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Problems with Swept Meshing

Posted Feb 24, 2012, 2:20 a.m. EST MEMS & Nanotechnology, MEMS & Piezoelectric Devices, Mesh, Structural Mechanics Version 4.1 36 Replies

Sankha Mukherjee
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Hi,

I am new to Comsol and know very little about different features of the software. I am interested in finding the Eigen frquencies of a layered resonator (using a 3D object)). The resonator has a square mass (500X500X5 micron^3) at the it's center. This square mass is held by four beam (250X120X3.3) attached at the center of it's edges. These fingers have 7 layers of different materials. The square mass does not have layers. Thickness of these layers vary between 10 nm and 2 microns. The separation between the bottom layer of the square mass (which is at Z=0) and the bollom layer of the fingers (which is at Z=1.7) is 1.7 microns, i.e. they are not on the same plane.

Now, I use the swept mess feature along with free triangular option. To do this I start from the top layers of the beams and move down. I mesh the square mass along with the bottom most layer of the beams.However, while doing this I get "Unsupported topology or domain".

Can you get me out of this?

-Sankha
36 Replies Last Post Aug 5, 2015, 9:47 a.m. EDT
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, 2:30 a.m. EST
Hi

sweep mesh can be quite tough on complex geoemtrry models. Basically it accepts only models that are made in layers that is all swept domains must have the same height in the sweep direction, and only one common boundary defining your top (or bottom) sweep mesh "seed" is allowed. Often you can simply cut your geometry with a few internal boundaries for the large parts to get the seep to go through.

Other times you an only sweep mesh some parts and must use thets for the rest, note that you must then "Convert" the sweep meshed on the boundaries of the thet mesh into "tris", check the doc and the "mesh CONVERT" node

--
Good luck
Ivar
Hi sweep mesh can be quite tough on complex geoemtrry models. Basically it accepts only models that are made in layers that is all swept domains must have the same height in the sweep direction, and only one common boundary defining your top (or bottom) sweep mesh "seed" is allowed. Often you can simply cut your geometry with a few internal boundaries for the large parts to get the seep to go through. Other times you an only sweep mesh some parts and must use thets for the rest, note that you must then "Convert" the sweep meshed on the boundaries of the thet mesh into "tris", check the doc and the "mesh CONVERT" node -- Good luck Ivar
Sankha Mukherjee
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Posted: 1 decade ago Feb 24, 2012, 6:06 a.m. EST
Hi Ivar,

Thanks for replying. As you had suggested, I used sweet mesh for the layered beams (not the square mass). Then I converted the resulting triangular mesh into tetrahedral mesh. Now, I tried to apply free tetrahedral mesh onto the square center mass but got error message. "Following features have problems, feature :free tetrahedral 1"..

How can I mesh the squaremass separately and build all the domains together? is sweep meshing the only solution for high aspect ratio layered models?

-Sankha
Hi Ivar, Thanks for replying. As you had suggested, I used sweet mesh for the layered beams (not the square mass). Then I converted the resulting triangular mesh into tetrahedral mesh. Now, I tried to apply free tetrahedral mesh onto the square center mass but got error message. "Following features have problems, feature :free tetrahedral 1".. How can I mesh the squaremass separately and build all the domains together? is sweep meshing the only solution for high aspect ratio layered models? -Sankha
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, 8:18 a.m. EST
Hi

sweep mesh is often the best yes (again meshing is an art, as well as some science ;)

By the way you do not need to convert all your sweep mesh to teths, just select the boundaries to your square mass and convert these boundaries only, you will have far less elements like that, otherwise with your very high aspect ratio you will have some issues on RAM too soon ?

by the way you could also consider to replace perhaps some of the thin layer to "surface layers"

Take another look to your square mass, perhaps by first meshing the reamining boundaries of the mass with tri, and then try to mesh the volume. Or consider to cut your mass, i.e. along some symmetry lines to make it into 2-4 domains

or play with the finess of your mesh for the square mass, try finer and finer until it solves, then try to identify where are the very dense mesh, does it make sens, or do you have some smll features, then are these important for the FEM results ?


--
Good luck
Ivar
Hi sweep mesh is often the best yes (again meshing is an art, as well as some science ;) By the way you do not need to convert all your sweep mesh to teths, just select the boundaries to your square mass and convert these boundaries only, you will have far less elements like that, otherwise with your very high aspect ratio you will have some issues on RAM too soon ? by the way you could also consider to replace perhaps some of the thin layer to "surface layers" Take another look to your square mass, perhaps by first meshing the reamining boundaries of the mass with tri, and then try to mesh the volume. Or consider to cut your mass, i.e. along some symmetry lines to make it into 2-4 domains or play with the finess of your mesh for the square mass, try finer and finer until it solves, then try to identify where are the very dense mesh, does it make sens, or do you have some smll features, then are these important for the FEM results ? -- Good luck Ivar
Sankha Mukherjee
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Posted: 1 decade ago Feb 25, 2012, 12:44 a.m. EST
Hello Ivar,

Thanks for replying.

Looks like meshing is a real 'art'. I have attached schematics of my model. All the layers in the beams are attached to the square mass. I tried meshing (sweep) the square first and then meshing the layered beams. No luck.
Tried sweeping layers, converted them and then meshing square mass (both sweep and tetrahedral). Did not work.
Tried to sweep from sides and then meshing the square mass. Did not work either!!

Is there anything left to be tried?

