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# NCEES #533 on 2008

## 5 posts in this topic

This is the unbalanced drum problem. Anyone understand it? This is the one problem I couldnt even get a grasp of how they arrived at the answer! They show charts and then whammo the answer. Not enough explanation for me anyway.

Anyone?? Where do they get the damping ratio of 0.5 even?

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Please post the question in detail

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I figured someone would ask that..... Here goes it...

A 24 inch diameter rotating drum is part of a machine that weighs 1 ton and will operate at 10,000rpm. The balance specification calls for an unbalance no greater than .3 oz-in. There are vibration isolations mounts on each of 4 corners of the platform supporting the machine. The system has a natural frequency of 17hz, and damping has been chosen as half the critical damping value.

Unknown to anyone during installation a 1/2lb bolt was left inside the 24" diameter drum of the machine. assume friction causes the bolt to act as if it were attached to the rotating drum. The max displacment amplitude of the steady -state response occurse at a frequency (as a percentage of the natural freq) that is most nearly:

a 71%

b 100%

c 141%

d 200%

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Eq. 58.4 defines Damping ratio. C is the damping coefficent and Cc is the critical damping. In this problem, since damping is half the critical damping, C equals half of Cc. Sustituting these values in Eq. 58.4 gives damping ratio as 0.5.

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Figure 58.17. For damping ratio = .5 and TR = 1.0, r = 1.41. This made sense to me at one point in time. Now I'm trying to retrace my logic.