ME 563 Mechanical Vibrations Lecture #3
Transcript of ME 563 Mechanical Vibrations Lecture #3
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ME 563 Mechanical Vibrations
Lecture #3 Calculating System Parameters
(Equivalent Mass/Stiffness)
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Pitching oscillation
Surging oscillation
Bouncing oscillation
F = M a Estimating System Parameters
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Equivalent Stiffness Example
K
L L/2
P
=
Keff
Methods for calculating equivalent stiffness:
- Energy methods - Strength of materials - Experimentation
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Equivalent Stiffness (Energy)
K
L L/2
P
=
Keff
A
B P
B
Model determines the “perspective” for calculating equivalent stiffness (P applied at point B).
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Equivalent Stiffness Example K
P
No slip
3D/4 D
=
Keff
A B
A
P
4
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Equivalent Stiffness Example
E2,I2,L2
P
=
Keff B
P B
1
2 E1,A1,L1
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Equivalent Mass Example
M, Icm
= Meff
xB K
L L/2 cm
B xB
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Equivalent Mass Example K
No slip
3D/4 D
= cm
B Meff
xB
M, Icm
7
xB
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Equivalent Parameters Example 8