Model order in curve fitting

[GMarsh]

Hi,

Can someone suggest how to decide the model order (or size) while curve fitting in modal analysis? As the curve fitting model order is increased, number of stable poles are increasing. But as some of these are computational modes, I want to know if there are any thumb rules or guidelines in selecting model order for a given type of structure - say lightly damped, heavily damped, etc. What is the minimum order one usually starts with ?

Thank you.

Kind regards
Geoff

 

[GMarsh]

Greg,

Though I didn't make a plot, I checked in FE and EMA. In the range 1200-2200 Hz, FE predicts 23 modes, EMA fits 95 modes. All seem to be genuinely stable. I used model size of 90. Considering that I am using POLYMAX routine in LMS to fit the modes, there is very less chance of computational modes as it automatically excludes them.

The fundamental mode is at 1290Hz. So I am not looking at below 1200. Of course I can't see any experimental modes also.

Thank you.

Kind regards
Geoff

 

[GregLocock]

so 1290 is the very first mode?

Cheers

Greg Locock


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[amanuensis]

So, since there is a query regarding the modal density. Below is the formula of the number of modes of a cylinder (or pipe structure):

N=(L/2k)*(f/fr)*{1+[(pi/2)/((f/fr)^0.5+0.5*(f/fr)^3.5)]^4}^1/4

where
L: length of cylinder
k=h/(12)^0.5 is radius of gyration and h is thickness of cylinder
f is the frequency range
fr = c/(2*pi*r) is the ring frequency, c is longitudinal wavespeed and r is radius of cylinder.
pi = 3.14159...

 

[GMarsh]

Greg, yes it is the first mode.

Amanuensis, Now what are the boundary conditions which apply to the equation. I mean free-fre or clamped free, etc.

And what value to input for f, if I want frequencies from say 1200 - 2200 Hz? Is it 1000? But then this can be 1000 Hz anywhere. Or do you mean the starting frequency of the band is fr ? Please elaborate a bit, if it's not a problem.

Thank you.

Kind regards
Geoff

 

[amanuensis]

Hi Geoff,
It's a good point you raise here. Indeed, there are several limitations in the use of this formula.
Only radial modes on a simply-supported, thin-walled cylinder are considered here (no in-plane compressional modes, no torsional modes, and so on).
But the advantage of an analytical model (compared to a numerical model) is to give you information about the behavior of the structure: namely, the cylinder mode count changes character around the ring frequency.
It might be interesting to see whether or not this ring frequency can be identified on both your experimental and numerical results.
It's certainly more efficient to try to find out the ring frequency (a property of this kind of structure) than applying foolishly this formula.

 

[GMarsh]

Hi Amanuensis,

Thank you for your response. I am really curious to know what you are saying. I really didn't get it right. I made the calculation as per the formula you gave. I got ring frequency 4477.56 Hz and mode count 60.86. Now what does these figures mean I have no idea.

As I asked earlier where does this mode count apply? I mean I chose 1000 Hz as frequency range. Does my above result mean that there are 60 modes around 4477 Hz within 1000Hz frequency range? Can you please give the reference of the book where this formula is discussed?

Thank you.

Kind regards
Geoff

 

[amanuensis]

This formula is extracted from the book :
Theory and application of Statistical Energy Analysis by Richard LYON(page 143 of the second edition of the book).
Actually, this theory (S.E.A.) uses the modal density as an input parameter for estimating the energy response of complex structure.
So in this book, mode counts and modal density are extensively discussed.

For my understanding, the ring frequency means that :
At greater frequency than the ring frequency, the mode count of a cylinder is the same as the one of a flat plate of equal surface area : the waves don't see the curvature of the cylinder.

Conversely, at lower frequency than the ring frequency, the mode count of a cylinder is very different from the one of a flat plate.

Last point. For the frequency range, it can be relevant to use the 1/3 octave frequency bands. Then you can plot the mode counts versus 1/3 octave frequency bands.

 

[GregLocock]

Try plotting number of modes (cumulative) vs frequency, for your FEA model, your modal analysis, and any formula such as the above.

This is a diagnostic, not an absolute aid.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[GMarsh]

Hi amaneunsis, Greg,

Thanks for your replies. I was hoping to get hold of that Lyon's book before responding. But I couldn't. Once I get it I will do what you suggested and if something interesting I will post it here.

Kind regards
Geoff

 

[amanuensis]

By the way, just for culture...

Lyon found out an amazing result in the 1960's!
He revealed a hidden relation between the lack of information and the irreversibility between two coupled modes!
His result is comparable to the Boltzmann's H-theorem which explains the irreversibility through the assumption of molecular chaos.