Thanks

Sankha
Hello Ivar, Thanks for replying. Looks like meshing is a real 'art'. I have attached schematics of my model. All the layers in the beams are attached to the square mass. I tried meshing (sweep) the square first and then meshing the layered beams. No luck. Tried sweeping layers, converted them and then meshing square mass (both sweep and tetrahedral). Did not work. Tried to sweep from sides and then meshing the square mass. Did not work either!! Is there anything left to be tried? Thanks Sankha

Attachments:

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Feb 25, 2012, 8:32 a.m. EST
Hi

are your x-y scales isotropic or are the beams very thin ?, one way would be to cut the square at the height of the lower beam boundary, mesh the beams with tri on top and sweep through, then convert the surfaces = boundaries como to the upper square and try toget that one into a fine thet, you should allow for small mesh, reduce the minimum size to about the value of the smallest mesh in the beam section. Thereafter you mes the lower part of the square with a normal thet mesh.

Another way that works 100% but generates very man mesh elements, is to cut the square block along all the layers of your beams, so you have a full transverse "lasagne" plate there (hope you know italian cuisine ;) then you can mesh the full top surface with tri and sweep through the rest of your parts all the way down. You might want to add several dimensions and ensure you have a few layer per layer thickness

--
Good luck
Ivar
Hi are your x-y scales isotropic or are the beams very thin ?, one way would be to cut the square at the height of the lower beam boundary, mesh the beams with tri on top and sweep through, then convert the surfaces = boundaries como to the upper square and try toget that one into a fine thet, you should allow for small mesh, reduce the minimum size to about the value of the smallest mesh in the beam section. Thereafter you mes the lower part of the square with a normal thet mesh. Another way that works 100% but generates very man mesh elements, is to cut the square block along all the layers of your beams, so you have a full transverse "lasagne" plate there (hope you know italian cuisine ;) then you can mesh the full top surface with tri and sweep through the rest of your parts all the way down. You might want to add several dimensions and ensure you have a few layer per layer thickness -- Good luck Ivar
Sankha Mukherjee
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Posted: 1 decade ago Feb 25, 2012, 5:56 p.m. EST
Hi Ivar,

I tried to cut the square mass into layers and sweep meshed top 7 layers (which are in contact with the beams) along with the layers of the beams. It worked fine. So, now the only layer left to mesh is the bottom most layer of the square mass. To do this, I first tried sweep mesh. Then I converted the layer in the square mass which is in contact with this layer and use tetrahedral meshing, but that did not work either. I think I am missing something here. Why can't I mesh this layer? This layer is not in contact with the beams!! It's in contact with the square mass only.
When I tried sweep mesh this layer from side, the error was " Failed to copy mesh between edges, from the source face to destination face". When I tried to mesh from bottom surface, the error was "Mesh on source and destination face do not match". Does this have to do with mesh size?

Thickness of the square mass is 5 micron. Beams are 3.3 microns thick. The length of the square mass is 500 microns. The length of the beams is 250 micron and width is 120 micron.


Thanks,

Sankha
Hi Ivar, I tried to cut the square mass into layers and sweep meshed top 7 layers (which are in contact with the beams) along with the layers of the beams. It worked fine. So, now the only layer left to mesh is the bottom most layer of the square mass. To do this, I first tried sweep mesh. Then I converted the layer in the square mass which is in contact with this layer and use tetrahedral meshing, but that did not work either. I think I am missing something here. Why can't I mesh this layer? This layer is not in contact with the beams!! It's in contact with the square mass only. When I tried sweep mesh this layer from side, the error was " Failed to copy mesh between edges, from the source face to destination face". When I tried to mesh from bottom surface, the error was "Mesh on source and destination face do not match". Does this have to do with mesh size? Thickness of the square mass is 5 micron. Beams are 3.3 microns thick. The length of the square mass is 500 microns. The length of the beams is 250 micron and width is 120 micron. Thanks, Sankha
Sankha Mukherjee
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Posted: 1 decade ago Feb 25, 2012, 11:10 p.m. EST
Hi Ivar,


I have been able to mesh the model using the "lasagne" approach.I am thankful to you for listening to my problem and helping me with it.

However, I have a new problem. When I solve the model, get the following error "Failed to evaluate variable Jacobian". I checked boundary conditions, material properties. Everything is fine. I wonder why this is happening?

My model is such that the bottom layer of the beams and the square mass are connected. i.e. they are of the same material and hence are continuous. Other layers in the beam are disconnected, i.e. they are sitting on the bottom layer. Now, the way I have meshed the system, it is not continuous (i.e. the bottom layer of the beams and the square mass are disconnected, I have defined these as separate blocks)!! I tried to make union of these layers, but then I could not mesh using the "lasagne" approach.

How can I get of this?

Thanks

Sankha



Hi Ivar, I have been able to mesh the model using the "lasagne" approach.I am thankful to you for listening to my problem and helping me with it. However, I have a new problem. When I solve the model, get the following error "Failed to evaluate variable Jacobian". I checked boundary conditions, material properties. Everything is fine. I wonder why this is happening? My model is such that the bottom layer of the beams and the square mass are connected. i.e. they are of the same material and hence are continuous. Other layers in the beam are disconnected, i.e. they are sitting on the bottom layer. Now, the way I have meshed the system, it is not continuous (i.e. the bottom layer of the beams and the square mass are disconnected, I have defined these as separate blocks)!! I tried to make union of these layers, but then I could not mesh using the "lasagne" approach. How can I get of this? Thanks Sankha
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Feb 26, 2012, 2:37 a.m. EST
Hi

I do not really catch you, I had the impression that all your layers where connected with "continuity".

