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Piezoelectric Devices with Electrical Circuit Help

Posted 2010年12月15日 GMT-5 14:56 MEMS & Nanotechnology, Piezoelectric Devices 28 Replies

Mike Bradley
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Hello -

Ive been using COMSOl for about 6 months, and working with Piezoelectric devices. I recently upgraded to the ACDC module to include SPICE models with my piezo component models. I would like to look at parameters such as output voltage some a set input force etc. But instead of purely open circuit solutions (floating potential) I want to be able to electrically load the piezo.



Mike B.
28 Replies Last Post 2014年3月23日 GMT-4 23:24
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago 2010年12月16日 GMT-5 02:15
Hi Mike

I'm sorry not to be ble to help here, but I wanted to state that I have the same issue on my "todo list" (but the list is looong and that subject has not managed to "float up", yet)

If I have understood the explanatons from COMSOL, its primary intended to couple the SPICE models to the lumped "ports" as the "spatial varying" physics are reduced to single node in-out-puts in this way

--
Good luck
Ivar
Hi Mike I'm sorry not to be ble to help here, but I wanted to state that I have the same issue on my "todo list" (but the list is looong and that subject has not managed to "float up", yet) If I have understood the explanatons from COMSOL, its primary intended to couple the SPICE models to the lumped "ports" as the "spatial varying" physics are reduced to single node in-out-puts in this way -- Good luck Ivar
Mike Bradley
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Posted: 1 decade ago 2010年12月16日 GMT-5 09:15
Ivar,

COMSOL does seems to want to use the Terminals and External U v I and I v U tools to couple from the piezo to the circuit and vice versa, in theory attaching a resistor to a piezo generator, can act to significantly damp any vibrations present in the device. Thanks for your reply; I will keep working on this. If I have success I will try to post the solutions. Please let me know of any developments.

Mike B.
Ivar, COMSOL does seems to want to use the Terminals and External U v I and I v U tools to couple from the piezo to the circuit and vice versa, in theory attaching a resistor to a piezo generator, can act to significantly damp any vibrations present in the device. Thanks for your reply; I will keep working on this. If I have success I will try to post the solutions. Please let me know of any developments. Mike B.
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago 2010年12月16日 GMT-5 10:09
Hi Mike

Indeed I would state that in theory AND in practive the presence of a resistor changes drastically the response of an PZT.

Most common PZT failure is to forget to short the leads when transporting the device, which can become quite expensive when you handle several kg large PZT stacks ;)

--
Good luck
Ivar
Hi Mike Indeed I would state that in theory AND in practive the presence of a resistor changes drastically the response of an PZT. Most common PZT failure is to forget to short the leads when transporting the device, which can become quite expensive when you handle several kg large PZT stacks ;) -- Good luck Ivar
Mike Bradley
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Posted: 1 decade ago 2010年12月16日 GMT-5 13:10
Ivar,

Indeed! The pyroelectric effect of the piezo can also generate a good jolt when curing adhesives and such. I've gotten a good zap on a few occasions from absent-mindedly handling piezo post cure.

Thanks again!

Mike B.
Ivar, Indeed! The pyroelectric effect of the piezo can also generate a good jolt when curing adhesives and such. I've gotten a good zap on a few occasions from absent-mindedly handling piezo post cure. Thanks again! Mike B.
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago 2010年12月16日 GMT-5 13:37
Hi

well, for me COMSOL is set up exactly for such things, but it's always somewhat tough the first time, that is also why I'm neither not there, yet ;)

Often it's worth to try a simple model, such as a bulk FEM resistor and loop it around a SPICE model (its also on my to-do list, as starter ;)

