Optimizing logarithmic decrement damping estimation through uncertainty propagation

This work derives an analytical expression for the optimal number of periods between samples when estimating damping using the logarithmic decrement method. This expression, obtained from an uncertainty analysis of the method's principal 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 corresponding to minimum uncertainty in the estimated damping ratio. This result led to the discovery of a constant optimal amplitude ratio offering a straightforward guideline that can be applied by the experimenter to obtain damping ratio estimates with minimum uncertainty. The derived expressions are applied to a series of numerical and experimental systems to confirm their validity.

Duke Scholars

Author Brian Mann Thomas Lord Department of Mechanical Engineering and Materia ...