The Jacobian error often comes from boolean expressions in the BCs or some Dirac or discontinous functions used therein

--
Good luck
Ivar
Hi I do not really catch you, I had the impression that all your layers where connected with "continuity". The Jacobian error often comes from boolean expressions in the BCs or some Dirac or discontinous functions used therein -- Good luck Ivar
Sankha Mukherjee
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Posted: 1 decade ago Feb 27, 2012, 12:37 p.m. EST
Hello Ivar,

My model is working fine. I do not have problems with meshing or boundary condition. The problem I have is that, one of the layers in the beams is a piezoelectric material. For these materials we do not have a Young's modulus and Poisson's ratio. All we have is elasticity matrix, coupling matrix, density and permittivity matrix. Now, when I give this data along with the properties of other layers I get the error. When I replace this layer with other materials ( e.g.single-crystal Si, Aluminium, Ag...)of known properties (Young's modulus, Poisson's ratio, density) , the model works fine and gives consistent results. This means that the error is arising because I am not able to input the properties of the piezoelectric material properly! Can you help me with this? I do not know how to include material properties of piezoelectric materials for Eigenvalue problems.

Thank you for your help.

-Sankha
Hello Ivar, My model is working fine. I do not have problems with meshing or boundary condition. The problem I have is that, one of the layers in the beams is a piezoelectric material. For these materials we do not have a Young's modulus and Poisson's ratio. All we have is elasticity matrix, coupling matrix, density and permittivity matrix. Now, when I give this data along with the properties of other layers I get the error. When I replace this layer with other materials ( e.g.single-crystal Si, Aluminium, Ag...)of known properties (Young's modulus, Poisson's ratio, density) , the model works fine and gives consistent results. This means that the error is arising because I am not able to input the properties of the piezoelectric material properly! Can you help me with this? I do not know how to include material properties of piezoelectric materials for Eigenvalue problems. Thank you for your help. -Sankha
Sankha Mukherjee
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Posted: 1 decade ago Feb 28, 2012, 1:16 a.m. EST
Hello Ivar,

There is another thing weird. I have modeled a cantilevered beam with 1 micron thick piezo material on top of it. I use the elasticity matrix, density, coupling matrix and relative permitivitty of the material. Interestingly the model runs and gives consistent values. However, when I use the samle material properties for the resonator with the square mass, Comsol shows errors. for the Eigen frequency analysis of piezo electric material, do we need to input Young's modulus, Poisson's ratio? I have read your other posts on Eigen Frequency analysis (where you talked about IEEE conventions..) of piezoelectric materials but unfortunately could not understand the method.

Since, all the beams have the piezo layer, do I have to define local CS for each one of them and give the eleasticity matrix or can I give the properties of the material wrt the global coordinate system?

Can you provide the link for IEEE conventions for piezoelectric materials?

Thanks

Sankha
Hello Ivar, There is another thing weird. I have modeled a cantilevered beam with 1 micron thick piezo material on top of it. I use the elasticity matrix, density, coupling matrix and relative permitivitty of the material. Interestingly the model runs and gives consistent values. However, when I use the samle material properties for the resonator with the square mass, Comsol shows errors. for the Eigen frequency analysis of piezo electric material, do we need to input Young's modulus, Poisson's ratio? I have read your other posts on Eigen Frequency analysis (where you talked about IEEE conventions..) of piezoelectric materials but unfortunately could not understand the method. Since, all the beams have the piezo layer, do I have to define local CS for each one of them and give the eleasticity matrix or can I give the properties of the material wrt the global coordinate system? Can you provide the link for IEEE conventions for piezoelectric materials? Thanks Sankha
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Feb 28, 2012, 2:32 a.m. EST
Hi

if you enter constant values directly into the tensor component you must "just" ensure you respect the required symmetries and antisymmetries when applicable.

But if you enter functions of "t" or of spatial coordinates "x,y,z,r" or of the dependent variables, then it's better to define them in piecevise or analyitcal functions (and call these in the materials data) AND to add some derivatives to these functions thereby such that the solver can extract the Jacobian correctly

--
Good luck
Ivar
Hi if you enter constant values directly into the tensor component you must "just" ensure you respect the required symmetries and antisymmetries when applicable. But if you enter functions of "t" or of spatial coordinates "x,y,z,r" or of the dependent variables, then it's better to define them in piecevise or analyitcal functions (and call these in the materials data) AND to add some derivatives to these functions thereby such that the solver can extract the Jacobian correctly -- Good luck Ivar
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Feb 28, 2012, 3:21 a.m. EST
Hi

check the doc carefully there the tensor components are specified, also in the help I believe, it is correct that solid and PZT have a different index convention

--
Good luck
Ivar
Hi check the doc carefully there the tensor components are specified, also in the help I believe, it is correct that solid and PZT have a different index convention -- Good luck Ivar
Sankha Mukherjee
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Posted: 1 decade ago Feb 28, 2012, 11:42 p.m. EST
Hello Ivar,

Many thanks for your reply. You have been a true support all these days.

I went through all you had advised yesterday. But the problem still persists. I am getting frustrated every time I try to solve this model. The Piezoelectric material in my model is ZnO and it turns out that Comsol has all the properties of ZnO (except for Poisson's ratio and Young's modulus') built-in it. I have attached simple version of my model with composite layers replaced by block of ZnO, for which I tried to run the simulations and got errors. When I use any other element (e.g. Aluminium,Cr, Cu) , the model runs perfectly. Surprisingly, When I use same properties of ZnO for a silicon cantilever beam with 1 micron ZnO coating (model attached), Comsol works! I am clueless about what is going wrong.!!!!