--
Good luck
Ivar
Hi well, for me COMSOL is set up exactly for such things, but it's always somewhat tough the first time, that is also why I'm neither not there, yet ;) Often it's worth to try a simple model, such as a bulk FEM resistor and loop it around a SPICE model (its also on my to-do list, as starter ;) -- Good luck Ivar
Bindu Madhava Rao Pydi
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Posted: 1 decade ago 2012年4月25日 GMT-4 11:06
I am working on a project on thermal energy harvesting using pyroelectric cells. I need to do some simulation for that. So could you please help me by providing materials for building a pyroelectric model in COMSOL and what physics involved in it
I am working on a project on thermal energy harvesting using pyroelectric cells. I need to do some simulation for that. So could you please help me by providing materials for building a pyroelectric model in COMSOL and what physics involved in it
Rocksmida
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Posted: 1 decade ago 2012年9月12日 GMT-4 19:01

Ivar,

COMSOL does seems to want to use the Terminals and External U v I and I v U tools to couple from the piezo to the circuit and vice versa, in theory attaching a resistor to a piezo generator, can act to significantly damp any vibrations present in the device. Thanks for your reply; I will keep working on this. If I have success I will try to post the solutions. Please let me know of any developments.

Mike B.


Hi, Mike, I am working on a project about the damping of a vibrating pzt cantilever using shunt circuit. But it seems that the circuit has no effect on the vibration. Do you have any suggestion？ Have you found a solution to your problem? Thanks
[QUOTE] Ivar, COMSOL does seems to want to use the Terminals and External U v I and I v U tools to couple from the piezo to the circuit and vice versa, in theory attaching a resistor to a piezo generator, can act to significantly damp any vibrations present in the device. Thanks for your reply; I will keep working on this. If I have success I will try to post the solutions. Please let me know of any developments. Mike B. [/QUOTE] Hi, Mike, I am working on a project about the damping of a vibrating pzt cantilever using shunt circuit. But it seems that the circuit has no effect on the vibration. Do you have any suggestion？ Have you found a solution to your problem? Thanks
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago 2012年9月13日 GMT-4 04:02
Hi

when correctly linked, the CIR physics definitively interacts with the PZT physics, but I must admit too it took me some tries to get it runing smoothly. There are alread a few examples on the Forum, try a "search" and I believe one in the emodel library (perhaps only for the newer versions ? as I'm not behind my WS these days I cannot check)

By the way COMSOL Web developpers:
what about allowing us to search the Forum with a "has_attachments" filter ? it could speed-up things, there are many goodies hard to find scattered around here ;)

We will see if they are listening ...

--
Good luck
Ivar
Hi when correctly linked, the CIR physics definitively interacts with the PZT physics, but I must admit too it took me some tries to get it runing smoothly. There are alread a few examples on the Forum, try a "search" and I believe one in the emodel library (perhaps only for the newer versions ? as I'm not behind my WS these days I cannot check) By the way COMSOL Web developpers: what about allowing us to search the Forum with a "has_attachments" filter ? it could speed-up things, there are many goodies hard to find scattered around here ;) We will see if they are listening ... -- Good luck Ivar
Rocksmida
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Posted: 1 decade ago 2012年9月13日 GMT-4 09:42
Thanks Ivar,

You mean there are models available for the shunt damping of PZTs? I searched through the forum and can not get such a example. Any further information? also, I posted another thread about my problem in details, can you have a look at it, especially at the "links" between the two module?
www.comsol.com/community/forums/piezoelectric/thread/31515/

Many thanks!
Thanks Ivar, You mean there are models available for the shunt damping of PZTs? I searched through the forum and can not get such a example. Any further information? also, I posted another thread about my problem in details, can you have a look at it, especially at the "links" between the two module? http://www.comsol.com/community/forums/piezoelectric/thread/31515/ Many thanks!
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago 2012年9月16日 GMT-4 02:53
Hi

what about this one ?
www.comsol.eu/community/forums/general/thread/17407/

note that a few open links has been corrected since 4.1 so it might be worth to rewrite it from scratch in 4.3, and not to attempt a "translation", my experience never fully trust "translations". (but I must admit I havent had any failures, when I do not follow my rule, since 4.2a, so things have improved ;)

