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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
In the presence of damping but without external forces, the solution to the linear vibration problem takes the form (compare with free vibration in Chapter 2)  
y=a0eiΩte(c2m)t
where Ω, the natural frequency of the damped point-mass spring system, is given by:  
Ω=ω02c24m2
When the damping coefficient c > 2m ω0, energy dissipation is so large that vibration motion cannot be sustained. The motion becomes that of the exponentially decay type instead of vibration. The value of c at which this happens ( cc = 2mω0) is called the critical damping. The more commonly used damping ratio is the damping coefficient expressed as a fraction of its value at critical damping  
ζ=ccc,cc=2mω0
In terms of the frequency (in Hz) and the damping ratio, the damped natural frequency is given by:  
f0=f01ζ2
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