Once again, many many thanks for helping me out with this analysis.

-Sankha
Hello Ivar, Many thanks for your reply. You have been a true support all these days. I went through all you had advised yesterday. But the problem still persists. I am getting frustrated every time I try to solve this model. The Piezoelectric material in my model is ZnO and it turns out that Comsol has all the properties of ZnO (except for Poisson's ratio and Young's modulus') built-in it. I have attached simple version of my model with composite layers replaced by block of ZnO, for which I tried to run the simulations and got errors. When I use any other element (e.g. Aluminium,Cr, Cu) , the model runs perfectly. Surprisingly, When I use same properties of ZnO for a silicon cantilever beam with 1 micron ZnO coating (model attached), Comsol works! I am clueless about what is going wrong.!!!! Once again, many many thanks for helping me out with this analysis. -Sankha
Sankha Mukherjee
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Posted: 1 decade ago Mar 1, 2012, 9:45 p.m. EST
Hello,

Since I have Piezoelectric material in my model, should I choose "Piezoelectric Devices" as the driving physics? I am confused here! I am not analyzing Piezo-electric properties of this layer though. It's just that, to obtain the resonance frequency I need to be able to provide the material properties and physics properly so that Comsol can understand it and run the Eigen Frequency analysis. I feel like very close to the solution. Just stuck at this last hurdle!

Will be waiting for your kind help.

Thanks

Sankha
Hello, Since I have Piezoelectric material in my model, should I choose "Piezoelectric Devices" as the driving physics? I am confused here! I am not analyzing Piezo-electric properties of this layer though. It's just that, to obtain the resonance frequency I need to be able to provide the material properties and physics properly so that Comsol can understand it and run the Eigen Frequency analysis. I feel like very close to the solution. Just stuck at this last hurdle! Will be waiting for your kind help. Thanks Sankha
Sankha Mukherjee
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Posted: 1 decade ago Mar 1, 2012, 10:28 p.m. EST
Hello,

Earlier I was using Solid mechanics as the driving physics for Eigen frequency analysis. I was getting error ' Failed to evaluate variable Jacobian '. Now I use Piezoelectric devices as the driving physics. Well, I do not get any error, but get imaginary frequencies.

All I am trying to model is a layered resonator which has (unfortunately!) a piezoelectric layer! Which physics should I select? How do I make Comsol understand that ZnO is a anisotropic material (has elasticity matrix) where as rest of the materials are isotropic material (has Young's modulus and Poisson's ratio) !!!!!!!!!!!!!!!!!


Thanks

Sankha
Hello, Earlier I was using Solid mechanics as the driving physics for Eigen frequency analysis. I was getting error ' Failed to evaluate variable Jacobian '. Now I use Piezoelectric devices as the driving physics. Well, I do not get any error, but get imaginary frequencies. All I am trying to model is a layered resonator which has (unfortunately!) a piezoelectric layer! Which physics should I select? How do I make Comsol understand that ZnO is a anisotropic material (has elasticity matrix) where as rest of the materials are isotropic material (has Young's modulus and Poisson's ratio) !!!!!!!!!!!!!!!!! Thanks Sankha
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Mar 2, 2012, 1:45 a.m. EST
Hi

1) complex eigenfrequencies means you have damping i.e. probably from the PZT ircuit, and you should get different frequency results for short and open circuit PZT

2) if you hve a combination of slid and PZT you need to add a second (or more) linear elastic material sub-nodes ,one for the isotropic, one for the anisotropic per orientation

3) normally you should not mix SOLID and PZD physics, as PSD cover SOLID already (+ parts of ES/EC + PZT materials physics)

--
Good luck
Ivar
Hi 1) complex eigenfrequencies means you have damping i.e. probably from the PZT ircuit, and you should get different frequency results for short and open circuit PZT 2) if you hve a combination of slid and PZT you need to add a second (or more) linear elastic material sub-nodes ,one for the isotropic, one for the anisotropic per orientation 3) normally you should not mix SOLID and PZD physics, as PSD cover SOLID already (+ parts of ES/EC + PZT materials physics) -- Good luck Ivar
Sankha Mukherjee
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Posted: 1 decade ago Mar 2, 2012, 9:27 p.m. EST
Hello Ivar,

Thanks for replying. To solve this problem, I computed the elasticity matrixes of the other layers and use this as the input. I made the components of the coupling matrix 0. However, I still get an imaginary Eigen Frequency (a+ib form)..

I did not understand the open circuit and short circuit part? I have not applied any voltage to the resonator! I am running the Eigen Frequency analysis. Do you mean, for the the Eigen frequency analysis of a layered Piezoelectric resonator we would always get an imaginary frequency?

When you say that I should apply an extra node do you mean in the Piezoelectric devices module, I tried to do that, but then the domains in the "Piezoelectric material model 1" node, same domains get overdriven. This happens because, when I use the Piezoelectric devices physics, all the domains are selected in the "Piezoelectric material model 1" automatically. Hence, when I try to use linear elastic material sub-nodes for the Isotropic materials (metals, polymers), these domains get overdriven.