--
Good luck
Ivar
Hi what about this one ? http://www.comsol.eu/community/forums/general/thread/17407/ note that a few open links has been corrected since 4.1 so it might be worth to rewrite it from scratch in 4.3, and not to attempt a "translation", my experience never fully trust "translations". (but I must admit I havent had any failures, when I do not follow my rule, since 4.2a, so things have improved ;) -- Good luck Ivar
Rocksmida
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Posted: 1 decade ago 2012年9月16日 GMT-4 15:28
Hi, Ivar,

Thanks for the reply. I checked the link you posted. It works in terms that the piezoelectric material can "drive" the external circuit as a voltage source. But my problem is the circuit does not affect the "piezoelectric model" as expected. For a shunted pzt, the electric energy should be dissipated by the external circuit and transferred to joule heat. But it seems COMSOL can not accomplish this.

How to model the damping reduction using COMSOL? Can COMSOL do this job?

Thanks!!
Hi, Ivar, Thanks for the reply. I checked the link you posted. It works in terms that the piezoelectric material can "drive" the external circuit as a voltage source. But my problem is the circuit does not affect the "piezoelectric model" as expected. For a shunted pzt, the electric energy should be dissipated by the external circuit and transferred to joule heat. But it seems COMSOL can not accomplish this. How to model the damping reduction using COMSOL? Can COMSOL do this job? Thanks!!
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago 2012年9月17日 GMT-4 02:55
Hi

COMSOL takes into account what you use as equations, indeed nothing more, the CIR is a theoretical circuit, so it has no T dependency, but the Joule heating energy is dissipated I*V term is in there.

Normally, you would see that your PZT beam, under eigenfrequency or better frequency domain sweep does change frequency in open loop, respective short cicuit conditions from the CIR part

Now I'm neither not sure I catch all what you are after ;)

--
Good luck
Ivar
Hi COMSOL takes into account what you use as equations, indeed nothing more, the CIR is a theoretical circuit, so it has no T dependency, but the Joule heating energy is dissipated I*V term is in there. Normally, you would see that your PZT beam, under eigenfrequency or better frequency domain sweep does change frequency in open loop, respective short cicuit conditions from the CIR part Now I'm neither not sure I catch all what you are after ;) -- Good luck Ivar
Rocksmida
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Posted: 1 decade ago 2012年9月17日 GMT-4 15:24
THanks, Ivar!

I think my problem is in the assignment of the circuit boundary conditions and the electric boundary conditions for the pzt. I set one of the electrode of the PZT beam as "ground" and the other one as "floating potential" with total charge "Q0=0" ; for the electric circuit module, I connect one terminal in the circuit via "External I vs. U1." and for the voltage, I selected the "flp" which indicates the floating potential terminal in PZT.

I think maybe the total charge "Q0=0" limited that the charges on the electrode is zero and means no charge flow or "current" flow into the pzt?

In this way, I did not see any frequency shift with or without the external circuit.

I want to make a closed loop with the pzt and circuit elements and hope the circuit will dissipate the electrical energy generated due to the vibration of the pzt beam.

Therefore, Ivar, can you show me the correct boundary conditions for the pzt and circuit modules and how to connect them together? Thanks!
THanks, Ivar! I think my problem is in the assignment of the circuit boundary conditions and the electric boundary conditions for the pzt. I set one of the electrode of the PZT beam as "ground" and the other one as "floating potential" with total charge "Q0=0" ; for the electric circuit module, I connect one terminal in the circuit via "External I vs. U1." and for the voltage, I selected the "flp" which indicates the floating potential terminal in PZT. I think maybe the total charge "Q0=0" limited that the charges on the electrode is zero and means no charge flow or "current" flow into the pzt? In this way, I did not see any frequency shift with or without the external circuit. I want to make a closed loop with the pzt and circuit elements and hope the circuit will dissipate the electrical energy generated due to the vibration of the pzt beam. Therefore, Ivar, can you show me the correct boundary conditions for the pzt and circuit modules and how to connect them together? Thanks!
Damiano Milani
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Posted: 1 decade ago 2012年9月17日 GMT-4 17:19
Hi,
I have your same problem. I don't know if it's better to couple the physics with a "Terminal" BC or "Floating potential".

