Forced Vibrations; Resonance
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Introduction |
Forced Vibration |
Amplitude of Forced Vibration |
Resonance and Resonant Frequency |
Bad Resonance |
Good Resonance |
Introduction
n Resonance is the tendency of a system to oscillate at larger amplitude at some frequencies than at others.
These are known as the system's resonant frequencies (or resonance frequencies).
At these frequencies, even small
periodic driving forces can
produce large amplitude
oscillations.
n Resonance phenomena occur with all types of vibrations or waves.
n In addition to mechanical resonance (the subject of this discussion) there is
Ø electromagnetic resonance
Ø resonance of quantum wave functions.
n Resonance was discovered by
Galileo Galilei with his
investigations of
pendulums and
musical strings in 1602.
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Forced Vibration
n
When
an alternating external force or motion is applied to a system.
n
Example: pushing
child on a swing
Ø Swing has natural frequency of
oscillation
Ø
Push at random frequency, little effect
Ø
Push at frequency = natural frequency, amplitude increases greatly |
 |
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Amplitude of Forced Vibration
n The system vibrates at the frequency of the external force, f
Ø f0 = (1/2 p)(k/m)1/2 = natural frequency
Ø The amplitude depends on the difference: f - f0
Ø Curve A is light damping and curve B is heavy damping
Ø As in the case of the swing above, the amplitude becomes large when f = f0
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 |
n When damping is small, increase in amplitude near f = f0 is very large
n This effect is known as resonance
n The natural vibrating frequency, f0, is known as its resonant frequency
Bad Resonance Examples
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 |
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Tacoma Narrows Bridge ("Galloping Gertie"), November, 1940 Washington state, wind frequency matched that of bridge |
Loma Prieta
earthquake of
Oct. 17, 1989 Nimitz Freeway, Oakland, Ca, due partially to resonance |
Good Resonance Examples
n Musical instruments
n Tuning a radio