Weird modes in square plate vibrations

Grasshopper Karamba3D
1

Dear experts,

I´ve found something weird using Natural Vibrations module to obtain the vibrational modes of a simple square plate simply supported at the corners. Whereas most modes look fine, e.g. mode 0 or 6 (see below), some of them seem wrong, e.g. try mode 8 or 13 in the blue slider. PlateVibrations.gh (21.0 KB) These latter modes do not have any amplitude, even using high deformation values in Display Scales tab from Model View component. I also tried to reduce Eps and increase MaxIter in NVibes without success.

Any ideas? Am I doing something wrong??

Modes “0” or “6” look good,

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but mode “8” looks “weird” or “null”…

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This is the script:

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Thanks in advance for your help!

2

Dear @Vigardo,

the weird displacement pattern comes from drilling degrees of freedom (see attached file:
PlateVibrations_cp.gh (20.4 KB)
).

In K3D shell elements do not have a drilling stiffness. That is why in case of a flat plate one needs to support one node against rotation about the axis perpendicular to the middle plane otherwise there is a rigid body mode in the system. The relation between the drilling DOFs of a shell element in K3D is not a rigid mechanism but maintained with a certain stiffness. This is I think the reason why it shows up in the Eigenfrequency calculation. I will check that however.

– Clemens

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3

Hi Clemens,

Thanks for your answer, it is highly appreciated!

Sorry, I´m a bit confused. First you say that K3D shell elements do not have drilling stiffness, but latter you say the relation between the drilling DOFs of a shell element in K3D is not a rigid mechanism but maintained with a certain stiffness. (I know these things are hard to explain here)

In case there exists such drilling stiffness in K3D shell elements, is there a way to adjust it?

I´m trying to reproduce Chladni figures (“nodal patterns”) on a flat square plate, at least virtually with K3D. A short video here if you´re curious.

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Do you think that your shell elements modal analysis would be accurate enough to obtain “real world” frequencies of plates?

Have you ever validated eigenfrequencies from your modal analysis with real data in this context?

Best,

4

Hi Vigardo,
the drilling dof-relation within a triangular element in K3D sets up a mechanism: when rotating one of these DOFs the other two will rotate about the same angle. That’ why blocking the drilling DOF in one node is sufficient for a flat plate.
I need to check whether the issue you face is related to the element-formulation or the eigenvalue-solver.
A quick workaround could be to place drilling-supports at all nodes.
– Clemens

1 Like