Discussion Forum

Hi

I beleive we have a definition issue here, at least for me in 2D you have only 1 rotational degree of freedom (DoF) so I call that usually a bending mode, torsional mode that is for me a rotation along a symmetry axis, so OK if your axis is along Z (perpendicular to the X-Y) plane you can get a pure torsional mode, but how do you fix your tube ? to really study a torsional mode then ?

Second, if you use the axisymmetric 2D mode, you are in a plane perpendicular to the axis hence the torsional mode will not be seen and you will only sort out the modes with an axial symmetry.

So you are left with the 3D mode. To make a long hollow tube you take the diference of 2 cylinders, and then you must decide how you support it for the boundary conditions.
Free-free modes you just run the eigenfrequency model as is, no boundary condition (BC) fixing, but you must choose to solve let's say 24 modes as the fist 6 are at 0Hz (or close to) and many of the higher modes will be doublets (same frequency) because of the symmetry of your model. such a system should run in a few seconds on a reasonnable workstation.

The first >0Hz torsional mode will be at a rather high frequency, as the fundamental torsion is free

Next step is to support the tube (fixed-free, fixed-fixed, or pinned-free ...), a crude methode is simply to "fix" one section, then you resolve and you will see quite different modes. Again several are doublets, typically the bending modes, your torsional mode will be a singlet, just as an axial compression modes.

Final step, if you have memory issues, ou might want to simulate only a pie section of the tube, then you must count your symmetries and/or anti-symmetries to get all modes, as these BC's are restaining the modes you may obtain, single symmetry plane = one set with symmetry and one other wth anti-symmetry, BC's, 2 symmetry planes = 4 sets for all 4 combinations of symmetry and antisymmetry and so on (this is a general statement degeneracy might appear depending on the symmetry of your part)

These modes are largely documented in the litterature, a good thing is to check your calculated values against an analytical calculation, i.e. "Formulas for Natural Frequency and Mode shapes" of R.D. Blevins, Krieger, 1979

Good luck
Ivar

Hi Ivar,

Thank you very much for the response. Its very useful.

Just another clarification regarding the definitions here – are axial compression modes == modes with an axial symmetry (in axissymmetric 2D mode) == longitudinal modes?

Btw, I am trying to obtain the eigenmodes/frequencies of a system of 2 solid cylinders, one inside the other. So, I guess, for the transverse modes, I can use geometry of 2 concentric circles in the plane-strain mode with free BCs on the external boundaries. For the rest, I will probably need to use the 3D mode.

Computational memory is not the issue here; the issue is that I need to separate the frequencies for the transverse and longitudinal modes. It would have been great if I could just insert some symmetry conditions to filter out the class of modes that I want…

Thanks again!

Hi SD

whell I agree everyone has his/her definitions, for me compression mode is one long the axis of symmetry, or the "long" axis of a beam, so you call it probably "longitudinal" mode.

One "watch-out" if you have several "geom" in COMSOL, in structural mode, and you calculate them all in eigenfrequency mode, you will see a long list of frequencies that are an ordered set of what comes from both/all "geom" (these are then mostly interleaved) and you must sort them: look at the absolute displacement on the images, not just the shape, you will easily get fooled. Therefore, I mostly have only one "geom" where I do physics calculations, the others are there at most for geoemtrical design (without any physics)

I would not use symmetries on BC as I find it to easy to overconstrain your system and miss information. If you are interested in sorting your modes (without looking systematically at each image) you could integrate the square of the displacements and rotations in 3D structural "Options Integration Coupling Variables, Subdomain Variables", i.e.:
Vol 1
UVW2 (u^2+v^2+z^2)/Vol
U2int u^2/Vol/UVW2
V2int v^2/Vol/UVW2
W2int w^2/Vol/UVW2
THuvw 0.25*((wy-vz)^2+(uz-wx)^2+(vx-uy)^2)/Vol
thu2 (0.25*(wy-vz))^2)/Vol/THuvw
thv2 (0.25*(uz-wx))^2)/Vol/THuvw
thw2 (0.25*(vx-uy))^2)/Vol/THuvw

I'm proposing here to square the displacements to get only the absolute values along x,y,z, but you might simplify these formulas and/or drop the normalisations.

You can plot them over the modes if you goto the "Postprocessing Domain Plot, General tab: select all modes, select "keep plot", Point tab: select any point, and type for the Expression U2int, select once Line Setting and tick "Legends", then APPLY (not OK yet), and continue with V2int "Apply", ...
(unfortunaltely one can not write [U2int V2int W2int thu2 thv2 thw2] in the expression list. it would be easier).

If you have a "long" part wih its axis along z then a compression mode or longitudinal mode would have a large relative W2 component (deformation along Z), while a twist mode (around the long axis) would have a large relative Theta_z=thw component. while a bending mode would appear with large thu2, thv2 or V2, U2

I'm also assuming that u,v,w are the dependent variables, you are in 3D structural mode and youre object is well aligned with the coordinates x,y,z and that you have basically a simple geometry such as a more or less regular beam or a tube.
Anyhow the increasing frequency values of the modes tells you that you have an increasing number of "wiggles" in your mode shape.

In ANSYS or NASTRAN you use the "mode participation factors" along your DoFs (degrees of freedom) to sort the modes and their importance, unfortunately this is not easy obtained today with COMSOL, I expect it to come soon in one of the newer releases, it's too usefull to eave it out.

There are a lot of books out there treating vibration modes, have a look at your library

Good luck
Ivar

Thank you very much for the responses and clarifications, Ivar. I have a background in photonics and hence always struggle with multiple definitions in structural mechanics!

I usually do use one geom, for the same reasons that you have mentioned. I have been postprocessing the results in MATLAB for getting the longitudinal modes. Thanks for the reply, now I am sure that my algorithm is finding the correct modes.

Well
with the years you learn to touch a lot of subjects, at least I'm in the happy situation to be able to, and with COMSOL, I'm really rediscovering physics (and PDEs) again, having fun with Structural, but also AC/DC, Thermal, MEMS, Fluidics, PZT, Chemistry, RF/optics, bu havn't had time to work on accoustics and earth science yet, what do you want more ?
Ivar

Hi,

I am working on a very similar model. I am doing a modal analysis of a pipe within a pipe. I am using a 3D model. My problem is, when I run the eigenfrequency solver, I get modes where my center pipe comes through my outer pipe. I tried establishing contact pairs to prevent this, but they do not seem to be making a difference.

Were you ever able to get your model to work? Did you have a similar issue?

Any suggestions would be appreciated.

Danielle

Dear Sir
I want to see the longitudinal and transverse stress in my model. I should see it under which? There are von mises stress for falure and first principal stress but i dnt knw what to use for finding the longitudinal stress.
Regards
Abid

Hi,
I am trying to simulate the evaporation of water droplet, The droplet is assumed to be pinned during evaporation. To keep the triple phase contact line fixed, I adopt the no-slip condition. However, the contact line between water droplet and substrate changes from 1415um to 1422.5 um during 5s. How to set parameter to get a pinned contact line during the evaporation?
I’m sure that I can make great progress in this simulation with your help.
Looking forward to your reply! Thanks !!



Sincerely,
Tian Tang