Minimizing error in the logarithmic decrement method through uncertainty propagation

• A formal uncertainty analysis of the logarithmic decrement is presented.
• The analysis results are condensed into a single, reusable guide.
• The guide indicates the number of periods to use for a common range of uncertainties.
• The guide is then applied to experimental data derived from image processing.

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.