# Intermittent Harmonics, Is there a physical explanation?

I am doing some frequency analysis of a vibration signal from a spinning rotor,

I am expecting to see peaks corresponding to the rotational frequency of the rotor. So the fundamental frequency should be ~0.7Hz, then I am assuming I should then see multiples of this corresponding to the harmonics?

I can clearly see peaks at ~ 1.4Hz, 2.8Hz, 3.5Hz, and 4.2Hz but nothing at 2.1Hz which I cant understand

I am not sure whether the explanation for this can be explained physically or if its related to my sensor setup / analysis methods? I dont think it is related to the frequency resolution since this is around 0.03 Hz which seems suitably low.

It seems likely to me that there is some kind of weighting to specific harmonics and the 2.1Hz harmonics is somehow damped but I can't think why this would be the case.

• You display several traces in your plot without explanation – user28715 Aug 12 '19 at 19:58
• @StanleyPawlukiewicz Well I don't think I can give away what specifically this is, and I also don't think it's important to my question. But you can just assume each trace represents a different amount of power given to the rotor if you want – Stephen Jackson Aug 13 '19 at 4:41
• how would you know what is is important? – user28715 Aug 13 '19 at 8:55
• Because each Trace is just a slightly different version of the same thing, if it makes you happy you can just pretend I put up a graph with just one of those lines – Stephen Jackson Aug 13 '19 at 12:11
• I’d actually be happier if you plotted is a loglinear scale. – user28715 Aug 13 '19 at 12:19

You have guessed it right. But before an explanation, you should make sure that your measuring setup is not the cause of this observation.

The fact that your fundamental frequency is 0.7 Hz. does not mean that you should see all harmonics of that frequency at 1.4 Hz., 2.1. Hz, 2.8 Hz. etc...

And furthermore, even if you would see those harmonics, their weights would most typically be different as suggested by the continuous-time Fourier series analysis of periodic waveforms.

The physical explanation is that your mechanical rotating system as a whole can be (approx) modeled as an LTI system with a self-frequency response composed of resonating or damping frequency modes...

And it seems that at 2.1 Hz., the system is not able to vibrate enough, some damping must be happening.

Nothing further can be stated at this point with the given information.

It's hard to tell from the picture but it looks like you have mainly even harmonics.

Even and odd harmonics have fairly different root causes. Loosely speaking, harmonics are caused by a non-linear input output relationship somewhere in your system. Even harmonics are caused by asymmetries, i.e. $$y(x) \neq -y(-x)$$. Odd harmonics are caused by the relation ship being "not flat" but still symmetric.

It's pretty common to have odd harmonics without even ones, but even without odd is more unusual. Maybe you have them, but they are too low in level to stick out over the noise floor.