ME 482

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Damped Forced Vibrations of Single Degree of
Freedom Systems
Single Degree of Freedom System with an applied
force f(t)
where f(t) can be of any form.
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Lets assume
Equation of Motion
Or, in another form
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Rotating Unbalance
? Speed of Machine (constant) e Its center of
mass is eccentric. m Mass of machine m0 Mass
of rotating component
Equation of Motion is given as
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Response due to Harmonic Excitation of Support
x Displacement of system y Displacement of
support
Equation of Motion
Defining z x - y, we get
Or,
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If we define, y Y sin (?t), then
Solution of this is calculated as before from z
Z sin (?t - ?)
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Response due to Multi-Frequency Excitations
Equation of Motion
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Solution
where
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Fourier Series Representation of Periodic
Functions
If the excitation force f(t) is a series
continuous function of period T, then
where
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An alternate form of Fourier series is given by
where
For the above system
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Particular (Steady-State) Solution