Torsional vibrations 1

[ThomasH]

Hi everybody.
I need a bit of help.
I am helping two students with their master thesis and the subject is a hybrid timber structure. That means that the core is built with concrete and the remaining parts with timber.
The problem is that there are torsional modes at relativly low frequencias, like the second mode. And then we need to check that the numbers are correct.

And I can't find the "formula" for the first torsional mode in my reference litterature. I have a formula from ChatGPT but the results from that does not fit with the calculations from FEM. So my hope is that somebody in the forum can help.

I have attached two files. One is a calculation for fists bending mode and first torsional mode in a pdf, the second is the same but MathCad Prime v10. The bending fits with other calculations, torsional doesn't fil.

Any help would be appreciated.
Thomas

 

[Ron247]

Not that I will be much help on this in the end, I need some clarification.

1. You say you attached 2 files, I see 1.
2. The file you did attach is steel, not wood or concrete. Are you using it as an example only?
3. You are looking for the formula for the 1st torsional mode?

 

[ThomasH]

Sorry, I should have been clearer. It is only an example and I need the formula for the first torsional mode of a steel tube. Preferably with a reference, then we can hopefully find the reference.
I thought I had attached two files. I will try again.
Thanks

Edit: I could not attach a Mathcad Prime file. But if you download the txt file and change the extension to mcdx it will hopefully work.
Edit2: Hope I haven't broken any rules now?

 

[Ron247]

I got this from ChatGPT and I have no idea how accurate it is. I already know that AI can access hundreds of information sources but some of them are not correct from what I can tell. Hope this helps. Everything below is from ChatGPT.

A good reference for understanding the first torsional mode of a steel tube—including its frequency and mode shape—can be found in vibration analysis or mechanical engineering texts that cover torsional dynamics. Here's a widely cited and authoritative reference:

---

Reference:


Meirovitch, L. (2001). Fundamentals of Vibrations. McGraw-Hill Education.

• Chapter: Torsional Vibrations
• Relevant topics: Torsional natural frequencies, mode shapes, circular shafts and tubes, boundary conditions
• Why useful: Offers detailed derivation of natural frequencies and mode shapes for torsional systems including hollow cylinders (tubes), both fixed-free and fixed-fixed.

---

If you're looking for an academic paper specifically focused on torsional modes in steel tubes, this is another good source:

---

Journal Article:


Blevins, R. D. (1979). Formulas for Natural Frequency and Mode Shape. Van Nostrand Reinhold Company.

• This book contains formulas for torsional frequencies of cylindrical structures (solid and hollow), which are often used in practice for estimating first mode torsional frequencies.

---

If you need help calculating or estimating the first torsional mode frequency for a specific steel tube (based on dimensions, material properties, and boundary conditions), I can walk you through it. Just let me know the parameters.

 

[GregLocock]

I was going to say that Blevins is the FEA dynamics reference. If you could include a sketch of the structure I could probably suggest a handcalc. Holzer's method springs to mind for a tower block, for example.

 

[GregLocock]

The formula you have for the torsional frequency is right in concept but wrong in detail. That is typical for LLM results.

 

[goutam_freelance]

Try this presentation from Texas A&M University
https://rotorlab.tamu.edu/me459/NOTES 9 Torsional Dynamics Overview.pdf

 

[GregLocock]

I get 80 Hz for first torsional for a free fixed tube of your dimensions. Your script has more than one error I think - using Kv1 is one.

 

[ThomasH]

I get 80 Hz for first torsional for a free fixed tube of your dimensions. Your script has more than one error I think - using Kv1 is one.

That was very interesting. The reason for the question is that with FEM we get the same result as the formula for bending. For torsion we get 80 Hz with FEM.

The difference between Kv1 and Kv2 is supposed to be thin vs thick walled tube. But I find the difference between them strange since I think the tube should be thin walled.

But, as you say, there has to be something more wrong.

Edit: I have changed to Kv2.

 

[GregLocock]

Well as I said, the final equation in your first pdf looks sensible but is wrong in detail. I must admit I'm surprised by the difference in Kv between the two methods, perhaps you'd get a better estimate if you dida thin wall assumption for Ip as well (ie m*(mean radius)^2).

The other thing that s a bit alarming is the enormous difference in frequency between bending and torsion, but a cantilever with L/d of 30 is pretty whippy. I'm used to car bodies where in the bad old days they were roughly equal, and these days torsion is only a bit higher than bending.

 

[ThomasH]

Greg,
You mentioned 80 Hz in a previous post, was that based on a hand calculation or FEM? If it was a by hand I am very interested in the details, if it was FEM, I have the same result.

I am a but stuck with this right now .

 

[GregLocock]

It was direct from Blevins, a corrected version of your last equation.
1/2/pi is replaced by 1/4

As I said this typical of LLM 'research'.

 

[ThomasH]

It was direct from Blevins, a corrected version of your last equation.
1/2/pi is replaced by 1/4

As I said this typical of LLM 'research'.

Greg
Thanks a lot for your help. I have enclosed a pdf with my calculations and no the results are more reasonable. It's not perfect yet but we are not "stuck" anymore.
And the students also say thanks.