Publications

Calculating damping from ring-down using hilbert transform and curve fitting

Sumali, Hartono S.; Kellogg, Rick A.

A cantilever beam is released from an initial condition. The velocity at the tip is recorded using a laser Doppler vibrometer. The ring-down time history is analyzed using Hilbert transform, which gives the natural frequency and damping. An important issue with the Hilbert transform is vulnerability to noise. The proposed method uses curve fitting to replace some time-differentiation and suppress noise. Linear curve fitting gives very good results for linear beams with low damping. For nonlinear beams with higher damping, polynomial curve fitting captures the time variations. The method was used for estimating quality factors of a few shim metals and PZT bimorphs.