Frequency analysis for cylindrical shell

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chlai
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Joined: Tue Jan 11, 2022 9:29 pm

Re: Frequency analysis for cylindrical shell

Post by chlai »

Hi @thschrader & @mac_the_bike

Many thanks for your interest and providing your point of views.

You are right. This model supposes to have 3 rigid-body modes. Their frequencies should be zero or numerical zero. The results from FreeCAD and Ansys both have these 3 modes. It is what I expect and thus I compare frequencies except these 3 rigid-body modes.
mac_the_bike wrote: Sat Jan 22, 2022 1:01 pm One feature of a vibration analysis of a cylinder, which is completely axisymmetric, is that the non RBM modes come in pairs, i.e 2 modes will have the same frequency, see Note 3. The RBM modes will not be in pairs.
In the figures there appear to be modes that are almost in pairs. This discrepancy can be assigned to at least the following:
1. the mesh is not the same over the surface. If you look at the TDC of the mesh you will a line of elements - this pattern doesn't appear anywhere else.
2. the nodes don't lie strictly on a cylinder, see Note 4.
This very well explains the pair modes I got and the difference between them. Could I ask if you have some references about this?
mac_the_bike wrote: Sat Jan 22, 2022 1:01 pm Note 2: I am also questioning the FreeCAD frequency values, of the second analysis, because if you divide the FreeCAD frequencies by PI the new numbers are close to the Ansys values.
Um... I am not sure if it is a coincidence or they really share some sort of relation. But I modify my analysis settings and get the results which are quite close to the analytical solution. See
chlai wrote: Sat Jan 22, 2022 6:26 pm As for my initial problem, I solve it with quad mesh and the analysis settings as attached.
chlai
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Joined: Tue Jan 11, 2022 9:29 pm

Re: Frequency analysis for cylindrical shell

Post by chlai »

thschrader wrote: Sat Jan 22, 2022 8:46 pm
chlai wrote: Sat Jan 22, 2022 6:26 pm ...
Reference:
Rayleigh, J. W. S. B. (1894). The theory of sound (Chapter X)
Arnold, R. N., & Warburton, G. B. (1949). Flexural vibrations of the walls of thin cylindrical shells having freely supported ends.

If there is any question or suggestion, please feel free to contact me

Best regards
I like the Reference.
Our ancestors were not stupid.
Thomas
:lol: :lol: I refer them because it is a very basic model and most of the thesis even these years still quote the formula from them
It still can be wrong in old papers sometimes ;) so correct me if you know anything regarding this problem
thschrader
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Re: Frequency analysis for cylindrical shell

Post by thschrader »

chlai wrote: Sat Jan 22, 2022 6:26 pm ...
I also calculate the analytical solution (Rayleigh's method, see ref. below) to verify the results.
The error is around 1% (except mode 2 of t=1mm, still finding the reason...)
...
If there is any question or suggestion, please feel free to contact me
In my opinion the shell with 1 mm is too thin.
When i remember shell-theory, a shell (from an engineering point of view) is defined as:
1. the shell thickness is small against the overall dimension
2. and the deformation of the shell is small against the thickness

Have a look at the deformation/thickness ratios. For 1 mm shell it is > 1,
so the theory is not valid.

I ran your file with triangle meshes, gives practically the same results.

Regards Thomas.
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davidosterberg
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Re: Frequency analysis for cylindrical shell

Post by davidosterberg »

thschrader wrote: Mon Jan 24, 2022 4:33 pm 2. and the deformation of the shell is small against the thickness

Have a look at the deformation/thickness ratios. For 1 mm shell it is > 1,
so the theory is not valid.
Sorry but the magnitude of deformation in a mode shape from a modal analysis is not physically meaningful.

Even if this was not the case it is not true that the displacement has to be small compared to the thickness.
What is true is that the deformations have to be small in the sense that there is no significant rotation.
thschrader
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Re: Frequency analysis for cylindrical shell

Post by thschrader »

davidosterberg wrote: Mon Jan 24, 2022 5:30 pm Sorry but the magnitude of deformation in a mode shape from a modal analysis is not physically meaningful.
Even if this was not the case it is not true that the displacement has to be small compared to the thickness.
What is true is that the deformations have to be small in the sense that there is no significant rotation.
Good points.

