×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs

Data error or curve fitting error?
4

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

RE: Data error or curve fitting error?

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


New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

RE: Data error or curve fitting error?

(OP)
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

RE: Data error or curve fitting error?

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


New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

RE: Data error or curve fitting error?

(OP)
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

RE: Data error or curve fitting error?

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


New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

RE: Data error or curve fitting error?

(OP)
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

RE: Data error or curve fitting error?

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


New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

RE: Data error or curve fitting error?

(OP)
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

RE: Data error or curve fitting error?

(OP)
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

RE: Data error or curve fitting error?

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


New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

RE: Data error or curve fitting error?

(OP)
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

RE: Data error or curve fitting error?

(OP)
Frequency resolution is 1Hz.

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

RE: Data error or curve fitting error?

GMarsh,

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?

(OP)
hacksaw,

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?

GMarsh,

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?

(OP)
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

RE: Data error or curve fitting error?

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


New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

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?

(OP)
Greg,

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?

Hi,
Do the amplified side correspond to the side where the accelerometer was located ?

RE: Data error or curve fitting error?

(OP)
Hi Amanuensis,

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?

OK, I now see what you mean.

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?

Lemma while I look at your detailed data. Plate type modes have the characteristic where the lowest frequency modes tend to have equal half wavelengths in each direction, that is, in your terminology, j=0 and then i is whatever it takes to match the j dimension in i. So if the cylinder is 10 units in circumference and 1 unit high, the lowest mode tends to be i=5.

It'll take me a couple of days to work through the spreadsheet.

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: Data error or curve fitting error?

(OP)
Ok Greg, take your time. I will wait for your reply.

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?

GMarsh,
Are you able to test or quantify the effect of excitation amplitude in your measurements?

RE: Data error or curve fitting error?

(OP)
hacksaw,

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?

(OP)
hacksaw,

Excellent!! Whether this concept applies to my problem or not, I felt very happy on seeing that mode shape smile2

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?

2
Leissa: " Vibration of Shells" a NASA report(1973) available as a bound volume or as a reprint, page 285, Fig. 3.142 in my copy.

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?

(OP)
Many thanks hacksaw. I found it now. I will read that. My problem may or may not be related to it. But gives me some information.

Hope Greg also will throw some light on this.

Geoff

RE: Data error or curve fitting error?

Hi Geoff

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


New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

RE: Data error or curve fitting error?

(OP)
Hi Greg, thank you for your replies. Sorry for getting back late. I am in a long leave. However checking my mails in between.

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?

if you excite the bending mode of your cylinder in addition to the higher order shell modes, you can see similar asymmetries if the amplitudes are large





RE: Data error or curve fitting error?

(OP)
hacksaw, thank you. But that concept as explained in the book applies to cylinder with initial bending stress. I visualise it something like some external moment being present when we do the impact testing, but not one caused due to a impact force which may cause excitation of bending moment. That is only momentary. Also considering that bending mode of such a shell exists at some high frequency, I don't think it should affect first fundamental mode, which is a shell mode.

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?

was thinking more along the line as an example, a milling tool exciting the shell modes which would consist of periodic excitation together with an average load that results in an applied moment.

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?

Rather than just retesting write a script to list the quadrature frequency of each measurement. Hopefully you'll see some logic in the grouping of the measurements. You could also look at Q ~D(pahase)/dFreq at quadrature.

FWIW I suspect 105_old was a bad hit.

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: Data error or curve fitting error?

(OP)
hackwsaw - interesting inference. But what you said applies to operational mode shape I guess because we are not considering here excitation due to milling tool. We are looking at simple modal testing using impact hammer. So I think mean force value and varying amplitude may not come in picture. It is just a single impulse of force.

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?

Eyeballing it, 105_new had a mag of about 750, 105_old is 1500, ergo 6 dB.

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


New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources