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.
Search for other works by this author on:
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)
$y=a0eiΩte−(c∕2m)t$
where Ω, the natural frequency of the damped point-mass spring system, is given by:
$Ω=ω02−c24m2$
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
$ζ=c∕cc,cc=2mω0$
In terms of the frequency (in Hz) and the damping ratio, the damped natural frequency is given by:
$f0′=f01−ζ2$
This content is only available via PDF.