Thanks,

Sankha
Hello Ivar, Thanks for replying. To solve this problem, I computed the elasticity matrixes of the other layers and use this as the input. I made the components of the coupling matrix 0. However, I still get an imaginary Eigen Frequency (a+ib form).. I did not understand the open circuit and short circuit part? I have not applied any voltage to the resonator! I am running the Eigen Frequency analysis. Do you mean, for the the Eigen frequency analysis of a layered Piezoelectric resonator we would always get an imaginary frequency? When you say that I should apply an extra node do you mean in the Piezoelectric devices module, I tried to do that, but then the domains in the "Piezoelectric material model 1" node, same domains get overdriven. This happens because, when I use the Piezoelectric devices physics, all the domains are selected in the "Piezoelectric material model 1" automatically. Hence, when I try to use linear elastic material sub-nodes for the Isotropic materials (metals, polymers), these domains get overdriven. Thanks, Sankha
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Mar 3, 2012, 5:48 a.m. EST
Hi

I have only 4.2a so you might no be able to open the file below, but the png show different frequencies obtained for a PZT+Al stack with one electrode GND, with both GND, one GND and the other at 1kV potential, and last the stationry prestressed GND+1kV case with an eigenfrequency therafter

Yo uget a change in frequency for open and shortened electrodes, from which you can extract the coupling quality factor, now the complex part means that the response is dephased due to damping in the PZD

These where done in linea mode (no geoemtrical non-linearity used)

--
Good luck
Ivar
Hi I have only 4.2a so you might no be able to open the file below, but the png show different frequencies obtained for a PZT+Al stack with one electrode GND, with both GND, one GND and the other at 1kV potential, and last the stationry prestressed GND+1kV case with an eigenfrequency therafter Yo uget a change in frequency for open and shortened electrodes, from which you can extract the coupling quality factor, now the complex part means that the response is dephased due to damping in the PZD These where done in linea mode (no geoemtrical non-linearity used) -- Good luck Ivar
Sankha Mukherjee
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Posted: 1 decade ago Mar 3, 2012, 9:20 a.m. EST
Hello,

Thanks a lot for replying. I understand that the complex frequencies are obtained because of the damping in the material. "Should we always get complex Eigen frequencies for a layered Piezoelectric resonator?". Because the results that you have sent me are for PZT connected in circuits!!!!

The problem is that I am new to Comsol and I do not know whether I have done the analysis properly or not. It is possible that I have done something wrong somewhere and that is why the imaginary Eigen frequency is arising.

1) Is there a way to check the accuracy of my simulation? How can I make sure that whatever I have done is correct.

2) Is there a way to calculate the error associated with the analysis? When I start modelling, there is this parameter "Relative tolerance". What this number means? The error associated with the analysis depends on this number.

Thanks

Sankha
Hello, Thanks a lot for replying. I understand that the complex frequencies are obtained because of the damping in the material. "Should we always get complex Eigen frequencies for a layered Piezoelectric resonator?". Because the results that you have sent me are for PZT connected in circuits!!!! The problem is that I am new to Comsol and I do not know whether I have done the analysis properly or not. It is possible that I have done something wrong somewhere and that is why the imaginary Eigen frequency is arising. 1) Is there a way to check the accuracy of my simulation? How can I make sure that whatever I have done is correct. 2) Is there a way to calculate the error associated with the analysis? When I start modelling, there is this parameter "Relative tolerance". What this number means? The error associated with the analysis depends on this number. Thanks Sankha
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Mar 3, 2012, 12:05 p.m. EST
Hi

I have not conneced it to any circuit, just left a gnd or a fixed voltage, the terminal is equivalent to adding a thin highly conductive electrode on the top so you have the same voltage over the full electrode.

From the moment you have a PZT that generates voltage when bent, and that you apply a voltage these will interact and you get the equivalent of a damping in the material, and this will depend on the impedance of your supply, hence different frequencies at the output. And complex eigenfrequencies. Check you books on PZT, Prof. Preumont has written several interesting ones ;)

--
Good luck
Ivar
Hi I have not conneced it to any circuit, just left a gnd or a fixed voltage, the terminal is equivalent to adding a thin highly conductive electrode on the top so you have the same voltage over the full electrode. From the moment you have a PZT that generates voltage when bent, and that you apply a voltage these will interact and you get the equivalent of a damping in the material, and this will depend on the impedance of your supply, hence different frequencies at the output. And complex eigenfrequencies. Check you books on PZT, Prof. Preumont has written several interesting ones ;) -- Good luck Ivar
Sankha Mukherjee
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Posted: 1 decade ago Mar 3, 2012, 3:40 p.m. EST

From the moment you have a PZT that generates voltage when bent, and that you apply a voltage these will interact and you get the equivalent of a damping in the material, and this will depend on the impedance of your supply, hence different frequencies at the output. And complex eigenfrequencies.


Hello,

When the PZT is bent it generates electrical voltage-this is understood. But "that you apply a voltage these will interact and you get the equivalent of a damping in the material" this is not clear. Do you mean when a PZT is oscillating if I apply a voltage to the electrode, then only Eigen Frequencies are obtained? If that is the case, I should not get Complex frequencies!!

Do you mean that because of oscillation DC voltage is generated at the electrodes and since the system is oscillating at the same time, coupling of these two phenomena results in complex Eigen frequencies?


Thanks

Sankha

[QUOTE] From the moment you have a PZT that generates voltage when bent, and that you apply a voltage these will interact and you get the equivalent of a damping in the material, and this will depend on the impedance of your supply, hence different frequencies at the output. And complex eigenfrequencies. [/QUOTE] Hello, When the PZT is bent it generates electrical voltage-this is understood. But "that you apply a voltage these will interact and you get the equivalent of a damping in the material" this is not clear. Do you mean when a PZT is oscillating if I apply a voltage to the electrode, then only Eigen Frequencies are obtained? If that is the case, I should not get Complex frequencies!! Do you mean that because of oscillation DC voltage is generated at the electrodes and since the system is oscillating at the same time, coupling of these two phenomena results in complex Eigen frequencies? Thanks Sankha
Sankha Mukherjee
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Posted: 1 decade ago Mar 3, 2012, 5:08 p.m. EST
Hello,

In my problem if I replace all the metallic layers with polymer (that is ZnO is sandwiched between polymer layers), I still get complex Eigen Frequency!! Since, there is no metal electrode I should not expect any damping to occur!

