Biomedical Engineering Reference
In-Depth Information
a
0.005
0.004
0.0045
0.0035
0.004
0.003
0.0035
0.0025
0.003
0.002
0.0025
0.0015
0.002
0.001
0.0015
0.0005
0.001
0.0005
0
0
-0.0005
0
0.05
0.1
0.15
0.2
0
0.05
0.1
0.15
0.2
t[s]
t[s]
b
0.1
0.15
0.1
0.05
0.05
0
0
-0.05
-0.05
-0.1
-0.1
-0.15
-0.15
0
0.05
0.1
0.15
0.2
0
0.05
0.1
0.15
0.2
t[s]
t[s]
Fig. 5.15
The aeroelasti
c
resp
on
se of the aeroelastic system for
model F
with the prescribed inlet
velocity; the graphs of
w
1
.t/,
w
2
.t/ in dependence on time t are shown for the different inlet
velocities (
a
) V
0
D
0:6 ms
1
and (
b
) V
0
D
0:65 ms
1
Tabl e 5. 2
Structural
parameters considered for the
model M
(male vocal fold)
Input data for model M
Shape
a
m
.x/
f
1
(Hz)
100
4:812
10
4
m (kg)
f
2
(Hz)
160
I (kg/m
2
)
2:351
10
9
c
1
(N/m)
56
0:771
10
3
e (m)
c
2
(N/m)
174:3
"
1
(s
1
)
6:12
10
5
120:35
"
2
(s)
0:55 ms
1
the structural vibrations are damped in time and the aeroelastic system is
stable. Nevertheless, the aerodynamic damping for the velocity 0:55 ms
1
is weaker
compared to the lower inlet velocity. With the further increase of the inlet velocity
to V
0
D 0:6 ms
1
the self-oscillations can be observed in Fig.
5.15
a. For the inlet
velocity V
0
D 0:65 ms
1
the vibrations of the vocal folds are growing very fast
(see Fig.
5.15
b). The simulation for V
0
D 0:65 ms
1
is only shown in the time
interval to 0:175s, where the computations crashed due to the high distortion of the
computational mesh.
Aeroelastic Simulations for Model M
Furthermore, the aeroelastic model of flow interaction with the vocal fold given
by the parabolic shape a
m
.x/ showninFig.
5.10
was analyzed. The structural
parameters are listed in Table
5.2
(see also [
39
,
40
]). The aeroelastic response
w
1
.t/,
w
2
.t/ is shown in Figs.
5.16
and
5.17
and plotted over time in terms of displacements
for the inlet flow velocities V
0
D 1:0-1:2 ms
1
. For the inlet velocities lower or
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