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Optimizing Logarithmic Decrement Damping Estimation via Uncertainty Analysis

Publication ,  Conference
Little, JA; Mann, BP
Published in: Conference Proceedings of the Society for Experimental Mechanics Series
January 1, 2020

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.

Duke Scholars

Published In

Conference Proceedings of the Society for Experimental Mechanics Series

DOI

EISSN

2191-5652

ISSN

2191-5644

ISBN

9783030122423

Publication Date

January 1, 2020

Start / End Page

19 / 22
 

Citation

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Little, J. A., & Mann, B. P. (2020). Optimizing Logarithmic Decrement Damping Estimation via Uncertainty Analysis. In Conference Proceedings of the Society for Experimental Mechanics Series (pp. 19–22). https://doi.org/10.1007/978-3-030-12243-0_3
Little, J. A., and B. P. Mann. “Optimizing Logarithmic Decrement Damping Estimation via Uncertainty Analysis.” In Conference Proceedings of the Society for Experimental Mechanics Series, 19–22, 2020. https://doi.org/10.1007/978-3-030-12243-0_3.
Little JA, Mann BP. Optimizing Logarithmic Decrement Damping Estimation via Uncertainty Analysis. In: Conference Proceedings of the Society for Experimental Mechanics Series. 2020. p. 19–22.
Little, J. A., and B. P. Mann. “Optimizing Logarithmic Decrement Damping Estimation via Uncertainty Analysis.” Conference Proceedings of the Society for Experimental Mechanics Series, 2020, pp. 19–22. Scopus, doi:10.1007/978-3-030-12243-0_3.
Little JA, Mann BP. Optimizing Logarithmic Decrement Damping Estimation via Uncertainty Analysis. Conference Proceedings of the Society for Experimental Mechanics Series. 2020. p. 19–22.
Journal cover image

Published In

Conference Proceedings of the Society for Experimental Mechanics Series

DOI

EISSN

2191-5652

ISSN

2191-5644

ISBN

9783030122423

Publication Date

January 1, 2020

Start / End Page

19 / 22