
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 ...