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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
8.17. Consider a uniform bar in bending, simply supported at both ends and subjected to the excitation,
f(x, t) = F (t)δ(x L/2),
where F (t) is an ergodic random process with ideal white noise power spectral density, and δ(xL/2) is
a spatial Dirac delta function. Derive expressions for the cross-correlation function between the response
at the points x = L/4 and x = 3L/4 and for the mean-square value of the response at x = L/4. Assume
constant m, c, and EI along the beam.
Solution: The equation of motion and boundary conditions are given by
EI
4
y
∂x
4
+ c
∂y
∂t
+ m
2
y
∂t
2
= F (t) δ (x L/2) for 0 < x < L
y (0, t) = 0
EI
2
y
∂x
2
0,t
= 0
EI
2
y
∂x
2
L,t
=
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Publisher Resources

ISBN: 9781439849897