Data error or curve fitting error?
Data error or curve fitting error?
(OP)
Hi,
I am trying to curve fit FRFs of a cylindrical casing. When I extract the modal parameters and see the mode shape, I am getting half of the mode shape quite amplified, as shown in attached document. Actually the lobes seen in mode shape should have been equally amplified along the periphery.
Can someone tell it is a mistake with FRF data or error in curve fitting? The FRFs have very good coherence and reciprocity.
Thank you in advance.
Kind regards
Geoff
I am trying to curve fit FRFs of a cylindrical casing. When I extract the modal parameters and see the mode shape, I am getting half of the mode shape quite amplified, as shown in attached document. Actually the lobes seen in mode shape should have been equally amplified along the periphery.
Can someone tell it is a mistake with FRF data or error in curve fitting? The FRFs have very good coherence and reciprocity.
Thank you in advance.
Kind regards
Geoff





RE: Data error or curve fitting error?
Cheers
Greg Locock
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RE: Data error or curve fitting error?
Thank you. As usual, counting on you for your useful replies.
Can you explain what you meant by 'analytically split mode'? I am curious to know what it is.
Also I didn't understand 'letting resonance frequency float around or setting it half way'. What do you mean by this?
I tried to fit using peak pick and circle fit. Though there is a little change in frequency, the mode shape remains same - half of the structure more amplified in mode shape. Any other hints?
Thanks & kind regards
Geoff
RE: Data error or curve fitting error?
An analytically split mode is where your analysis has taken one step too many and split one actual mode into two, typically with different damping factors, and of course different frequencies. I've never seen a mode actually split in two spatially as yours has, but it is common to see one part of a structure emphasised more in one of the pair than the other.
Presumably your FEA and or hand calcs show no such ludicrous mode shapes.
Cheers
Greg Locock
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RE: Data error or curve fitting error?
It is not analytically split mode. The two mode shapes I posted are symmetric modes of same mode shape. Probably due to non-symmetry of boundary conditions the frequencies were slightly different. Each mode shape has only part of the structure emphasised. So there is no split in frequency or damping. I mean no split mode.
For e.g. (referring to the mode shape in previous word document), 1361Hz is supposed to have 6 'petals' in mode shape. But only 3 are amplified. Other 3 are there, but the amplitude is so low that I have to amplify the amplitude so much then only I can see some shape. That is why I am doubting if the acquired FRF's amplitude is right for all nodes. I am attaching a highly amplified mode shape where you can see other 'petals' magnified to some extent.
However I will post the Nyquist diagram which you suggested.
FE mode shapes are perfect with 6 petals equally shown. But when I do harmonic analysis around the resonance frequency, I can see such half-amplified mode shape away from resonance. Then I thought I might have fitted a computational mode. But it's not. I checked it.
Many thanks for your support.
Geoff
RE: Data error or curve fitting error?
Sorry those plots are not what I meant. I'd like the Argand plane plots of the FRF for a node on the quiet and and active side of the mode shape at the lower frequency, say.
Cheers
Greg Locock
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RE: Data error or curve fitting error?
It might be I mixed up two things so it is not clear in my previous post.
First thing (to clarify what I said): the frequency of two symmetric modes is not the same. 1361 and 1367 Hz. Now I am thinking (not read anywhere) that this could be due to how the cylinder is clamped at the bottom. Ideally we should get both identical frequencies (as in FE). But we generally end up with this deviation in frequencies and I think it is due to bc. Now is this right? If not, what is causing this deviation ?
Second thing: I gave the previous plot only to tell that in fact all 'petals' (antinodes) are there in mode shape but not seen due to amplification problem.
I attach here the Nyquist diagrams which you asked for. I am showing data at two points: 21 and 105. 21 is on the side where mode shape is clearly amplified and 105 is on where it is not sufficiently amplified. While 21:21 is a drive point FRF. Other is not - it is w.r.t accelerometer at 21 point only.
Could you infer something from these? What are you intending to see from these graphs ?
Kind regards
Geoff
RE: Data error or curve fitting error?
Cheers
Greg Locock
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RE: Data error or curve fitting error?
What were you expecting from Nyquist plot and could you see that?
Kind regards
Geoff
RE: Data error or curve fitting error?
Cheers
Greg Locock
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RE: Data error or curve fitting error?
1st Nyquist plot is for a drive point FRF at node 21.
2nd Nyquist plot is a transfer FRF at node 105 measured at node 1.
That is both the FRFs are measured by accelerometer situated at node 21.
Thank you
Geoff
RE: Data error or curve fitting error?
Does your Fea have the six wave mode as its lowest frequency mode?
Cheers
Greg Locock
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RE: Data error or curve fitting error?
