Data error or curve fitting error? 4

[GMarsh]

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

 

[GregLocock]

Looks like you've got an analytically split mode there, it makes no physical sense. I bet if you try a manual circle fit you'll get it to look sensible, just let the resonant frequency float around or set it half way between.

Cheers

Greg Locock


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[GMarsh]

Greg,

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

 

[GregLocock]

Can you post Nyquist diagrams of that part of the spectrum for a node on on each side of the structure with the resonant frequencies indicated?

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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[GMarsh]

Greg, now I think I understood what you were thinking about my mode shapes.

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

 

[GregLocock]

Where did you get the idea that things can behave like this? How can a bc switch itself on for a mode at ~1300 Hz, and off for 1310 hz (or whatever the interval is)?

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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[GMarsh]

Greg,

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

 

[GregLocock]

In my experience you can't suppress half a mode shape. My hand wavy explanation would be that the energy required to flatten half the ring in bending would be very high so the frequency would have to be very high. Are the modes in general in the right order?

Cheers

Greg Locock


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[GMarsh]

Yes. They are in right order. That is the first fundamental mode.

What were you expecting from Nyquist plot and could you see that?

Kind regards
Geoff

 

[GregLocock]

I don't understand the plot, what are the two different color lines? Also you say that 107 is wrt the accelerometer at 21 I assume you mean force.

Cheers

Greg Locock


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[GMarsh]

The one in black is the actual FRF and the one in red is the curve fitted one.

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

 

[GregLocock]

So 23 has an amplitude about2.6 times that of 105 at that freq. I'd have guessed more than that from the mode shape.

Does your Fea have the six wave mode as its lowest frequency mode?

Cheers

Greg Locock


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[GMarsh]

Yes Greg. Six wave mode is the first mode of this cylinder. Then 7, then 5, 4, etc.

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

 

[GregLocock]

Odd, I'd have thought the first mode would be an ellipse. What frequency resolution were those argand plots?

Cheers

Greg Locock


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[GMarsh]

Frequency resolution is 1Hz.

The elliptical mode is somewhere above or near 50th mode.

 

[hacksaw]

GMarsh,

the first figure posted is not the mode shape rather it is the forced response of your shell

 

[GMarsh]

hacksaw,

What made you think so? It is a mode shape obtained after proper curve fitting FRFs.

Thanks, Geoff

 

[hacksaw]

GMarsh,

Your FRF is the total response and consists of a weighted sum of all the modal contributions not the individual modes themselves.

 

[GMarsh]

hacksaw, I understand what you said. But that doesn't answer my question yet and also I didn't get a clue as to why you thought it might be a forced response shape.

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

 

[GregLocock]

Argand plots are great if you have a cursor, not so great if they don't.

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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