The Comsol guide suggests to use Terminal for the circuit, but in this way I get 0 V in all the circuit.

Using "Floating potential" instead, the piezoelectric model seems to behave like a voltage source, but the circuit has no effect on it.

If necessary, I can make a simple model to show better the problem.
Hi, I have your same problem. I don't know if it's better to couple the physics with a "Terminal" BC or "Floating potential". The Comsol guide suggests to use Terminal for the circuit, but in this way I get 0 V in all the circuit. Using "Floating potential" instead, the piezoelectric model seems to behave like a voltage source, but the circuit has no effect on it. If necessary, I can make a simple model to show better the problem.
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago 2012年9月21日 GMT-4 07:40
Hi

as often, I had forgotten about the mesh density: to really see any difference in PZT eigenfrequency versus CIR load you must ensure you have enough elements in the thickness of the PZT, ideally >> 5 !

--
Good luck
Ivar
Hi as often, I had forgotten about the mesh density: to really see any difference in PZT eigenfrequency versus CIR load you must ensure you have enough elements in the thickness of the PZT, ideally >> 5 ! -- Good luck Ivar
Mike Bradley
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Posted: 1 decade ago 2012年9月21日 GMT-4 09:49
You want a terminal if you are coupling to a circuit. External I and External I v U both work. But you need to make sure the drop-downs are all selected properly that link the associated circuit currents back into the FEA model to result in "coupled physics". Also make sure you are using the fully coupled direct solver. I've had little success with the segregated solvers in these applications. Remember you can manually type in variables, parameters and globals in many of the text boxes in COMSOL to link difference modules.
You want a terminal if you are coupling to a circuit. External I and External I v U both work. But you need to make sure the drop-downs are all selected properly that link the associated circuit currents back into the FEA model to result in "coupled physics". Also make sure you are using the fully coupled direct solver. I've had little success with the segregated solvers in these applications. Remember you can manually type in variables, parameters and globals in many of the text boxes in COMSOL to link difference modules.
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago 2012年9月21日 GMT-4 14:27
Hi

but COMSOL 4.3 flags a warning with CIR and eigenfrequency solver nodes, so I suspect something is not working here, allthough CIR works OK with harmonic sovers which is a similar iomega development.

Then, I cannot either get any k^2 value, as I got back in 3.5 time, or was it all just a mesh effect ? to see a difference in PZT modal sweep behaviour for a low and high impedance.

In anycase you can mimic that in PZD, from my undersanding with a high low impedance and 0 pwer in, or a voltage or charge terminal input. You see the effet if you plot and look carefully on the voltage across the PZT. But the eigenmodes, and frequency sweep show only a single coupled peak with resonance and anti-resonance one upon the other, and no separation.

Hence we need to get the damping factors correctly in here to get results as per "Vibration Control of Active Structures" from Preumont

--
Good luck
Ivar
Hi but COMSOL 4.3 flags a warning with CIR and eigenfrequency solver nodes, so I suspect something is not working here, allthough CIR works OK with harmonic sovers which is a similar iomega development. Then, I cannot either get any k^2 value, as I got back in 3.5 time, or was it all just a mesh effect ? to see a difference in PZT modal sweep behaviour for a low and high impedance. In anycase you can mimic that in PZD, from my undersanding with a high low impedance and 0 pwer in, or a voltage or charge terminal input. You see the effet if you plot and look carefully on the voltage across the PZT. But the eigenmodes, and frequency sweep show only a single coupled peak with resonance and anti-resonance one upon the other, and no separation. Hence we need to get the damping factors correctly in here to get results as per "Vibration Control of Active Structures" from Preumont -- Good luck Ivar
Foreas Lield
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Posted: 1 decade ago 2012年10月29日 GMT-4 22:23

Hi,
I have your same problem. I don't know if it's better to couple the physics with a "Terminal" BC or "Floating potential".

