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# Flow Induced Vibration of Power and Process Plant Components: A Practical Workbook

By
M. K. Au-Yang, Ph.D., P.E.
M. K. Au-Yang, Ph.D., P.E.
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ISBN-10:
0791801667
No. of Pages:
494
Publisher:
ASME Press
Publication date:
2001
The motion represented by the equation
$y(t)=a0cosωt+b0sinωt$
or, in more compact complex variable notation,
$y(t)=a0eiωt$
is called simple harmonic motion. Most vibrations and noise we encounter belong to the category of linear vibration and consist of a linear combination of simple harmonic motions of different amplitudes, frequencies and phases. The frequency of a point mass-spring system is given by:
$ω=kmradian∕s$
The frequency in cycles/s, or Hz, is related to the frequency in radians/s by,
$f=ω2πHz$
The instantaneous velocity and acceleration of a vibrating point mass is given by:
$V(t)=ẏ(t)=iωy(t)$

$α(t)=ӱ(t)=−ω2y(t)$
The velocity of propagation of a wave is given by:
$c=fλ$
Vibrations can be represented in the time domain (time histories) or in the frequency domain (power spectral densities). Both contain the same information.
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