Page 7 - Vibrations 5
P. 7
Multi-degree of freedom systems
A system with several components each with their own
resonance is more representative of a real machine.
Consider the free vibrations of the two masses which have
F 1 acting on the first and F 2 acting on the other.
These can be two components within a mechanical
structure which are attached to each other.
̈ + ( + )̇ − ̇ + ( + ) − =
2 2
1
1
2
2 2
1
1
1
2
1 1
̈ − ̇ + ( + )̇ − + ( + ) =
2
3
2 1
2
3
2
2 1
2
2
2 2
1 0 ̈ 1 + 2 − 2 ̇ 1 + 2 − 2 1 1
1
1
( ) ( ) + ( ) ( ) + ( ) ( ) = ( )
0 2 ̈ 2 − 2 + 3 ̇ 2 − 2 + 3 2 2
2
2
These are now coupled equations as you would expect, as
one mass moves the other will as well.
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