The Comsol guide suggests to use Terminal for the circuit, but in this way I get 0 V in all the circuit.

Using "Floating potential" instead, the piezoelectric model seems to behave like a voltage source, but the circuit has no effect on it.

If necessary, I can make a simple model to show better the problem.


I just began to use comsol for piezoelectric energy harvesting. May you show me your model ? Thanks.
[QUOTE] Hi, I have your same problem. I don't know if it's better to couple the physics with a "Terminal" BC or "Floating potential". The Comsol guide suggests to use Terminal for the circuit, but in this way I get 0 V in all the circuit. Using "Floating potential" instead, the piezoelectric model seems to behave like a voltage source, but the circuit has no effect on it. If necessary, I can make a simple model to show better the problem. [/QUOTE] I just began to use comsol for piezoelectric energy harvesting. May you show me your model ? Thanks.
Foreas Lield
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Posted: 1 decade ago 2012年10月29日 GMT-4 22:41
Hi

May I ask a question about using comsol for piezoelectric patch?
I am analyzing a very simple patch. Under the same boundary, if using different mesh desity ,I will get different voltage on the patch surface.
I just don't understand why this phenomena is going on like this. Can you give me help?

Thanks.

Good luck.

Foreas Lield
Hi May I ask a question about using comsol for piezoelectric patch? I am analyzing a very simple patch. Under the same boundary, if using different mesh desity ,I will get different voltage on the patch surface. I just don't understand why this phenomena is going on like this. Can you give me help? Thanks. Good luck. Foreas Lield
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago 2012年10月30日 GMT-4 02:21
Hi

you should consider meshing as a "digiizing" of your model. Just as with a sound wave, one need to catch at least 3 points per periode (if possible rather 10) in FEM we need several mesh elements per wave periode, for displacements, as well as several mesh elements across thin features to redolve any gradients of all our dependent variables.

Therefor meshing is a delicate affaire, one often need to remesh a few time once having observed the different variables and their changes in spatial directions from the first solutions

The crude way is "just" to remsh finer overall until the results stabilise, but it's often faster to solve to select locally where to remesh and act, but that needs some experience, so its jus to start ;)

--
Good luck
Ivar
Hi you should consider meshing as a "digiizing" of your model. Just as with a sound wave, one need to catch at least 3 points per periode (if possible rather 10) in FEM we need several mesh elements per wave periode, for displacements, as well as several mesh elements across thin features to redolve any gradients of all our dependent variables. Therefor meshing is a delicate affaire, one often need to remesh a few time once having observed the different variables and their changes in spatial directions from the first solutions The crude way is "just" to remsh finer overall until the results stabilise, but it's often faster to solve to select locally where to remesh and act, but that needs some experience, so its jus to start ;) -- Good luck Ivar
Foreas Lield
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Posted: 1 decade ago 2012年10月30日 GMT-4 03:54
Hi, thanks a lot.
I have another problem. I have compared the results of COMSOL and ANSYS for one patch. I found that the voltage for ansys is 62V around and the result for COMSOL is 76V. Did you encounter that problem? Can you give me some tips?

Thanks again.

Good luck.

Foreas Lield
Hi, thanks a lot. I have another problem. I have compared the results of COMSOL and ANSYS for one patch. I found that the voltage for ansys is 62V around and the result for COMSOL is 76V. Did you encounter that problem? Can you give me some tips? Thanks again. Good luck. Foreas Lield
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago 2012年10月30日 GMT-4 04:15
Hi

you have to check the equations used, and the mesh density in both. In COMSOL it's simple all equations are given, from my time with ANSYS it was far wose as motly it was a block box, but that might have changed with the time.

You must enure all hypothesis are the same, that you use the same mesh density and discretization level (2nd order mostly with COMSOL check the PZD physics tab, not sure how it is with ANSYS).

