Minimizing error in the logarithmic decrement method through uncertainty propagation |
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Authors: | Dennis J. Tweten Zach Ballard Brian P. Mann |
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Affiliation: | Mechanical Engineering and Materials Science Department, Duke University, Durham, NC 27708, United States |
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Abstract: | Logarithmic decrement is a well known approach for estimating the damping ratio from a time history. This paper uses uncertainty propagation to unveil how uncertainties in different quantities can impact damping ratio estimates. More specifically, the trade-off between the number of periods N between the first and final peaks and measurement noise is addressed. The insights gained from this analysis are condensed into a single graphic or guide which provides the ideal number of periods N to use for a common range of measurement uncertainties and damping ratios. The guide is then applied to experimental data derived from image processing to estimate the damping ratio. |
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