Environmental Engineering Reference
In-Depth Information
2
2
∂
∂
f
∂
∂
f
+
µ
=
0
21
2
2
x
R
.
If.z.=.0;.z.=.h;.f.=.0;
2
2
∂
∂
f
∂
∂
f
+
µ
=
0
.
.
(5.54)
12
2
2
x
R
h. is. the. height. of. the. section. of. a. propeller. blade. and. R. is. the. radius. of. a.
propeller.blade.
These.boundary.conditions.are.known.by.the.function.of.delections:
6
m x
R
n y
h
π
π
.
f
=
sin
sin
.
(5.55)
mn
Here,. m. and. n. are. whole. digits. and. are. determined. as. a. number. of. semi-
waves.in.the.x.and.z.direction.
k =
R
.
Wet.designate
h
;
.
k.is.the.present.geometrical.parameter.(relationship.of.radius.and.propeller.
blade.to.height).
We.can.determine.natural.frequencies.f
mn.
as:
1 2
/
1 2
/
4
2
2
π
g
h
m
k
m
k
2
4
f
=
D
+
2
D n
+
2
D n
3
.
(5.56).
mn
1
3
2
h
η
The.frequency.of.the.basic.tone.(m.=.1,.n.=.1).will.be:
1 2
/
2
π
g
h
(
)
1
/
2
2
4
f
=
D
+
2
D k + D k
..
.
(5.57)
11
1
3
2
2
η
h
The.frequency.of.the.second.tone.(m.=.2,.n.=.2).will.be:
1 2
/
2
4
π
g
h
(
)
1
/2
2
4
f
=
D
+
2
D k + D k
.
.
(5.58).
22
1
3
2
2
η
R
The.frequency.of.the.third.tone.(m.=.3,.n.=.3).will.be:
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