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Optimizing Logarithmic Decrement Damping Estimation via Uncertainty Analysis

  • Jared A. LittleEmail author
  • Brian P. Mann
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)

Abstract

The logarithmic decrement method is perhaps the most common technique for estimating the damping ratio of linear systems with viscous damping. The approach directly relates the damping ratio to two samples collected from peaks of a recorded free oscillation. These peaks are separated by one or more oscillation periods and are inherently influenced by experimental uncertainty. Literature on the method indicates that improved estimates are sometimes obtained with more periods between samples. However, it is unknown when improvements can be expected for a given data set because there is a trade-off between the chosen number of periods and measurement noise. A guideline for selecting the number of periods which minimizes uncertainty in estimated damping is desired.

In this work, an analytical expression is derived for the optimal number of periods between peaks. This expression, obtained from an uncertainty analysis of the logarithmic decrement equation, is shown to be a function of only one system parameter: the damping ratio. This suggests that for linear systems with viscous damping there is a unique, damping-dependent period choice which guarantees minimum uncertainty in the estimated damping ratio. This result is used to obtain an optimal amplitude ratio which offers a simple, accurate, and easy to implement guideline for selecting a second sample. The derived expressions are applied to a set of numerical systems to confirm their validity.

Keywords

Logarithmic decrement Uncertainty analysis Optimization System identification Damping 

References

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    Meirovitch, L.: Fundamentals of Vibrations. Waveland Press, Long Grove (2010)Google Scholar
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    Tweten, D.J., Ballard, Z., Mann, B.P.: Minimizing error in the logarithmic decrement method through uncertainty propagation. J. Sound Vib. 333(13), 2804–2811 (2014)CrossRefGoogle Scholar
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    Hughes, I., Hase, T.: Measurements and Their Uncertainties: A Practical Guide to Modern Error Analysis. Oxford University Press, Oxford (2010)zbMATHGoogle Scholar

Copyright information

© Society for Experimental Mechanics, Inc. 2020

Authors and Affiliations

  1. 1.Department of Mechanical Engineering and Materials Science, Pratt School of EngineeringDuke UniversityDurhamUSA

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