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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
7.7. Consider a three degree-of-freedom system with property matrices:
[m] =
m 0 0
0 m 0
0 0 m
, [c] =
c 0 0
0 c 0
0 0 c
, [k] =
3k k k
k 3k k
k k 3k
.
Determine the natural frequencies and the modal matrix. Assume that mass 1 is subjected to a white
noise random force of intensity S
0
. Find the mean-square value of the displacement response of mass one,
R
X
1
X
1
(0) . What is the percent error if the autocorrelation functions are approximated using Equation
7.42?
Solution: From the eigenvalue problem
[k] ω
2
[m]
{u} = {0},
the eigenvalues and eigenvectors are given by
ω
2
m
k
= 1, 4, 4,
where the last two eigenvalues are repeated. The eigenvector associated ...
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Publisher Resources

ISBN: 9781439849897