1

(

vij 2 vij v ji

DDD=+,). (9.34)

9.3.2 Vibration reduction index

Determining data for flanking sound transmission is complicated, both by prediction and
by measurement. In practice, one is normally compelled to use less accurate data than
e.g. reduction indexes for walls and floors. Recently, a series of international standards
has been developed for laboratory measurements of flanking sound transmission, both
for airborne and impact sound transmission (see ISO 10848). This should contribute to a
greater understanding of the problem and make more accurate data available.
The velocity level difference across a junction, which was introduced above is, as
opposed to a sound reduction index, not an invariant quantity as it depends on the actual
energy losses in the receiving element. This is quite analogous to the difference in sound
pressure level between two rooms which is dependent on the absorption area in the
receiving room. An invariant quantity for transmission across a junction is defined in EN
12354–1, being called vibration reduction index having the symbol Kij. From this
quantity, we may find the velocity level difference between elements i and j by
correcting for the actual energy losses. We shall present examples below but for a
complete picture we shall start with a presentation of the “classical” calculations
concerning bending wave transmission across plate intersections involving three (T-
junction) and four plates (see Cremer et al. (1988)).

9.3.2.1 Bending wave transmission across plate intersections

In Cremer’s pioneering work one assumes that a plane bending wave is incident on an
intersection involving three plates or four plates (see Figure 9.18), showing cross
sections. All plates are assumed to be of infinite extent and a bending wave in the plate
of thickness h 1 is assumed to be incident normally to the axis of the intersection, which is
normal to the plane of the paper.

h 1 h 3 = h 1

h 2

h 4 = h 2

h 1

h 2

h 3 = h 1

Figure 9.18 Cross sections through junctions involving three and four plates.