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problem with eigenfrequency

Posted Feb 23, 2012, 8:04 a.m. EST MEMS & Nanotechnology, MEMS & Piezoelectric Devices, Mesh, Studies & Solvers, Structural Mechanics Version 3.5a 3 Replies

Lebedev Gor
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Hi all,

My project consists in calculating the eigenfrequency of a piezoelectric beam. For the experience, I apply 10V on the top, the ground is on the bottom. After, I mesh the beam, I solve and I obtain the eigenfrequency value.

But my problem is that when I change the mesh (I increase the number of elements), my eigenfrequency value change. And this until the solve stop because I'm out of computer memory. I think it isn't normal.
I can't obtain a correct eigenfrequency and I don't know why! If someone have a solution, please write me.

I work in 2D with MEMS module/Structural mechanics/Piezo plane stress

Thank you

3 Replies Last Post Feb 24, 2012, 8:51 a.m. EST
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Feb 23, 2012, 3:13 p.m. EST
Hi

I agree one should expect a saturation or stabilisation of the eigenfrequency values when the mesh becomes fine "enough". but this depends a little on the model and how it is set-up + the RAM size of your PC.

Perhaps, if your beam has a high aspect ratio and you are looking for high frequency modes that you really need a very high mesh density, or that a structured mesh would help.

Do not foget you solve for displacement, so your mesh must be denser (5-8 elements per mde wavelength in the material), if not you might have aliasing and your frequency will drift off with the mesh.

Have you estimated roughly by hand what you expect to find as frequency and spatial wavelength ??

--
Good luck
Ivar
Hi I agree one should expect a saturation or stabilisation of the eigenfrequency values when the mesh becomes fine "enough". but this depends a little on the model and how it is set-up + the RAM size of your PC. Perhaps, if your beam has a high aspect ratio and you are looking for high frequency modes that you really need a very high mesh density, or that a structured mesh would help. Do not foget you solve for displacement, so your mesh must be denser (5-8 elements per mde wavelength in the material), if not you might have aliasing and your frequency will drift off with the mesh. Have you estimated roughly by hand what you expect to find as frequency and spatial wavelength ?? -- Good luck Ivar
Lebedev Gor
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Posted: 1 decade ago Feb 24, 2012, 6:54 a.m. EST
Hi Ivar,

Indeed the lenght is 260µm and the thickness is 180nm,so the ratio is important. In this case, what is the solution?
According to the datasheet, the eigenfrequency is in order of some 10kHz. The computer memory is 64Gbits, I this it is adequate. I give you in attachment my model (the PZT beam between the two electrods).
After, I would like to compare severals beam (lenght between 260 and 600µm), so the ratio increase? It is possible to realize this?

Thanks
Hi Ivar, Indeed the lenght is 260µm and the thickness is 180nm,so the ratio is important. In this case, what is the solution? According to the datasheet, the eigenfrequency is in order of some 10kHz. The computer memory is 64Gbits, I this it is adequate. I give you in attachment my model (the PZT beam between the two electrods). After, I would like to compare severals beam (lenght between 260 and 600µm), so the ratio increase? It is possible to realize this? Thanks
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Feb 24, 2012, 8:51 a.m. EST
Hi

one trick and comment. For such shapes, you should add a new Definition View node and unders Axis uncheck the "Preserve aspect ratio" andhit the geoemtry rescale ion to see the geoemtry better (but your dimension are now distorted, so when you mesh do not be scared it looks awful ;)
Sorry in 3.5 its elsewhere perhaps as a icone even but you have also the possibility to unlock axis scales

If you check your geoemtry, you have a few very small gaps, these might mess up your mesh. If these are relevant for your design (probably as they look more OK in the normal view), I would suggest, in case of meshing issues, that you cut up all your domains into rectangles (be "cubic" dfor such things) this adds a few internal boundaries but allows you to use easier structured and sweep mesh.

Another minor issue, you do not need to add two extra linear Elastic materials, if both are isotropic, you need only to add specific Linear material nodes when you mix isotropic and anisotropic materials. The material list tells COSMOL to refer to the correct material data so materials and linear elastic nodes might mix

But I get also strange shapes depending on the mesh, even if I remove the 4 pads, particularly with structured mesh, while I get a certain coherrnce with the results with thets. Your aspect ratio is really extreme. perhaps you should consider shell elements for the free memebrane but these are not that easy to knit in with strucutral

--
Good luck
Ivar
Hi one trick and comment. For such shapes, you should add a new Definition View node and unders Axis uncheck the "Preserve aspect ratio" andhit the geoemtry rescale ion to see the geoemtry better (but your dimension are now distorted, so when you mesh do not be scared it looks awful ;) Sorry in 3.5 its elsewhere perhaps as a icone even but you have also the possibility to unlock axis scales If you check your geoemtry, you have a few very small gaps, these might mess up your mesh. If these are relevant for your design (probably as they look more OK in the normal view), I would suggest, in case of meshing issues, that you cut up all your domains into rectangles (be "cubic" dfor such things) this adds a few internal boundaries but allows you to use easier structured and sweep mesh. Another minor issue, you do not need to add two extra linear Elastic materials, if both are isotropic, you need only to add specific Linear material nodes when you mix isotropic and anisotropic materials. The material list tells COSMOL to refer to the correct material data so materials and linear elastic nodes might mix But I get also strange shapes depending on the mesh, even if I remove the 4 pads, particularly with structured mesh, while I get a certain coherrnce with the results with thets. Your aspect ratio is really extreme. perhaps you should consider shell elements for the free memebrane but these are not that easy to knit in with strucutral -- Good luck Ivar

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