I wonder why this problem is arising!

Thanks

Sankha

Hello, In my problem if I replace all the metallic layers with polymer (that is ZnO is sandwiched between polymer layers), I still get complex Eigen Frequency!! Since, there is no metal electrode I should not expect any damping to occur! I wonder why this problem is arising! Thanks Sankha
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Mar 4, 2012, 2:17 a.m. EST
Hi

for me a complex eigenfrequency should be seen as a phasor (amplitude and phase) indicating that the response is dephased w.r.t the excitation (you also observe this if one look at the eigenfrequency metallic beam with damping).

The reason why a PZT changes frequency physe in open and closed circuit (charge acumulation and charge exchange) is that the PZT charge generated from the bending of the beam interacts with the bending motion (and differently in charge accumulation and charge exchange mode)

--
Good luck
Ivar
Hi for me a complex eigenfrequency should be seen as a phasor (amplitude and phase) indicating that the response is dephased w.r.t the excitation (you also observe this if one look at the eigenfrequency metallic beam with damping). The reason why a PZT changes frequency physe in open and closed circuit (charge acumulation and charge exchange) is that the PZT charge generated from the bending of the beam interacts with the bending motion (and differently in charge accumulation and charge exchange mode) -- Good luck Ivar
Sankha Mukherjee
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Posted: 1 decade ago Mar 4, 2012, 5:00 a.m. EST
Hello Ivar,

Thanks for replying. I understand what you mean by damping in PZT leading to complex Eigen frequencies. Infact in case of damping of coated cantilevers stress and strain are out of phase by a loss angle that has direct correspondence with the damping ratio.

But what is bothering me is that when I remove all metal layers and replace them by polymer, I still end up with complex Eigen frequencies. I am a beginner in Comsol, and doubt that I have done something wrong. Would it be possible for you to look at my model and let me know If what I have done is correct at all !!


I am attaching my model with this mail.


Thank you,

Sankha
Hello Ivar, Thanks for replying. I understand what you mean by damping in PZT leading to complex Eigen frequencies. Infact in case of damping of coated cantilevers stress and strain are out of phase by a loss angle that has direct correspondence with the damping ratio. But what is bothering me is that when I remove all metal layers and replace them by polymer, I still end up with complex Eigen frequencies. I am a beginner in Comsol, and doubt that I have done something wrong. Would it be possible for you to look at my model and let me know If what I have done is correct at all !! I am attaching my model with this mail. Thank you, Sankha

Attachments:

Sankha Mukherjee
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Posted: 1 decade ago Mar 9, 2012, 4:24 p.m. EST
Hello Ivar,

I have been reading about damping in PZT for last few days to find out the reasons for obtaining complex Eigen frequencies. It appears that complex frequencies are obtained if dielectric losses or mechanical losses have been defined in the model. Is there a way of removing these definitions from the model. If I use 'Piezoelectric material properties' these parameters are selected by default. However, the numbers in permitivitty and loss vectors are set to as zero. My question is since the vectors are zero, should we still see damping?

It would be of immense help if you could spare some time and look at model just to ensure that I have not made any mistakes.

Thanks

Sankha
Hello Ivar, I have been reading about damping in PZT for last few days to find out the reasons for obtaining complex Eigen frequencies. It appears that complex frequencies are obtained if dielectric losses or mechanical losses have been defined in the model. Is there a way of removing these definitions from the model. If I use 'Piezoelectric material properties' these parameters are selected by default. However, the numbers in permitivitty and loss vectors are set to as zero. My question is since the vectors are zero, should we still see damping? It would be of immense help if you could spare some time and look at model just to ensure that I have not made any mistakes. Thanks Sankha

Attachments:

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Mar 10, 2012, 3:58 a.m. EST
Hi

I do not understand why you want to remove this additional information, that is due to the material proerties and the way you drive your device. For me these are essential and part of the model.

If you want to have a real value to work with, use the "phasor" notation and separate the amplitude and phase
lamb = lamb_r + i*lamb_i = sqrt(lamb_r^2+lamb_i^2) * exp(-i*atan(lamb_i, lamb_r))

see also the web with "phasor Wiki" and "phasor Wolfram"

For me there is no reasons neither mahematical nor physical why the eigenfrequencies should be only "real"

--
Good luck
Ivar
Hi I do not understand why you want to remove this additional information, that is due to the material proerties and the way you drive your device. For me these are essential and part of the model. If you want to have a real value to work with, use the "phasor" notation and separate the amplitude and phase lamb = lamb_r + i*lamb_i = sqrt(lamb_r^2+lamb_i^2) * exp(-i*atan(lamb_i, lamb_r)) see also the web with "phasor Wiki" and "phasor Wolfram" For me there is no reasons neither mahematical nor physical why the eigenfrequencies should be only "real" -- Good luck Ivar
Sankha Mukherjee
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Posted: 1 decade ago Mar 13, 2012, 7:19 p.m. EDT
Hello Ivar,

Thanks for explaining the phasor notation. For last few days I was trying to study the frequency response of my samples. I wanted to give the model a frequency sweep from 100 Hz to 30000 Hz. To start with I studied frequency response of a simple cantilever beam, a plate and got consistent results. However, when I try to simulate frequency response of my sample COMSOL gives following error -

"Failed to find a solution for the initial parameter. The relative error (X) is greater than the relative tolerance Returned solution has not converged."