The Eigenforms can be scaled, ok.
The deformations must be small, still my opinion.
You must linearize the equations.

This thread is a good opportunity to refresh my brain.
I like old books. The deformations are small compared to shell-thickness
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davidosterberg
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Re: Frequency analysis for cylindrical shell

Post by davidosterberg »

thschrader wrote: Mon Jan 24, 2022 9:18 pm I like old books. The deformations are small compared to shell-thickness
1) This is not the case for a normal shell, and especially not for ANSYS SHELL181 that even supports large rotations.
Anyway for a linear modal analysis the displacements are small by definition. So thickness does not matter.

2) As I stated earlier in the thread. Calculix is not using shell theory (unlike Ansys). That is why we see the discrepancy. Calculix is internally expanding the shell elements into solid brick elements. This does not work if the element aspect ratio is very large.

Check out the calculix documentation. Where it is also mentioned that there are issues with extreme aspect ratio towards the end.
https://web.mit.edu/calculix_v2.7/Calcu ... ode39.html

Edit:
In OP's problem. The aspect ratio (element length / shell thickness) is in excess of 500. It is too much for a solid brick element.
mac_the_bike
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Re: Frequency analysis for cylindrical shell

Post by mac_the_bike »

  • chlai
    This very well explains the pair modes I got and the difference between them. Could I ask if you have some references about this?
    Unfortunately I don't have any references to the fact that these come in pairs.

    As davidosterberg stated the magnitude is not meaningful. Also the type of analysis that is being performed is a "small displacement vibration analysis", so you can consider the numbers in the mode to be as small as you want. The numbers that are output for the mode shape depend on the type of normalisation that is being performed, e.g. mass normalised.

chlai
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Re: Frequency analysis for cylindrical shell

Post by chlai »

Dear @thschrader & @davidosterberg

Thanks for your replies. It becomes more and more clear whats happening in this model.
I did some experiments based on your suggestions and would like to share my results.

I agree that 1 mm shell is very thin in this case(also rare in reality). So below I use thickness = 10 mm to do the analysis.
thschrader wrote: Mon Jan 24, 2022 4:33 pm I ran your file with triangle meshes, gives practically the same results.
Yes, the triangle mesh with 2nd order (S6) gets similar results with quad mesh with 1st order(S4) for t=10mm (max. 300mm mesh size). But the calculation time is vary (my PC: 17.4s vs 7.6s). However, both mesh types can converge, so I think either mesh type is acceptable in this case.
davidosterberg wrote: Mon Jan 24, 2022 9:39 pm Check out the calculix documentation. Where it is also mentioned that there are issues with extreme aspect ratio towards the end.
https://web.mit.edu/calculix_v2.7/Calcu ... ode39.html
In CalculiX doc, it is recommended to use reduced integration mesh when the aspect ratio is very large (more than 40). There are 2 kinds of reduced integration shell mesh S4R & S8R in CalculiX.
S4R seems to have some hourglass problem and S8R has quite good results.
result_compare_t10_S8R.png
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S8R mesh .inp file
Cylinder_Shell_450.txt
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Regards
chlai
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Joined: Tue Jan 11, 2022 9:29 pm

Re: Frequency analysis for cylindrical shell

Post by chlai »

I made a fem example of this frequency analysis since there is no example of such a model yet (frequency analysis for a cylindrical shell with quad4 element type). The mesh size is slightly adjusted and the result has about 1% error compare to the cylindrical shell theory.
result_compare_t10_250.png
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It is my first time make contribution to FC FEM wb :oops: I think this is just an fem example rather than something big so I made a PR to Bernd’s femexample branch. Hope this example could help other users if they encounter a similar model or as a reference for shell frequency analysis.
Attachments
Cylindrical_Shell_Frequency_Analysis_Example.FCStd
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bernd
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Re: Frequency analysis for cylindrical shell

Post by bernd »

very cool example. We should add it to the FreeCAD FEM examples ... I have been offline for some time. Has it been merged into master? If not. Rebase your branch https://github.com/chlai1012/FreeCAD/co ... ll-example on master and squash all example commits into one commit and go for a PR here https://github.com/FreeCAD/FreeCAD/pulls

cheers bernd
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