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FIGURE P13.25
13.26 Find the natural frequencies
ω
mn
,m,n
=
1
,
2
,
3
,
...
for a circular plate with no central
hole if the outer rim at
r
=
b
is simply supported. Set
ν
=
0
.
3
.
b
2
K
1
/
2
C
mn
Answer:
ω
mn
=
ρ
C
mn
m
0
1
2
n
0
4.977
13.94
25.65
1
29.76
48.51
70.14
2
74.20
102.80
134.33
13.27 Determine the natural frequencies
ω
mn
for a circular plate with no central hole if the
outer edge at
r
=
b
is clamped. Set
ν
=
0
.
3
.
b
2
K
1
/
2
C
mn
Answer:
ω
mn
=
ρ
C
mn
m
0
1
2
n
0
10.216
21.26
34.88
1
39.77
60.82
84.58
2
89.10
120.08
153.81
13.28 Calculate the critical (buckling) in-plane radial force per unit length
(
n
r
)
cr
applied
at the outer edge
of a circular plate with no center hole for (a) a simply
supported outer edge and (b) a fixed outer edge. There are neither nodal circles nor
nodal diameters present in the buckling mode shapes.
(
r
=
b
)
C
b
2
Answer:
n
cr
=
(a)
C
=
4
.
191
,
(b)
C
=
14
.
68
13.29 Find the critical in-plane radial force per unit length
(
n
r
)
cr
applied at the outer edge
(
(a) The outer edge
is fixed and the inner edge is free. (b) The outer edge is simply supported and the
inner edge is free. There are neither nodal circles nor nodal diameters present in the
buckling mode shapes.
r
=
b
)
of a circular plate with a center hole from
r
=
0to
r
=
a
.
C
b
2
=
Answer:
n
cr
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