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Forced Vibration of Vertical Simply Supported Beam with 'Overhang'

Posted Feb 26, 2013, 3:19 p.m. EST Acoustics & Vibrations, Structural Mechanics Version 4.3, Version 4.3a 6 Replies

Tim Spencer
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Hi,

I'm trying to simulate the forced vibration of a beam that stands vertical and is supported by two simple supports that are shaken back and forth by a motor as in the attached schematic. I've also attached a model where the support separation is 335mm and the free length is 1599mm. I have a couple of questions I hope someone can help me with.

I've managed to perform the eigenfrequency study but the frequencies that result do not agree with ANSYS or my mathematical result (which do agree with each other). I also have a test rig running and observations of shuttle oscillation frequency agree with ANSYS and mathematical results. The results from the mathematical study and ansys put the first 3 frequencies at approximately 0.4Hz, 2.9Hz, and 8.3Hz. For some reason the first 3 eigenfrequencies from COMSOL are around 1Hz, 6.4Hz and 18Hz. Is someone able to shed some light on why this occurs? Is there a problem with my COMSOL model?

Also, in going ahead and just assuming that the frequencies are OK I've tried to do a frequency domain study to find the stresses in the beam using the eigenfrequencies obtained. I've tried adding a harmonic perturbation boundary load to the free end (just arbitrary for now at 10ms-2) but there is no deflection around the 6.4Hz eigenfrequency I found (I haven't tried other eigenfrequencies yet). Is the lack of damping the problem? My preference for FEA is COMSOL so I'd really like to find out how to do this. Haven't tried the stress study in ANSYS.

For some background to the project I've attached a video of the sculpture that this project concerns (skip to about half way to see it going). It is a Len Lye piece and the owner wants to build a larger version. Hence the FEA analysis.

Video:
www.youtube.com/watch?v=X2mFnXpNBwo

Any help would be much appreciated

Tim

Attachments:

6 Replies Last Post Mar 13, 2013, 10:40 a.m. EDT
Tim Spencer
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Posted: 1 decade ago Feb 26, 2013, 3:33 p.m. EST
Attached is the unsolved model
Attached is the unsolved model

Attachments:

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Feb 27, 2013, 2:21 a.m. EST
Hi

are you sure you are mesh independent with only 1 element across the thin blade ? Or use shell elements

And your prescribed z=0 condition on the full blade length top and bottom will seriously change your mode shape, you could restrict it to your cylinder top/bottom pivots, or use a rigid connector on the first cylindrical pivot

So far I have never caught COMSOl with wrong results, once my model is correctly set-up ;)

--
Good luck
Ivar
Hi are you sure you are mesh independent with only 1 element across the thin blade ? Or use shell elements And your prescribed z=0 condition on the full blade length top and bottom will seriously change your mode shape, you could restrict it to your cylinder top/bottom pivots, or use a rigid connector on the first cylindrical pivot So far I have never caught COMSOl with wrong results, once my model is correctly set-up ;) -- Good luck Ivar
Henrik Sönnerlind COMSOL Employee

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Posted: 1 decade ago Feb 27, 2013, 3:53 a.m. EST
Hi,

Using roller conditions on the cylindrical pivots is dangerous. With only a slight numerical error in the direction of the normal (and here the mesh is rather coarse) the constraints will also get a tangential component. This will make the pivot clamped.

As Ivar suggests: Try rigid connectors on the pivots instead if you want to stay with solid modeling.

Concerning mesh resolution: For computing eigenfrequencies, one element through the thickness should be enough, as long as the shape functions are quadratic (the default).

The deviation in the eigenfrequency is a factor 2.5. This means that the stiffness is a factor 2.5^2 = 6 too high. You can check the model by doing a static analysis with a tip load, and compare with a static solution.

Regards,
Henrik
Hi, Using roller conditions on the cylindrical pivots is dangerous. With only a slight numerical error in the direction of the normal (and here the mesh is rather coarse) the constraints will also get a tangential component. This will make the pivot clamped. As Ivar suggests: Try rigid connectors on the pivots instead if you want to stay with solid modeling. Concerning mesh resolution: For computing eigenfrequencies, one element through the thickness should be enough, as long as the shape functions are quadratic (the default). The deviation in the eigenfrequency is a factor 2.5. This means that the stiffness is a factor 2.5^2 = 6 too high. You can check the model by doing a static analysis with a tip load, and compare with a static solution. Regards, Henrik
Nagi Elabbasi Facebook Reality Labs
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Posted: 1 decade ago Feb 27, 2013, 11:39 p.m. EST
Hi Tim,

Based on the thickness and overhang length of the beam, and its material properties, it seems that the COMSOL solution is correct. The first frequency should be around 1 Hz according to the cantilever vibration equations.

Nagi Elabbasi
Veryst Engineering
Hi Tim, Based on the thickness and overhang length of the beam, and its material properties, it seems that the COMSOL solution is correct. The first frequency should be around 1 Hz according to the cantilever vibration equations. Nagi Elabbasi Veryst Engineering
Tim Spencer
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Posted: 1 decade ago Mar 2, 2013, 6:01 p.m. EST
Thank you all for the valuable feedback. I'm working on developing a more efficient mesh
Thank you all for the valuable feedback. I'm working on developing a more efficient mesh
Victor Soares
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Posted: 1 decade ago Mar 13, 2013, 10:40 a.m. EDT
Could you please upload the complete model when you get it working ?
Could you please upload the complete model when you get it working ?

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