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D. Rocchesso: Sound Processing
mass points
visco-elastic links
CORDIS-ANIMA
Using the Laplace transform, the system (39) can be converted into
R
k
f
k
m
m
1
1
2
x
x
x
1
2
2
Figure 12: Two coupled mechanical oscillators
X
1
(s) =
1
m
1
s
2
+ Rs + k
1
[F (s) + (k
1
+ Rs)X
2
(s)] = H
1
(s) [F (s) + G(s)X
2
(s)]
X
2
(s) =
1
m
2
s
2
+ Rs + (k
1
+ k
2
)
(k
1
+ Rs)X
1
(s) = H
2
(s)G(s)X
1
(s) ,
(39)
and this can be represented as a feedback connection of filters, as depicted in
figure 13. This simple example gives us the possibility to discuss a few different
H (s)
G(s)
G(s)
H (s)
2
f
E
I
x
x
2
1
1
R
Figure 13: Block decomposition of the coupled oscillators
ways of looking at physical models. One of these ways is the cellular approach,
where complex linear systems are obtained by connection of mass points (H
1
and H
2
in our example) and visco-elastic links. Such approach is the basis of the
CORDIS-ANIMA software developed at ACROE in Grenoble [20]. Another pos-
sibility, is to look for functional blocks in the system decomposition. In figure 13
we have outlined three functional blocks:
E - exciter: a dynamic physical system that can elicit and sustain an oscilla-
tion by means of an external forcing term;
R - resonator: a dynamic physical system (with small losses) that sustains
the oscillations;