Page 18 - Vibrations 5

or

−0.008 −0.4 0 1

( −0.2 −0.208 −0.4 ) ( 2) = 0

0 −0.428 0.192 3

This gives,

−0.008 − 0.4 = 0 or = 0.02
2
2
1
1
Also

−0.428 + 0.192 = 0 or = 0.044
1
2
3
3
The mode shape for the frequency is,
2
1

= ( 0.02 ) for = √0.808
2
2
0.044

Using the third eigenvalue,

0.8 − 2.149 −0.4 0 1

( −0.2 0.6 − 2.149 −0.4 ) ( 2) = 0
0 −0.428 1 − 2.149 3

or

−1.349 −0.4 0 1

( −0.2 −1.549 −0.4 ) ( 2) = 0

0 −0.428 −1.149 3

This gives,

−1.349 − 0.4 or = −3.372
1
2
2
1
Also,

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