Linear viscous SDOF methods
SDOF Damping-Ratio Extraction
Use exact logarithmic decrement for an unforced exponential free decay, or the conventional half-power FRF estimate only for a stationary, isolated, lightly damped mode.
Method result
NASA/TM-2016-218227, Extracting Damping Ratio from Dynamic Data and Numerical Solutions, Table 1 and sections 1.1/A.2, identifies the common SDOF assumption. It marks logarithmic decrement exact for an unforced SDOF exponential decay and the measured-spectrum half-power formula approximate for ζ<0.05.
For an FFT magnitude FRF, fl and fu are selected at 1/√2 of peak amplitude. For a PSD/quadratic quantity, use one-half of the peak. The denominator is the measured peak-center frequency fp in this approximation—not an automatically known undamped natural frequency. NASA distinguishes the exact power-curve relationship from the commonly measured FRF approximation.
MIT OpenCourseWare separately teaches damping estimation from measured free response for an SDOF system.
No universal modal result: closely spaced modes, leakage, inadequate frequency resolution, noise, non-proportional/non-viscous or nonlinear damping, changing boundary conditions and non-stationarity require curve fitting or another validated modal-identification method. This page does not claim ISO 1940/21940 compliance.
