2. Estimating Frequency & Damping

In many cases (especially with noisy data), it is better to build up a list of modal frequencies & damping in the Modal Parameters spreadsheet by curve fitting in small cursor bands using as few modes as possible.  In this example, since the FRFs are relatively noise free, frequency & damping for all 10 resonance peaks will be estimated at once.

Fitting One FRF

To estimate frequency & damping by curve fitting only the first M#,

Notice that the graph background changes color to indicate the selected M#.

Frequency & damping estimates for 10 modes will be listed in the modal parameters spreadsheet, as shown below.

Frequency & Damping Curve Fit of One Trace.

Vertical Frequency Lines

The frequency estimate for each mode in the Modal Parameters spreadsheet is displayed as a vertical line on the Mode Indicator graph.

Half Power Point Damping

The damping estimate for each mode is displayed as a horizontal line crossing the vertical frequency line where,

Width of the Damping Line = 2s, s = half power point (or 3 dB point) damping  (in Hz)

The half power point damping (2s) is approximately equal to the width of the resonance peak at 70.7 % of the FRF peak magnitude value.  Alternatively, the half power point damping (2s) is approximately equal to the width of the resonance peak at half (50%) of the FRF peak magnitude squared.  The FRF magnitude squared is considered a power quantity, hence the name half power point damping.

Zoomed Display of Frequency & Damping Estimates.

Global Frequency & Damping Estimates

Even though frequency & damping can be estimated from one FRF, more accurate estimates are usually obtained by doing a Global curve fit on all (or several selected) FRFs.

Now frequency & damping estimates extracted by curve fitting all 99 FRFs, are added to the Modal Parameter spreadsheet.

Global Frequency & Damping Estimates from 99 FRFs.