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

 

[hacksaw]

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

 

[GMarsh]

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

 

[amanuensis]

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

 

[GMarsh]

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

 

[amanuensis]

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...

 

[GregLocock]

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


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[GMarsh]

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

 

[hacksaw]

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

 

[GMarsh]

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

 

[hacksaw]

Leissa covers the change in mode shape albeit for static deformations, see attached

 

[GMarsh]

hacksaw,

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

 

[hacksaw]

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

 

[GMarsh]

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

 

[GregLocock]

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


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[GregLocock]

Here's the phase plot, I'd say the original 105 was a bad hit, both damping and quadrature are off compared with the other three.

Cheers

Greg Locock


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[GMarsh]

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.

 

[hacksaw]

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

 

[GMarsh]

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

 

[hacksaw]

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.,

 

[GregLocock]

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


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