Determining natural frequency

Question

Having never done vibration analysis, I'm wondering if anyone has experience in determining the natural frequency of a solid using an accelerometer. Aside from knowing that we can produce a voltage signal through the accelerometer, and that we in some way need to condition this through a fourier transform, I am completely stumped.
Can anyone provide a simple explanation, and hopefully any more complex knowledge of how to go about solving this problem?
Thanks,
Justin
Just as a post note, I'm really completely unfamiliar with vibrations
analysis, and am hoping to learn enough through this process to really
understand the problem and its solution...
Any help is appreciated!
Message Edited by g0dam0ng1n53ct5 on 12-17-2009 09:01 AM

Answer 1

OK, I dug up the old code (I'm talking 1994 here).
The TRANSFER function is a statement of the relationship between the independent measurement (Y) and the driving force (X).
You hit point A with force X, and at point B, you see a movement Y.
The transfer function is dependent on structure geometry, materials, mounting, supports, maybe termperature, etc. 
That is frequency-dependent, so doing it in the frequency domain provides a lot of info at one time. 
Here are comments from my 1994 code:
       F(x)     F*(x)           |F(x)|^2
Sxx = ------ * -------     =   ----------   (no phase information)
        N         N               N^2
       F(y)     F*(x)
Sxy = ------ * -------
        N         N
                      Cross power spectrum          Sxy
Transfer function = ------------------------   =   -----
                         Power spectrum             Sxx
             | Sxy | ^2
Coherence = -------------
             Sxx  *  Syy
where:
  F(x) is the complex Fourier transform of the time domain signal x, and
  F*(x) is the complex conjugate of the Fourier transform of x, and
  N is the number of points in x.
Note that SXX is the magnitude squared.  It is faster to compute the square of the magnitude than it is to compute the magnitude. Although the complex-to-polar VI would look simpler on the diagram, it would take longer since it computes the magnitude proper, (an extra square-root operation), and it computes the angle (extra arc-tangent operations).
Since N^2 is a term in both Sxy and Sxx, and since we are dividing one by the other, we do not need to explicitly divide by N^2; it is cancelled automatically.
Here is the code to process a single channel:
I'm not sure of the comment "this is much faster..." anymore, as I've tested it recently and found it not the case.  But it was true in 1994. 
And here is the code to handle the actual Xfer function:
Note that I had an implicit rule that the first channel in the array was always the reference channel, i.e. the hammer (stimulus).  Any other channel(s) were response channels - you can get transfer functions between one stimulus point and any number of response points with one recording.
The middle section there is averaging: you may or may not want to do that.  It's averaging from several hammer blows.
What you get out is a complex spectrum (in the TRANSFER FUNCTION array).
At each frequency, there's a complex number (R+jI) that describes how well the vibration travels from point A to point B. 
If this function shows a clear peak at say, 583 Hz, then the structure in question is best at transferring vibration at that frequency.
If the MAGNITUDE of that peak is close to 1.0, then it's very resonant.  If the magnitude is much lower, it's very damped.
(If it's greater than 1.0... RUN!  It's about to come off it's mountings !)
You also get a COHERENCE spectrum, I'm not as well versed on the uses of that. 
Steve Bird
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