I have tried using very small amplitudes (body load in Z =0.1 N/m3) and have chosen sweep-step such a way that the resonance frequencies are be avoided. Unfortunately the problem persists.I do not have a clue as to why this is happening.

-Sankha
Hello Ivar, Thanks for explaining the phasor notation. For last few days I was trying to study the frequency response of my samples. I wanted to give the model a frequency sweep from 100 Hz to 30000 Hz. To start with I studied frequency response of a simple cantilever beam, a plate and got consistent results. However, when I try to simulate frequency response of my sample COMSOL gives following error - "Failed to find a solution for the initial parameter. The relative error (X) is greater than the relative tolerance Returned solution has not converged." I have tried using very small amplitudes (body load in Z =0.1 N/m3) and have chosen sweep-step such a way that the resonance frequencies are be avoided. Unfortunately the problem persists.I do not have a clue as to why this is happening. -Sankha
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Mar 14, 2012, 2:28 a.m. EDT
Hi

start much simpler, even I would say in 2D with a sandwitch bar of metal+ 1 pzt layer and fix at one end, then do a eigenfrequency analysis and a frequency domain sweep over a few modes. This will give you allt eh difficulties to get :
1) mesh compatible with the expected modes (and in thickness to resolve the fields and stress correctly)
2) required damoing to pass the resonances and not stop on the first one
3) time stepping settings and tuning to follow the resoanance increas and skip overt the peak, and get the decay, and so on for all modes (even with damping)

Then finally you can go to your major example. Do not forget it's over constraint, and that your example is solely relying on stress extension => needs a more intense meshing and hence far moretime to solve

But you will get there I'm sure, it's just that there are so many buttons to tweak in COMSOL, that learning is quicker with a simpler example

--
Good luck
Ivar
Hi start much simpler, even I would say in 2D with a sandwitch bar of metal+ 1 pzt layer and fix at one end, then do a eigenfrequency analysis and a frequency domain sweep over a few modes. This will give you allt eh difficulties to get : 1) mesh compatible with the expected modes (and in thickness to resolve the fields and stress correctly) 2) required damoing to pass the resonances and not stop on the first one 3) time stepping settings and tuning to follow the resoanance increas and skip overt the peak, and get the decay, and so on for all modes (even with damping) Then finally you can go to your major example. Do not forget it's over constraint, and that your example is solely relying on stress extension => needs a more intense meshing and hence far moretime to solve But you will get there I'm sure, it's just that there are so many buttons to tweak in COMSOL, that learning is quicker with a simpler example -- Good luck Ivar
Sankha Mukherjee
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Posted: 1 decade ago Mar 14, 2012, 3:16 a.m. EDT
Hello Ivar,

Thanks for your reply. Although I am bit nervous whether I will be able to get it done!! But never mind, I had a hard time finding out the resonance frequencies and at the end I managed to solve it. I would give my best and with your expert suggestions I am sure I will be able it this time also.

Sankha
Hello Ivar, Thanks for your reply. Although I am bit nervous whether I will be able to get it done!! But never mind, I had a hard time finding out the resonance frequencies and at the end I managed to solve it. I would give my best and with your expert suggestions I am sure I will be able it this time also. Sankha
Sankha Mukherjee
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Posted: 1 decade ago Mar 14, 2012, 4:01 a.m. EDT
Hello,

It would be of real help if you could share with me any simple model of a resonator with a PZT for which frequency domain analysis was done. I have COMSOL 4.1.

Many thanks.

-Sankha
Hello, It would be of real help if you could share with me any simple model of a resonator with a PZT for which frequency domain analysis was done. I have COMSOL 4.1. Many thanks. -Sankha
Sankha Mukherjee
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Posted: 1 decade ago Mar 14, 2012, 10:57 p.m. EDT
Hello Ivar,

As usual I have encountered a problem with very thin layers. As you had advised I started with a very simple model. a cantilever 100 microns (Gold) with 10 micron ZnO. Did not work. I studied the 'Shear Bender' example in the COMSOL library and understood that to find out FRF of a PZT one should use ground-electric potential instead of body loads. Then I tried to use this BC to model the cantilever beam. I applied 100 micron Gold on top of ZnO. SO now the PZT (10 micron) was sandwitched between 2 gold layers (each 100 micron). But still it would not work!

Then I tried increasing the tickness of PZT and changed it to 20 microns and Walla!! it worked. So I realize that the problem I am encountering is because I have very thin layers in my geometry!! In my model I have metal layers of 10 nm and polymer layers of 2 microns. Since COMSOL is unable to handle 10 microns PZT, will it ever be able to handle a PZT layer of 200 nm and metal layer of 10 nm?

