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Probabilistic Models for Dynamical Systems, 2nd Edition
book

Probabilistic Models for Dynamical Systems, 2nd Edition

by Haym Benaroya, Seon Mi Han, Mark Nagurka
May 2013
Intermediate to advanced content levelIntermediate to advanced
764 pages
6h 43m
English
CRC Press
Content preview from Probabilistic Models for Dynamical Systems, 2nd Edition
The characteristic equation is given by
det
k
11
2
k
12
k
21
k
22
2
= 0.
For our problem, the natural frequencies are ω
1
= 19.1 rad/s and ω
2
= 35.7 rad/s. The modal matrix is
given by
[P ] =
1
2
1 1
1 1
.
The force spectrum is given by
S
F F
(ω) =
1
2π
−∞
R
F F
(τ) e
iωτ
=
T
T
1
|τ|
T
e
iωτ
dτ.
Then, the force spectrum is
S
F F
(ω) =
4 sin
2
(ωT/2)
T ω
2
.
The next figure show the force spectrum.
S
F F
(ω) for T = 2.
The response spectrum is given by
[S
XX
(ω)] = [H
(ω)] [S
F F
(ω)] [H (ω)]
T
,
where
[H (ω)] =
[K] ω
2
[M]
1
or, equivalently the response spectrum is given by
[S
XX
(ω)] = [P ] [H
(ω)] [P ]
T
[S
F F
(ω)] [P ] [H(ω)] [P ]
T
,
where H
11
(ω) = 1/
ω
2
ω
2
1
.
211
7.12. Two disks with mass ...
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Publisher Resources

ISBN: 9781439849897