# 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. :)

• I don't know if you're a member of the www.researchgate web site, but if you are then maybe the following will be of some value to you: <researchgate.net/publication/…> – Richard Lyons Aug 8 '15 at 0:56
• Can I please ask if there was a resolution to this question? – A_A Oct 1 '16 at 9:28

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

• I couldnt understand the concepts of transfer function etc. associated with the method shown above, however the reference took me others, that explained a little more about the subject. – Chintan Pathak Jul 5 '15 at 11:53
• Check this one (engineering.purdue.edu/UCIST/TeachingModules/UG%20Exercises/…) out and it might help you understand the idea of a transfer function. – Dainy Jul 5 '15 at 21:06
• This one seems a good answer. The beam will vibrate at the frequency you impose to it. It will not change its vibration to the natural frequency. (It will only pick the natural frequency if you set an initial displacement and then let it loose). -- If your imposed vibration is the natural frequency, you will see a siginificant increase in amplitude. ----- So, if you try several different frequencies and perform one FFT for "each" of these frequencies, the FFT with the highest peak will very likely be the closest to the first natural frequency. – Daniel Möller Jul 27 '16 at 19:43
• Another easier way to find natural frequencies is to turn off the oscilator and just hit the beam once. A beam has several natural frequencies, and depending on the direction you hit and where you hit, one of them will prevail (but you will probably see traces of the others). Normally, the two most important ones are vertical and horizontal vibrations. But there may also be torsional vibration and their harmonics. Longitudinal vibrations also exist (compression-tension) – Daniel Möller Jul 27 '16 at 19:47

Vibration analysis is often done using the steady state response of the system. I presume your upper time domain graph is the output of the system you're trying to measure, based on one of the harmonic inputs. In other words, you're hitting your cantilever beam base with a series of harmonic excitations (eg: input 1f, measure output/take FFT, input 2f, measure output/take FFT, input 3f, measure output/FFT, etc.) similar to the description in the following link (see section 5.4.6):

http://www.brown.edu/Departments/Engineering/Courses/En4/Notes/vibrations_forced/vibrations_forced.htm

So the FFT results should show you the amplitude versus frequency response (similar to the graph shown in the link), from which you can obtain the natural frequency and damping coefficient of your system.

But it should be cautioned that vibration analysis is a complex and wide-ranging field. There is a lot of specialized knowledge for different structures, machinery, etc., and your methods should be appropriate to the problem.

In order to check system's resonance, we should get FRF(frequency response function), the ratio between input fft and output fft. Output signal's fft depends on input signal's signature. Only with fft of output signal, we can't insist the pick of frequency is resonance.