Chap 3' Harmonically Excited Vibration

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Chap 3. Harmonically Excited Vibration
Consider pure harmonic excitation for
understanding the behavior of a simple
system
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Nondimensional Amplitude
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Complex Frequency Response
Frequency Response Function (System Transfer
Function)
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3.2 Rotating Unbalance
Equation of motion is
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3.3 Rotor Unbalance
Static Unbalance
Dynamic Unbalance
Example 3.3-2 A thin disk is supported on spring
on spring-mounted bearings. When run at 300 rpm
counterclockwise (ccw), the original disk
indicates a maximum amplitude of 3.2 mm at 30
ccw from a reference mark on the disk. Next, a
trial weight of 2.5 oz is added to the rim at
143 ccw from the reference mark, and the wheel
is again run at 300 rpm ccw. The new amplitude
of 7 mm is then found at 77
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3.4 Whirling of Rotating shafts
Whirling rotation of the plane in which the
center of geometry is not the
axis of rotation
Whirling of shaft
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Phase of different rotation speeds
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3.5 Support Motion
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3.6 Vibration Isolation To protect a delicate
object from transmitted forces,
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3.7 Energy Dissipated by Damping Damping is
present in all system internal molecular
friction Structural damping sliding friction
Coulomb damping fluid resistance Viscous
damping Since mathematical description of damping
is quite complicate, simplified damping modal
such as viscous has been developed to evaluate
the system response.
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3.8 Equivalent Viscous Damping Equivalent
damping Ceq equate the energy dissipated by the
viscous damping to that of the nonviscous damping
force with assumed harmonic motion
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3.9 Structural Damping From experiments of most
structural metals, damping is independent of the
frequency and proportional to the square of the
amplitude
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Compare to viscous damping at resonance
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3.10 Sharpness of Resonance
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3.11 Vibration Measuring Instruments
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3.11 Vibration Measuring Instruments