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=
u
(
L
/
=
with the boundary conditions
u
(0)
2)
0. The corresponding finite dif-
ference equations are
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
2
−
1
00000
···
0
u
1
u
2
u
3
u
4
u
5
u
6
.
u
9
u
10
u
1
u
2
u
3
u
4
u
5
/
−
12
−
1
0000
···
0
0
−
12
−
1
000
···
0
00
−
12
−
1
00
···
0
000
−
12
−
1
0
···
0
1
.
5
=
λ
0000
−
12
−
1
···
0
u
6
/
2
.
.
.
.
.
.
.
u
9
/
.
.
.
.
.
.
.
.
.
0
···
0000
−
12
−
1
2
u
10
/
0
···
00000
−
11
4
where
L
20
2
P
E I
0
λ
=
Write aprogram thatcomputes the lowest buckling load
P
of the column with
the inverse powermethod. Utilize the banded forms of the matrices.
18.
P
L
θ
3
L
k
L
θ
2
k
θ
1
k
The springssupporting the three-bar linkage are undeformedwhen the linkage
ishorizontal. The equilibrium equations of the linkage in the presence of the
horizontalforce
P
can be shown to be
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
=
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
653
332
111
θ
1
θ
2
θ
3
111
0 11
001
θ
1
θ
2
θ
3
P
kL
where
k
is the spring stiffness.Determine the smallest buckling load
P
and the
corresponding modeshape.
Hint
: the equationscan easilyrewritteninthe stan-
dard form
A
θ
=
λ
θ
, where
A
issymmetric.
19.
u
1
u
2
u
3
k
k
k
k
2
m
m
3
m
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