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# Natural Frequency from Nyquist Plots

## Natural Frequency from Nyquist Plots

(OP)
Please can someone shed light on Nyquist Plots?  Specifically how to read natural frequency and damping factor from them.

Claire

### RE: Natural Frequency from Nyquist Plots

You got a problem. The Nyquist plot doesn't show the frequency, you have to know what it is. Many analysers move a cursor along the trace and allow you to read off the frequency.

The damping factor can be defined in many ways, often in electronic work it is defined at the half power point.

On a pure SDOF mode this would be where the amplitude falls to 1/sqrt(2) of the maximum. This is the diameter of the circle, parallel to the real axis, and the bandwidth is simply the difference in frequency at the two ends of the diameter. The fractional bandwidth is deltaf/resonant frequency.

When you are analysing complex systems it is usually easier to work off the Bode plot for the whole frequency range, and then use the Nyquist plot to look at each mode, and the interaction between neighbouring modes.

Just thinking back to your first question, the resonant frequency is somewhere in the sector with the longest chordlength, for simple systems.

I strongly advise you to set up an analytical 2DOF model, and examine the behaviour where damping is high, and the resonant frequencies are similar. This may persuade you that Nyquist plots ain't all that useful in some circumstances.

Cheers

Greg Locock

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