Any idea what might be causing such uneven mode shape amplification? Do you see any error in FRF data or in curve fitting?
If I know where the error lies, at least I can repeat that stage.
Many thanks
Geoff
RE: Data error or curve fitting error?
Cheers
Greg Locock
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RE: Data error or curve fitting error?
The elliptical mode is somewhere above or near 50th mode.
RE: Data error or curve fitting error?
the first figure posted is not the mode shape rather it is the forced response of your shell
RE: Data error or curve fitting error?
What made you think so? It is a mode shape obtained after proper curve fitting FRFs.
Thanks, Geoff
RE: Data error or curve fitting error?
Your FRF is the total response and consists of a weighted sum of all the modal contributions not the individual modes themselves.
RE: Data error or curve fitting error?
I did impact hammer testing at those points, obtained FRFs and then curve fitted them using standard Polymax algorithm in LMS and that is the mode shape for the first mode. I did the same in another modal software also with LSCE. Same result - half the casing is vibrating more than other half.
As I said earlier, I can observe such half shape in FE harmonic analysis just few Hz away from resonance. Then I thought I might be fitting some computational mode near to a true mode. But not - it is a clear first peak and also the algorithm Polymax automatically removes computational modes.
Thank you.
Geoff
RE: Data error or curve fitting error?
Quickest solution, please give me the freq,re,im table for 21R/21R and 105R/21R FRFs, over a frequency range that thoroughly covers the two peaks in question and their shoulders.
Also you mentioned that reciprocity was OK, that probably needs quantifying. so do you have xR/yR and yR/xR where y and x are nodes with strong responses at the lower and higher frequencies? Also you say the coherence was good-how good?
I completely fail to understand the sequence of mode shapes you are describing. Are we looking at a trivial side effect of modes elsewhere in the system?
Cheers
Greg Locock
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RE: Data error or curve fitting error?
I am just struck by the asymmetry of the mode shape as you and GL are.
Fascinating series of test and discussion I'll listen up and learn
am planning a similar test set up for an entirely different measurement
RE: Data error or curve fitting error?
Many thanks for your support.
You raised four points:
1. Nyquist plots data - please find attached excel workbook where I gave data for first two peaks effectively from 1250Hz to 1450Hz. The first experimental mode is at 1361Hz. I gave data for 21R/21R and 105R/21R. I plotted Nyquist plots as well.
Also I did another quick test and found that my drive point response amplitude changes reasonably between two hits. I don''t know if it is some non-linearity. Anyhow, I gave Nyquist data for this new test data. These worksheets are named as ReImag_XX_XX_New. As you can see earlier there was 2.5 times difference. Now it is 3 times. The 21R/21R magnitude increased. Please see graph.
2. Reciprocity - Please find attached the snapshots in word document.
3. Coherence - Within the frequency range up to 8-10 kHz, it is >0.97. Please find attached snapshots of coherence in the same word document.
Reciprocity and coherence are for old data - I mean the data which we are discussing till now.
4. Sequence of mode shapes - I attached in the excel workbook, last sheet, the FE predicted modes and the mode shape description in terms of circumferential and axial waves. As you can see you don't find one proper order. But if you plot frequency on y-axis and no. of waves on x-axis, you will get a cup shaped plot which is typical of shell structures. FE data is showing this pattern.
While I have some doubt that test data may not be that accurate, I did quick curve fit with the new data acquired. There also I find half modeshape amplified for first mode.
Kind regards
Geoff
RE: Data error or curve fitting error?
Do the amplified side correspond to the side where the accelerometer was located ?
RE: Data error or curve fitting error?
I think it doesn't matter. However, the accelerometers are there on both sides: I have two references: 21 and 105. In the mode shape shown, 21 is amplified and 105 not. But I can another mode shape where it is amplified in between (as it is symmetric mode to the first one so the amplification falls in between the two nodes).
Geoff
RE: Data error or curve fitting error?
Do you know the perturbation method?
Let's suppose your cylinder be perfectly symmetrical, with no defaults. Then the two modes would be mingled with one same resonance frequency : 1364,2 Hz.
Let's now suppose that a little perturbation is added to your system.
Then the two modes are going to diverge from one to another, such as two magnets North-North or South-South. The perturbation behaves as a repulsive force between the two modes.
This is my explanation, not the truth...
RE: Data error or curve fitting error?
It'll take me a couple of days to work through the spreadsheet.
Cheers
Greg Locock
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RE: Data error or curve fitting error?
Just calculating on what you said about transmission of waves:
V = n l; V - velocity of sound, n - frequency, l - wavelength
Taking V as 6000 m/s (from approx source from internet), n as 1361 Hz (experimentally observed first frequency), l comes to 4.4. Then with the concept of propagation of equal half wavelengths on both sides of circumference, the first mode should have 8 or 9 waves. How we are seeing 6 waves mode as the fundamental one ?
