Modal Shape from Experimental FRF
Modal Shape from Experimental FRF
(OP)
Hi all, I am performing an experimental modal analysis of a beam and I am trying to get the mode shapes from the FRF measured. I have read in many articles and books that the mode shapes (unscaled) may be obtained from the peak amplitudes of the imaginary part of the FRF, as in lightly damped structures the imaginary part reaches maximum values while the real part gets zero values at the resonant frequency. My problem comes when I plot the real and the imaginary parts of the FRF, it seems that they are interchanged, so I can observe peaks in the real part that provide the correct modal shapes and values of zero in the real part for the resonant frequencies. I have also found a thesis that states that for structures with small damping, the undamped modal shapes match with the real part of the FRF. I find the information is contradictory, can someone help me? and what is the reason why any of the parts (real/imaginary) give the modal shapes?





RE: Modal Shape from Experimental FRF
"so I can observe peaks in the real part that provide the correct modal shapes and values of zero in the *imaginary* part for the resonant frequencies"
RE: Modal Shape from Experimental FRF
If you are looking at FRF derived from VELOCITY (derivative of displacement), these phase relationships would be shifted by 90, and the FRF would be primarily imaginary for lightly-dampedsystem.
If you are looking at FRF derived from ACCELERATION (derivative of velocity), these phase relationships would be shifted by another 90, and the FRF would be primarily real again for lightly damped system system (opposite the polarity of the FRF dervied from displacement).
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(2B)+(2B)' ?
RE: Modal Shape from Experimental FRF
However, to add to previous discussion. Let's talk about FRF from displacement for lightly damped system. We said it was primarily real. That simply means the magnitude of FRF is closely approximated by the real part over most of the range.
Another thing to mention: the imaginary part (of FRF from displacement) will be close to zero everywhere except resonance. Don't know if that's what you were referring to.
I'll shut up now.
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(2B)+(2B)' ?
RE: Modal Shape from Experimental FRF
http://macl.caeds.eng.uml.edu/umlspace/aug99.pdf
It says that the imaginary part of the FRF is directly related to the residues, and the residues to the modal shape, so that is the reason why one can know the shape, but not in the adequate scale.
As it is shown in the pdf, the plot of the imaginary part of the FRF presents some positive and negative peaks, and their amplitude and sign stablish the shape.
The problem is that the plot of the imaginary part of my FRF does not correspond with the graphics shown in the article. Instead of that, the real part present this shape. I tried to get the mode shapes from the real part and the results seem correct (the first, second and third bending mode shapes). So, it would be correct?
And referring to your comment, I know that the imaginary part (of FRF from displacement) should be close to zero everywhere except resonance, but that is not what happens to mine, it reaches maximum values at resonance (it behaves as the real part!!).
Apart from that, my objective is to get the modal shapes of the beam, do you know any method to calculate them?
Thanks!!!
RE: Modal Shape from Experimental FRF
At resonance: real part of FRF is 0 (as it transitions between plus and minus), imaginary part is non-zero. Therefore at resonance, the magnitude and sign of imaginary part completely characterize the FRF at resonance (since real part is zero). Combining this info (magnitude and sign of imaginary part of displacement FRF at a specific resonant frequency) from several spatial positions allows to construct mode shape at that frequency.
Is your FRF derived from displacement ? (if from velocity, I could imagine it would act the way you describe).
Perhaps you can post an example.
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(2B)+(2B)' ?
RE: Modal Shape from Experimental FRF
H(w)=Ha(w)/(-w^2)
where H(w) is the receptance, Ha(w) the accelerance, and w the frequencies.
In both cases, accelerance or receptance, the real part should be zero at resonance. In case of velocity, the mobility has the contrary behaviour, and it shows a maximum in the real part at resonance...I can't see what is happening.
So, what do you think about the thesis I mentioned before? That one that states that for structures with small damping, the undamped modal shapes match with the real part of the FRF... they are describing what I obtain, but I don't see the sense...
RE: Modal Shape from Experimental FRF
What you quoted from a thesis (we can get them from the real part) sounds wrong, unless they are talking about velocity.
Why your data doesn't match the expected results as shown in the linked pdf: hard to figure. Maybe an example plot would provide some small clue. There are a lot of knowledgeable people on the forum (many moreso than me).
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(2B)+(2B)' ?
RE: Modal Shape from Experimental FRF
Do you know any method to calculate the mode shapes?
RE: Modal Shape from Experimental FRF
Integrating to displacement from acceleration does not alter that.
If you post one or more of your FRFs as a bode plot or preferably raw data I'll have a look at it and tell you whether you are dealing with bad data.
With very lightly damped systems it can be difficult to get enough resolution at the peaks, this is one reason why your coherence drops at the peaks.
It can be very instructive to look at the Nyquist (or Argand) domain of the data, and if you have 3 or more lines in the bandwidth of the mode a circle fit is a nice way of doing curve fits, but for a lightly damped system it'll give the same answer, since the diameter of the circle is the imaginary value at quadrature.
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Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Modal Shape from Experimental FRF
As a said, I want to calulate the mode shapes, and I found some formulae (pdf attached). Are they correct? What other methods do you know to calulate them?
RE: Modal Shape from Experimental FRF
RE: Modal Shape from Experimental FRF
¡ Thanks for your attention !
RE: Modal Shape from Experimental FRF
At this point we are deeply into bizarro world since the linear analysis of your FEA model will give you the mode shapes directly.
So what you are doing is synthesising time histories based on known mode shapes and assumed damping and scaling, for each mode, and then trying to re-extract the mode shape you first thought of.
Is that really a sensible approach?
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Modal Shape from Experimental FRF
My objective is to create a model that behaves as the real beam, and the way of calibrating it is looking at the natural frequencies and the mode shapes (with modal assurance criteria MAC)of both.
I am trying to simulate the real setup with the model: the impact hammer is the punctual impact force and the accelerations are obtained with the transient analysis instead of the accelerometers. Then the postprocess is the same for both: I obtain the FRF with the FFT of the input and output with Matlab and then represent them and extract the parameters that allow me to compare them. I am doing this to represent the real process and to consider damping, since the modal analysis does not take it into account. Maybe it would be better just to run the modal analysis assuming very little damping, I don't know. But the problem of obtaining the experimental mode shapes would continue...
RE: Modal Shape from Experimental FRF
I'm afraid there must be something wrong with your experimental setup if you are getting zero phase at resonance, if you are plotting displacement/force or acceleration/force.
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Modal Shape from Experimental FRF
The first peak and the response below it look very odd.
The second peak is at quadrature, ie is behaving correctly.
Try reducing the damping of all the modes, particularly the low frequency ones.
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Modal Shape from Experimental FRF
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Modal Shape from Experimental FRF
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Modal Shape from Experimental FRF
If you examine the change in phase at the second resonance it is clear that you are dealing with overlapping modes, very likely bending and torsional.
RE: Modal Shape from Experimental FRF
However every mode shape fitter I have ever seen is happy to create semi infinite number of modes to explain every little bump in every FRF, which is not helpful. The art now is to balance the desire to be able to resynthesise all the FRFs accurately, vs a believable number of modes.
Ideas like bending modes and torsion modes are human constructs, structures don't differentiate between them, unless the structure is very simple or carefully modified. For instance 30 years back cars rarely had a pure torsion mode and a pure bending mode, they typically had a front end torsion with lots of bending, and a rear end torsion with lots of bending, or something like that. Now they are designed with FEA, and we get the pure modes, because that's what we ask for.
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Modal Shape from Experimental FRF