Civil Engineering Reference
In-Depth Information
inside a subsystem. Implicitly; all quantities
E
,
n
and
W
are functions of frequency and
generally we shall use the angular frequency ω in the equations.
A simple practical example is depicted in
Figure 7.3
, a freely suspended plate
forced into vibrations by the sound field set up in the room by a loudspeaker. In section
7.3.1
below we shall apply the equations, which follow from the assumptions above, to
calculate the amount of vibration resulting from a given input power to the room.
W
W
in
in
in
in
W
W
W
W
'
12
'
12
2
2
1
1
n
n
E
E
2
2
1
1
'
21
'
21
W
W
diss
diss
diss
diss
W
W
W
W
Figure 7.2
System with two components (subsystems).
V
S
W
Figure 7.3
Example of a system with two components; a room being the acoustic component having volume
V
and a free hanging panel of area
S
as the solid structure.
Assumption no. 1 above gives
Wa E
diss
= ⋅
,
(7.1)
where
a
is factor of proportionality. As shown earlier (see section 6.4.1), we found for a
plate, having an area
S
and a mass
m
per unit area, that the relationship between the its
mean square velocity and mechanical power
W
was given by
2
WmS
=
ωη
⋅
u
=
E
ωη
,
(7.2)
Δ
ω
