Civil Engineering Reference
In-Depth Information
Energy will be lost by radiation to the surroundings and by the exchange of energy
by a thermal coupling. We shall look at the possible combinations when the radiation
losses and the conductivity in the coupling, respectively, either has a low or high value.
The number of squares in
Table 7.1
represents the energy (temperature) inside the
subsystems for the different combinations, certainly giving just a qualitative picture. A
situation which we shall look into further on is when the radiation losses are small
combined with a high conductivity, i.e. strong coupling. In this case the subsystems are
“sharing” the energy; there will be a so-called
equipartition
of energy.
Table 7.1
A qualitative picture of the energy (temperature) in the thermal system shown in
Figure 7.1.
Radiation loss
High
Low
Conductivity
System 1
System 2
System 1
System 2
High
Low
Transferring this model into a vibroacoustic one having resonant acoustic volumes
(rooms etc.) and resonant solid structures, we may establish the following analogous
quantities:
•
Thermal radiation losses
Ù
Losses due to absorption, internal losses in
materials characterized by the reverberation time
T
60
or loss factor η.
•
Conductivity
Ù
Measure of the coupling strength, coupling loss factor η
ij
(may also be given by an impedance).
•
Temperature (energy)
Ù
Sound pressure level in room, vibration level
(velocity etc.) of solid structures.
•
Thermal capacity
Ù
Modal density.
The last item is not self-evident but it is connected to one of the most important
assumptions for SEA.
7.2.2
Basic assumptions
The most important assumptions behind the method are the following:
1.
The loss of energy within a subsystem is proportional to the total energy of the
subsystem.
2.
The energy transmitted from one subsystem to another is proportional to the
modal energy difference.
3.
The forces driving the different subsystems are independent, statistically
speaking. We may add the energy response resulting from these forces to
arrive at the total (modal) energy of each subsystem.
To give an illustration of these assumptions and express them in a mathematical form,
we shall again start with a system having two components or subsystems, marked 1 and
modal densities
n
1
and
n
2
. The symbol
W
represents the power;
W
in
for input power,
W
´
for transmitted power between subsystems and
W
diss
for the energy dissipated or lost
