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Lecture 12

AER 403 Lecture Notes - Lecture 12: Damping Ratio, AccelerometerPremium

5 pages62 viewsWinter 2015

Department
Aerospace
Course Code
AER 403
Professor
Fengfeng Xi
Lecture
12

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Logarithmic decrement
ln(x/x)ln[ent/en(td)]lnend  12 nd
Since
 2/(12)1/2
dn
then
  [2 /(12)1/2 ]2 /(12)1/2
nn
If δ is obtained from measurement, ξ can be determined as
2 21/2  /[(2)  ]
For ξ<<1
  2     / 2
Note that δ=(1/(n-1))ln(x1/xn)
c=ξc =ξ2mω Cn
26,
| 30
Example 8.4: damping determination
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From given recorded vibration response, it is required to determine the
damping ratio.
26, | 31
Example 8.4
Solution From the plot,
x1 = 0.85, x2 = 0.45, x3 = 0.25, τd = 15.5-3.5 = 12 (s)
δ = ln(0.85/0.45) = 0.64
or δ = (1/2) ln(0.85/0.25) = 0.63
ξ = δ/[(2π)2 + δ2]1/2 = 0.64 /[(2π)2 + 0.642] 1/2= 0.101
Or ξ = δ/(2π) = 0.64/6.28 = 0.102
(x1 and x2)
(x1 and x3)
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Overdamped-Nonoscillatory motion
• If ξ>1 (c>cC), it is overdamped, and the roots are s1,2 = [- ξ ± (ξ2 -
1)1/2]ωn
• Solution is given as
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