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### Logarithmic Decrement

Course: CIVIL ENGI CE 573, Fall 2005
School: Purdue
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Word Count: 101

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573: CE Structural Dynamics Logarithmic Decrement Matlab Example &gt;&gt; u1 = udata(2) u1 = 96.5749 &gt;&gt; u2 = udata(10) u2 = 83.9971 (Located from the plot.) (Located from the plot.) &gt;&gt; delta = log(u1/u2) delta = 0.1395 u = log k , k = 1. uk +1 &gt;&gt; xi = delta/sqrt(delta^2 + 4*pi^2) xi = 0.0222 &gt;&gt; Td = (10-2)*0.25 Td = 2 &gt;&gt; w =...

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573: CE Structural Dynamics Logarithmic Decrement Matlab Example >> u1 = udata(2) u1 = 96.5749 >> u2 = udata(10) u2 = 83.9971 (Located from the plot.) (Located from the plot.) >> delta = log(u1/u2) delta = 0.1395 u = log k , k = 1. uk +1 >> xi = delta/sqrt(delta^2 + 4*pi^2) xi = 0.0222 >> Td = (10-2)*0.25 Td = 2 >> w = (2*pi)/(Td*sqrt(1-xi^2)) w = 3.1424 (About 5% error in .) >> = u7 udata(52) u7 = 38.4136 >> delta = 1/(7-1)*log(u1/u7) delta = 0.1537 >> xi = delta/sqrt(delta^2 + 4*pi^2) xi = 0.0244 >> Td = (52-2)*0.25/6 Td = 2.0833 >> w = (2*pi)/(Td*sqrt(1-xi^2)) w = 3.0168 (About 0.5% error in .) >> approxxi = delta/(2*pi) approxxi = 0.0245 (Not much change in value of .) u 1 = log k , k = 1& n = 6. n uk + n (Recall that t for each sample is 0.25.)
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