Biomedical Engineering Reference
In-Depth Information
Tabl e 5. 1
Structural
parameters considered for the
model F
(female vocal fold)
Input data for model F
Shape
a
f
.x/
f
1
(Hz)
100
3:274
10
4
m (kg)
f
2
(Hz)
160
I (kg/m
2
)
1:341
10
9
c
1
(N/m)
44:8
1:133
10
3
e (m)
c
2
(N/m)
84:6
"
1
(s
1
)
6:12
10
5
120:35
"
2
(s)
a
0.575
0.0005
0.0004
0.0004
0.57
0.0002
0.0003
0.565
0
0.0002
0.56
0.0001
-0.0002
0.555
-0.0001
0
-0.0004
0.55
-0.0002
-0.0006
0.545
-0.0003
-0.0008
0.54
-0.0004
0.535
-0.0005
-0.001
0
0.01
0.02
0.03
0.04
0.05
0
0.01
0.02
0.03
0.04
0.05
0
0.01
0.02
0.03
0.04
0.05
t[s]
t[s]
t[s]
b
0.79
0.008
0.006
0.007
0.005
0.785
0.006
0.004
0.78
0.005
0.003
0.775
0.004
0.002
0.003
0.77
0.001
0.002
0.765
0.001
0
0.76
0
-0.001
0
0.01
0.02
0.03
0.04
0.05
0
0.01
0.02
0.03
0.04
0.05
0
0.01
0.02
0.03
0.04
0.05
t[s]
t[s]
t[s]
c
1.11
0.0002
0.0001
0
1.108
-0.0002
0
-0.0001
1.106
-0.0002
-0.0004
1.104
-0.0003
-0.0006
1.102
-0.0004
-0.0008
1.1
-0.0005
-0.001
-0.0006
1.098
-0.0012
-0.0007
1.096
-0.0014
-0.0008
1.094
-0.0016
-0.0009
-0.0018
-0.001
1.092
0
0.01
0.02
0.03
0.04
0.05
0
0.01
0.02
0.03
0.04
0.05
0
0.01
0.02
0.03
0.04
0.05
t[s]
t[s]
t[s]
Fig. 5.1
2
The
m
ean inlet velocity oscillations (
left column
) and the aeroelastic response of the
system
w
1
.t/,
w
2
.t/ (
middle
and
right columns
)for
model F
and the prescribed inlet pressure
boundary conditions. The inlet pressure was chosen (
a
) p
D
100 Pa, (
b
) p
D
200 Pa, (
c
)
p
D
400 Pa
The vibrations of the vocal fold in Figs.
5.12
and
5.13
dies out for all the values
of the inlet pressure with no significant decrease or increase of the aerodynamic
damping. Particularly, the aerodynamic damping is quite strong for all studied cases.
The aeroelastic instability was never observed for the physically relevant values
of the inlet pressure (values of p up to 5;000Pa were tested). This behavior is
probably caused by “additional damping” effects due to the prescribed inlet pressure
boundary condition. Particularly, in Figs.
5.12
and
5.13
the inlet velocity oscillations
are shown, where the inlet velocity is increasing with a wider opening of the glottal
part g.t/ and similarly decreasing with a narrower enclosure of g.t/. The inlet
velocity oscillations (as well as consequently the flow rate oscillations) influence
the aerodynamic forces and are leading to damped vibrations of the structure.
Aeroelastic Simulations for Model F with Inlet Velocity Condition
The problem with the same input parameters used in previous section was also
numerically analyzed with the inlet velocity boundary condition.
Search WWH ::
Custom Search