Did I get what you are saying ? I think not. Anyway I will read some book on shells and work on this.
Amanuensis - I understood your perturbation concept. But it still doesn't explain why we are seeing amplification of half mode.
Kind regards
Geoff
RE: Data error or curve fitting error?
Are you able to test or quantify the effect of excitation amplitude in your measurements?
RE: Data error or curve fitting error?
I think you are asking about non-linearity checking. Yes. I did some tests by varying the level of exciting force. As I said, I am noticing a variation in my drive point response. So definitely there is some non-linearity. I read some literature on non-linear normal modes, etc. But at the moment it is beyond my grasp and time to follow all those procedures.
But I really wonder if non-linearity would cause such a mode shape behaviour.
Thank you, Geoff
RE: Data error or curve fitting error?
RE: Data error or curve fitting error?
Excellent!! Whether this concept applies to my problem or not, I felt very happy on seeing that mode shape
The thing is FE doesn't predict this. FE shows equal amplitude for all the modes.
By the way, can you tell from which book you got this picture from and which chapter / page ? I will see if I can lay my hand on it.
Thank you.
Geoff
RE: Data error or curve fitting error?
He refers to V.I. Weingarten "free vibrations..." AIAA J., Vol. 3 1965 for the case of static bending moments, but the figure is from a German publication by P. Seggelke, Dec. 1963
he talks about mode splitting when the shell is subject to bending, so it may be along the lines of GL's discussion
the figure leaped off the page when first spotted, I was equally struct by the similarity to your mode shapes
RE: Data error or curve fitting error?
Hope Greg also will throw some light on this.
Geoff
RE: Data error or curve fitting error?
Houston we have a problem, here's the magnitude plots for your 4 tests, 21 and 105 old and new. As you can see repeatbility is only good to 6dB or so, which is to say, not very good.
Is there a reason to prefer working on 'new' or would you rather I stuck to the original ones?
Cheers
Greg Locock
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RE: Data error or curve fitting error?
Cheers
Greg Locock
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RE: Data error or curve fitting error?
I think what you said is very true. I have no specific reason for going with new or old results. But the fact is I am observing the half mode shape amplification when using both the FRFs - 21/21 and 105/105 as new driving FRFs.
I read the chapter which hacksaw suggested in 'Vibration of Shells' textbook. The actual context in which the referred diagram was given is the effect of presence of initial stress at the ends of cylinder. As the bending stress increases the symmetry of the mode shape is getting affected and finally results in such a half-amplified mode shape.
But for my problem I didn't see any initial stress on the ends of casing. It is a simple clamped-free case .So I think what you suggested might be one indicator. But I am not sure how and whether I will rectify the problem by doing another set of tests.
RE: Data error or curve fitting error?
RE: Data error or curve fitting error?
Am I right in saying so? Can you elaborate / explain your statement, if I am wrong ?
Thank you.
Kind regards
Geoff
RE: Data error or curve fitting error?
the alternative is that you have some asymmetry in the shell that is not being noticed. It could be the assembly stresses due to bolting sequences, etc.,
RE: Data error or curve fitting error?
FWIW I suspect 105_old was a bad hit.
Cheers
Greg Locock
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RE: Data error or curve fitting error?
Greg - I am sorry. I don't know what you meant by calculating 'quadrature frequency' at each measurement. I have 144 FRFs. So did you mean to say to find the first fundamental frequency exactly at quadrature for all these and then to group them ?
And by "Q ~D(Phase)/dFreq", I hope you are asking me to calculate Q-factor, again for the first fundamental mode.
And now I am again re-looking at your previous graphs. Can you please tell how you arrived at that 6dB for repeatability ? I mean what reference you took for amplitude dB calculation ? And looking at your phase plot, we can see that the 'new' data quadrature is very good. So I think I will go ahead with new drive point FRFs.
Many thanks Greg, hacksaw for all your useful tips and discussion.
Kind regards
Geoff
RE: Data error or curve fitting error?
Quadrature is merely the frequency near 1366 hz where phase = +/-90 degrees. A lot of modal analysis consists of writing little scripts to page through EVERY FRF in the survey looking for clues.
Q is proportional to d(phase)/d(frequency), that is a high Q mode has a rapid change of phase.
Sorry I got my olds and news muddled, 105 old has the right damping but the wrong frequency, 105 new has the right frequency but the 'wrong' damping. If I were analysing by hand I'd use the response at quadrature for this modeshape, and let the 'frequency' slither around between 1365 and 1367.
Cheers
Greg Locock
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