Page 17 - Vibrations 5

Using the first eigenvalue,

0.8 + 0.557 −0.4 0 1

( −0.2 0.6 + 0.557 −0.4 ) ( 2) = 0

0 −0.428 1 + 0.557 3

or

1.375 −0.4 0 1

( −0.2 1.157 −0.4 ) ( 2) = 0
0 −0.428 1.557 3

1.375 − 0.4 = 0
2
1

0.2 + 1.157 + 0.4 = 0
3
1
2
0.428 + 1.557 = 0
3
2
Leaving

= 3.437 and = −9.447
1
1
3
2
The mode shape for the frequency is,
1

1

= ( 3.437 ) for = √0.557
1
1
−9.447

Using the second eigenvalue,

0.8 − 0.808 −0.4 0 1

( −0.2 0.6 − 0.808 −0.4 ) ( 2) = 0
0 −0.428 1 − 0.808 3

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