MIDTERM EXAM REVIEW
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REVIEW
Excitation force 50N
normal to face
m=6.66kg
Modal damping 5%
k=10000N/m
m 081.SLDASM
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3
Natural frequency with the equations of motion method
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Natural frequency with the energy method
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What angular and linear damping will give us 5% modal damping?
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Steady state displacement
amplitude at load application;
excitation with resonant
frequency
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Natural frequency
m 081.SLDASM
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Steady state displacement
amplitude at load application;
excitation with resonant frequency
m 081.SLDASM
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Problem 1
Vibration isolation
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Problem 2
Vibration isolation
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Problem 3
Oscillating load 10N
m = 10kg
k = 1000N/m
c= 5Ns/m
Base
Calculate amplitudes of displacement, velocity and acceleration at resonance
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Problem 3
Solution method 1
Method of
undetermined
coefficients
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Problem 3
Solution method 2
Using the formula
Inman p. 116
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Problem 3
Solution method 3
SW Simulation
Amplitude of
displacement at
resonance 0.2m
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Problem 4
ω2 excitation
Total mass
m = 450kg modeled as a distributed mass
Material
custom with very low density
Dynamic unbalance
m0e = 0.35kgm
Each spring
Damping
8.85kN/m
ζ = 30%
Find the amplitude of displacement ω = 100rad/s
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Problem 4
Solution method 1
Method of undetermined
coefficients
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Problem 4
Solution method 2
Using the formula
Half amplitude of vibration for ω >> ωn
Even though 100rad/s is not “much” large than the natural frequency)
= 0.00067m
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Problem 4
Solution method 3
Using SW Simulation
washing_machine.SLDASM
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Problem 5
A 45kg machine is placed at the end of a 1.6m cantilever beam: E=200,000MPa, b=0.1m, h=0.1245m
We assume that the beam is weightless (questionable assumption)
As it operates it produces a harmonic force of magnitude 125N. At what operating speeds will the machine’s steady
state amplitude be less than 0.2mm?
125N
 
2.35 e 6
 228
45
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Problem 5
Analytical solution
Inman p. 119
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Problem 5
Numerical solution
ω/228 < 0.85
ω/228 < 1.13
ω < 194 rad/s
ω < 257 rad/s
f < 30.8 Hz
f < 40.9 Hz
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Problem 6
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Problem 7
at least
So we need to add at a mass
of at least 171kg to the turbine
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