Resonance with sidebands - need explanation

[dculp1]

The attached file shows the frequency response for a metal plate (in air) that is being driven at the center resonance by a source that is nominally sinusoidal. The measured amplitudes are perpendicular to the plane of the plate. Some of the amplitudes are approximately 90 degrees out of phase (i.e., when some amplitudes are maximum, others are zero and vice versa).

What might be causing the two small sidebands? Could these be some kind of nonlinear effect? Could these have anything to do with the amplitude phase shift along the plate? (Although these sidebands could be true resonances, I am somewhat skeptical because of their symmetry with respect to the main resonance.)

Thanks,
Don Culp

 

[GregLocock]

When you get phase angles of 90 degrees you are seeing energy transferred, so are starting to violate some of the assumptions in a simple mode shape.

I don't know how many dB those sidebands are relative to the main peak -20 dB or -40 dB? I'd be seriously into don't worry about it territory in that case, from a practical perspective.

Sorry, no specific advice, be interesting to hear other people's opinions.




Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[electricpete]

Two thoughts.

1 - Sidebands can occur when a pure sinusoid is processed with a finite length window. For a rectangular window, the first sidebands are 2.5 bins on each side of the center frequency.
What type of window did you use and how many bins are those sidebands away from the center frequency? And as Greg asked, how many db down?

2 - Are you sure your excitation is a constant frequency. Small frequency modulation shows up as sidebands around the fundamental frequency (sideband spacing is the modulating frequency, just like for A.M.).


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[dculp1]

The magnitude of the center resonance is approximately 10x that of the sidebands. The frequency difference between the lower sideband and the center resonance is 250 Hz; for the upper sideband this difference is 225 Hz. (These may not be completely accurate since the frequency was only sampled at every 25 Hz.)

The frequency scan also shows a resonance at 250 Hz. Would this explain the sidebands?

electricpete -

Can you explain what a "bin" is?

When you say that "a pure sinusoid is processed with a finite length window", is this sinusoid the driving sinusoid or the pickup signal that was used to create the frequency response plot?

GregLocock --

The plate is longer than it is wide. With the 90 degree phase shift, the animated modeshape looks somewhat like a wave that is traveling along the length, except that there is a node between adjacent maxima. I don't think that energy is being transferred because the plate is vibrating in air (i.e., essentially no load).

I'm concerned about the sidebands because the measured modeshapes are different than those predicted by FEA. Although FEA indicates low stress, fatigue failures have occurred.

Don Culp

 

[electricpete]

I think we can pretty much rule out my first item.

When you say that "a pure sinusoid is processed with a finite length window", is this sinusoid the driving sinusoid or the pickup signal that was used to create the frequency response plot?

It would be your pickup signal. I was assuming it might be a sinusoid and the sidebands might be an artifact of processing. But based on the further info you provided, it is apparently not the case.....

Can you explain what a "bin" is?

My term bin width is related to the frequency resolution in an FFT. Something like
BW = (Fsample /2) / (N/2) where N and Fsample are number of points and sample frequency input to the FFT. You said the frequency was "sampled" at 25hz and I understand that as equivalent to what I called bin width.

You also said the sideband spacing is in the neighborhood of 250hz. That puts the sidebands around 10 bin-widths out from the center peak... much too far to be related to windowing (based on absence of other peaks closer and farther... would only make sense to me if this was the first sideband). [A correction to my earlier comment - first sideband at approx 2.5 bin-widths on either side of center corresponds to Hanning window, not rectangular... rectangular is only 1.5). Also, rectangular window sidebands drop to 10% of the center at about 5 bin widths out. Most of the other windows are far below 1% of center at 5 bin widths out. Again, there is lots to indicate these are not just an artifact of your window and disprove my item #1.

So you have 250hz sidebands around some high frequency (? 2000hz?). And then you have 250hz signal all by itself. I think there is something else going on in your system at 250hz. Some guesses:

One thing could be torsional oscillation at 250hz. The torsional oscillation causes the frequency modulation and sidebands as discussed above. There can be a small degree of coupling of torque to radial vibration which results in the 250hz signal all by itself. What do you have driving this?

Another thing could perhaps be linear vibration of some part of the system at 250hz which modulates the higher 2000hz frequency vibration somehow. Maybe change in alignment of a 2000hz rotating shaft when one of the connected components is vibrating at 250hz.


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[VibeAC]

Are you really "sampling" at 25Hz, or are you referring to the frequency resolution? Fsamp=25Hz is not fast enough for the frequencies you are talking about.

I could see how the lower peak might be due to aliasing, but not the higher one.

Andrew Gorton, MSc
Noise & Vibration Consultant

http://www.PapadimosGroup.com

 

[MikeyP]

Is this the response to a single frequency sine excitation or the response of a sine sweep across a resonance?

If it is a single frequency, then there are clearly some leakage issues.

How are you getting the mode shape? is it the operating deflection shape at this single frequency? How far away are other modes from this one? Is it just a flat plate? how is it supported? Is the plate mounted in a frame?

M

--
Dr Michael F Platten

 

[electricpete]

My two cents fwiw (sorry if I am butting in the wrong place)

dculp1 is not referring to a 25hz sample rate. He is referring to a 25hz bin width.

There is no window that comes anywhere close to having 10% magnitude at 10 bin widths outside of the center frequency. So it doesn't look like leakage to me. It looks like more than single-frequency excitation of a linear system. Requires non-linearity or modulation.



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[dculp1]

electricpete --

<< Are you sure your excitation is a constant frequency. Small frequency modulation shows up as sidebands around the fundamental frequency (sideband spacing is the modulating frequency, just like for A.M.). >>

The excitation is nominally sinusiodal at the center resonance. However, I suppose there could be some other small drive components at other frequencies. It may be of interest that the frequency response data shows a resonance at approximately 250 Hz, which is also approximately the separation of the sidebands from the main resonance. It's amplitude is ~1/2 that of the side band amplitudes (but see my comments below). FEA shows a bending resonance at ~250 Hz which partially involves the support structure. Could this be the modulating frequency? (Note: the main resonance is between 20 kHz and 50 kHz. I have the exact value but can't be more specific.)

The drive is piezoelectric.

The frequency response data is at every 25 Hz. The data is from an outside source so I don't know the sample rate. The response data actually extends to approximately 2x the main resonant frequency. Excluding the sidebands, no other resonances can be detected except the one at ~250 Hz (although FEA shows many other resonances).

When I said "The magnitude of the center resonance is approximately 10x that of the sidebands", this was taken from the response data. However, because the data was taken at every 25 Hz and because this is a high Q system (narrow bandwidth), the plot may not have captured the true peak of the center resonance. The same is also true of the sidebands and resonance at 250 Hz.

MickeyP --

<< Is this the response to a single frequency sine excitation or the response of a sine sweep across a resonance? >> Your first assumption is correct - the plate is driven at its natural frequency (as desired).

The plate is cantilevered but the support is not completely rigid (i.e., the support is also excited although the mode of the main resonance is known to be primarily associated with the plate).

 

[electricpete]

You could perhaps request the actual time data. Most likely it will either look like amplitude modulation or frequency modulation. Knowing which one I guess gets you a small step closer to understanding the situation.

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[MikeyP]

Given the configuration, it seems unlikely that the frequency variation is due to the structure (unless the "clamped" support is non-linear) so my guess is a frequency modulation on the drive signal or in the shaker(?) that is doing the driving.

M

--
Dr Michael F Platten

 

[SomptingGuy]

I agree with electricpete. It's amazing how often the answer just leaps out when you can see this.


- Steve