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ME 563 Mechanical Vibrations
Lecture #3 Calculating System Parameters
(Equivalent Mass/Stiffness)
Pitching oscillation
Surging oscillation
Bouncing oscillation
F = M a Estimating System Parameters
1
Equivalent Stiffness Example
K
L L/2
P
=
Keff
Methods for calculating equivalent stiffness:
- Energy methods - Strength of materials - Experimentation
2
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).
3
Equivalent Stiffness Example K
P
No slip
3D/4 D
=
Keff
A B
A
P
4
Equivalent Stiffness Example
E2,I2,L2
P
=
Keff B
P B
1
2 E1,A1,L1
5
Equivalent Mass Example
M, Icm
= Meff
xB K
L L/2 cm
B xB
6
Equivalent Mass Example K
No slip
3D/4 D
= cm
B Meff
xB
M, Icm
7
xB
Equivalent Parameters Example 8
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