Thanks

Sankha

Hello Ivar, As usual I have encountered a problem with very thin layers. As you had advised I started with a very simple model. a cantilever 100 microns (Gold) with 10 micron ZnO. Did not work. I studied the 'Shear Bender' example in the COMSOL library and understood that to find out FRF of a PZT one should use ground-electric potential instead of body loads. Then I tried to use this BC to model the cantilever beam. I applied 100 micron Gold on top of ZnO. SO now the PZT (10 micron) was sandwitched between 2 gold layers (each 100 micron). But still it would not work! Then I tried increasing the tickness of PZT and changed it to 20 microns and Walla!! it worked. So I realize that the problem I am encountering is because I have very thin layers in my geometry!! In my model I have metal layers of 10 nm and polymer layers of 2 microns. Since COMSOL is unable to handle 10 microns PZT, will it ever be able to handle a PZT layer of 200 nm and metal layer of 10 nm? Thanks Sankha
Sankha Mukherjee
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Posted: 1 decade ago Mar 16, 2012, 1:17 a.m. EDT
Hello Ivar,

I have tried different mesh densities in the X-Y plane and in the thickness direction. Still not able to run the frequency domain analysis. Any innovative thoughts as to how to get out of this?

Thanks

Sankha
Hello Ivar, I have tried different mesh densities in the X-Y plane and in the thickness direction. Still not able to run the frequency domain analysis. Any innovative thoughts as to how to get out of this? Thanks Sankha
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Mar 19, 2012, 3:00 a.m. EDT
Hi

there is no reason why COMSOL should not be able to model even nm structures (it works OK for me at least in my current 4.2a version, and it did so too for 3.5a)

But have you checked first that you get
1) a dispalcement in statonary mode,
2) that you know the eigenfrequencies,
3) you do a frequency scan fine enough around th eigenfrequency so the solver manages to follow, including that you have enough damping deined so that your resonant peak is finite ?

The most common erro in PZD is to not set up the corret polarization direction, note that the default corrdinate system is mostly NOT the best one (in 2D) to get any displacement, and do not forget that thePZD module has a different elasticity matrix ordering, following the IEEE convention, than from the standard "solid". This is all written in thehelp, and doc, and on the main PZD node tab

--
Good luck
Ivar
Hi there is no reason why COMSOL should not be able to model even nm structures (it works OK for me at least in my current 4.2a version, and it did so too for 3.5a) But have you checked first that you get 1) a dispalcement in statonary mode, 2) that you know the eigenfrequencies, 3) you do a frequency scan fine enough around th eigenfrequency so the solver manages to follow, including that you have enough damping deined so that your resonant peak is finite ? The most common erro in PZD is to not set up the corret polarization direction, note that the default corrdinate system is mostly NOT the best one (in 2D) to get any displacement, and do not forget that thePZD module has a different elasticity matrix ordering, following the IEEE convention, than from the standard "solid". This is all written in thehelp, and doc, and on the main PZD node tab -- Good luck Ivar
Sankha Mukherjee
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Posted: 1 decade ago Mar 19, 2012, 3:23 a.m. EDT
Hello Ivar,

It's good to hear from you. I had almost given up on the frequency analysis of my model. But now I feel like trying again. I have done Eigen frequency analysis of my design and have got consistent results. I have used the material properties from the COMSOL materials library. I have used extremely fine mesh and have tried Frequency sweeps close to the resonance frequency and far away from resonance frequency. What I have not done are the followings-

1) Stationary study 2) Have not used "enough damping denied". While I understand statioary study, I do not understand "enough damping". Could you write in short what do you mean by enough damping and how to implement that in Comsol. I think that might work.


Thanks

Sankha
Hello Ivar, It's good to hear from you. I had almost given up on the frequency analysis of my model. But now I feel like trying again. I have done Eigen frequency analysis of my design and have got consistent results. I have used the material properties from the COMSOL materials library. I have used extremely fine mesh and have tried Frequency sweeps close to the resonance frequency and far away from resonance frequency. What I have not done are the followings- 1) Stationary study 2) Have not used "enough damping denied". While I understand statioary study, I do not understand "enough damping". Could you write in short what do you mean by enough damping and how to implement that in Comsol. I think that might work. Thanks Sankha
Subhabrata Nath
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Posted: 9 years ago Aug 5, 2015, 6:38 a.m. EDT
Hi buddy. I am a MTech scholar currently new to this software, and I need some help regarding it. Can u plz ping me back when u get this??
Hi buddy. I am a MTech scholar currently new to this software, and I need some help regarding it. Can u plz ping me back when u get this??
Walter Frei COMSOL Employee

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Posted: 9 years ago Aug 5, 2015, 9:47 a.m. EDT
Dear Subhabrata,

This latest question is a bit off topic from the original thread, so we instead suggest that you post your specific questions in the new thread and provide details about exactly what you have questions about.

If you are new to the software, then we do suggest the Introduction to COMSOL Multiphysics booklet, available here:
www.comsol.com/documentation/IntroductionToCOMSOLMultiphysics.pdf
And that you browse the Application Gallery for examples closest to what you investigating:
www.comsol.com/models

Since this original thread is now several years old and has been inactive for some time, we will close it for further comments. It will remain visible if anyone wants to reference the discussion in a new thread.

Best Regards,
Walter
Dear Subhabrata, This latest question is a bit off topic from the original thread, so we instead suggest that you post your specific questions in the new thread and provide details about exactly what you have questions about. If you are new to the software, then we do suggest the Introduction to COMSOL Multiphysics booklet, available here: http://www.comsol.com/documentation/IntroductionToCOMSOLMultiphysics.pdf And that you browse the Application Gallery for examples closest to what you investigating: http://www.comsol.com/models Since this original thread is now several years old and has been inactive for some time, we will close it for further comments. It will remain visible if anyone wants to reference the discussion in a new thread. Best Regards, Walter

Note that while COMSOL employees may participate in the discussion forum, COMSOL® software users who are on-subscription should submit their questions via the Support Center for a more comprehensive response from the Technical Support team.

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