The half-power bandwidth method can be used to estimate the damping ratio and corresponding Q value from the frequency response function of a structure which has been excited by base motion or an applied force. The structure may be a multi-degree-of-freedom (MDOF) system as long as the modal frequencies are separated by a sufficient frequency margin so that the spectral peaks are distinct.

Here are some resources.

half_power_bandwidth.pdf

notes_on_frequency_resolution.pdf

An Introduction to Frequency Response Functions: frf.pdf

(Download and then reopen to see full equations.)

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Matlab GUI scripts:

Force or Base Excitation, with Frequency Response Function Magnitude: half_power_bandwidth.zip

Force Excitation, with Complex Frequency Response Function: half_power_bandwidth_fc.zip

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Here is a Matlab script that will perform a modal curve-fit for a multi-degree-of-freedom system. The script extracts modal frequencies and damping from a complex FRF. mdof_frf_curvefit.m

Supporting function: mdof_frf_curvefit_phase1.m

The method in these scripts is described in: mdof_frf_curvefit.pdf

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See also:

Damping Value Conversion Calculator

Vibrationdata Signal Analysis Package – modal FRF option

Vibration Isolation Basics

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Here is a newsletter with an example of the half-power bandwidth method applied to the Ares-1X roll-out: May2010_NL.pdf

– Tom Irvine

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