Interpreting the FFT results of a structural vibration problem System: Cantilever beam type models, with an accelerometer on the end. The beam base is excited at various frequencies in harmonic fashion on a shake table. This results in vibration in the beam. The accelerometer is ICP type, and details here. This accelerometer connects to a compatible FFT analyzer, make OROS-34, details here. 

Results:
Graph of response - acceleration v/s time

 

Graph of FFT of above signal - acceleration v/s frequency

 

Problem:  I want to understand what the FFT of the original signal means. For example, I have heard that the FFT of the acceleration-time signal would give the natural frequency of the system, as the natural frequency would have the greatest contribution. So the spike in the graph of FFT should correspond to natural frequency. 

Can anyone suggest some reference for the theory above ? 

If this is true, then whatever be the base excitation, the natural frequency of the structure should not change, the spikes in the acc-freq curve for other frequencies should match this one. This also doesnt happen. 

Better images: 

Graph of acceleration vs time for excitation freq of 15Hz with displacement amplitude of 50mm. 


Graph of FFT of previous curve, i.e. acceleration vs freq


The vertical red line in the image FFT image is a marker for reading X and Y coordinates at peak. 

As per the suggested methods and theory, the frequency of oscillation of the structure should be same as forcing freq, however the FFT peak is far from that. 

Promise: No more edits. :)
If the beam is under the excitation of a sweeping wave, then the peak(s) in the FFT of the response is not necessarily the natural frequency of the beam. As an extreme, if you are exciting the beam with a constant frequency omega, your FFT of the acceleration time history will have a dominant peak at omega.

However, if the beam is under random excitation, or an impulse, the first peak in you FFT will be your natural frequency. And there is a method named "peak-picking method" to find out the natural frequency. Here is a reference for that: Google books