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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
Section 7.2: Response to Random Loads
7.4. Consider the two degree-of-freedom system shown in Figure 7.1 where F
1
= 0 and, in addition to
F
2
, random force F
3
is applied to the second mass. The force spectrum is given by
[S
F F
(ω)] =
S
F
2
F
2
(ω) S
F
2
F
3
(ω)
S
F
2
F
3
(ω) S
F
3
F
3
(ω)
.
Derive an expression for the matrix response spectrum [S
XX
(ω)] in terms of the force spectrum, the
modal matrix, and the matrix frequency response function [H ()].
Solution: The transfer function H
ij
(ω) relates the i
th
response to force applied at the j
th
coordinate. The
transfer function matrix is given by
(
¯
H (ω)
)
=
H
11
H
12
H
12
H
21
H
22
H
22
.
Since, F
1
= 0, the spectral densities are all equal ...
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Publisher Resources

ISBN: 9781439849897