Then you must check the response to the mesh, by for both programmes double the mesh density and recompare

It's not that easy to compare, as there are many parameters involved, for some tools everything is written out, for other less

--
Good luck
Ivar
Hi you have to check the equations used, and the mesh density in both. In COMSOL it's simple all equations are given, from my time with ANSYS it was far wose as motly it was a block box, but that might have changed with the time. You must enure all hypothesis are the same, that you use the same mesh density and discretization level (2nd order mostly with COMSOL check the PZD physics tab, not sure how it is with ANSYS). Then you must check the response to the mesh, by for both programmes double the mesh density and recompare It's not that easy to compare, as there are many parameters involved, for some tools everything is written out, for other less -- Good luck Ivar
Foreas Lield
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Posted: 1 decade ago 2012年10月30日 GMT-4 04:59
Hi, thanks. I have learned so much.

I will try to recompare.


Good luck.

Foreas Lield
Hi, thanks. I have learned so much. I will try to recompare. Good luck. Foreas Lield
Foreas Lield
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Posted: 1 decade ago 2012年11月20日 GMT-5 21:16
Hi, Ivar
I have another problem. For multilayer cantilever structures, I want to know how to choose multiple faces or bodies to define the boundary and load conditions. Now, I have to choose one by one, which is so inconvenient.


Best wishes,

Foreas Lield
Hi, Ivar I have another problem. For multilayer cantilever structures, I want to know how to choose multiple faces or bodies to define the boundary and load conditions. Now, I have to choose one by one, which is so inconvenient. Best wishes, Foreas Lield
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago 2012年11月21日 GMT-5 01:21
Hi

in 4.3 you have some new options in the definition Selection nodes, about adjacent entities, else you have the selection box. For complex models, I agree there can be very many items to select, and it takes time, just to restart because one find ou the geometry CAD model needs an update. That is where livelink to CAD is usefull

--
Good luck
Ivar
Hi in 4.3 you have some new options in the definition Selection nodes, about adjacent entities, else you have the selection box. For complex models, I agree there can be very many items to select, and it takes time, just to restart because one find ou the geometry CAD model needs an update. That is where livelink to CAD is usefull -- Good luck Ivar
Foreas Lield
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Posted: 1 decade ago 2012年12月10日 GMT-5 01:59
Hi, Ivar

Thank you for your kind help and suggestions. I am just confused about the analysis of piezoelectric harvester by COMSOL. Can you give me your email or other contact information?

Best wishes.

Foreas Lield
Hi, Ivar Thank you for your kind help and suggestions. I am just confused about the analysis of piezoelectric harvester by COMSOL. Can you give me your email or other contact information? Best wishes. Foreas Lield
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago 2012年12月10日 GMT-5 02:13
Hi

use the forum, then there are others too to help, as I'm a full time employee in a private R&D company I cannot answer you over other means,
I use the FORUM for my training and I must say since it has arrived I learn the tricks far quicker and I can only advice all persons wanting to learn COMSOL, take an hour to reply to questions on the Forum, you will learn a lot ;) It pushes you to read the thick documentation section by section, or to learn how to best scroll over it, via search and indexing functions. Everything is in there, but finally "all physics" is therin

Another source for good practicve is following the webinars and to go over the model library examples

--
Good luck
Ivar
Hi use the forum, then there are others too to help, as I'm a full time employee in a private R&D company I cannot answer you over other means, I use the FORUM for my training and I must say since it has arrived I learn the tricks far quicker and I can only advice all persons wanting to learn COMSOL, take an hour to reply to questions on the Forum, you will learn a lot ;) It pushes you to read the thick documentation section by section, or to learn how to best scroll over it, via search and indexing functions. Everything is in there, but finally "all physics" is therin Another source for good practicve is following the webinars and to go over the model library examples -- Good luck Ivar
Abid Iqbal
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Posted: 1 decade ago 2014年3月23日 GMT-4 23:24
Hi Ivar
I am doing Piezo electric simulation. I want to see the effect of the varying temperature on the output piezoelectric open circuit voltage. I thought it will be better to start observing the resonance frequency with changing temperature. i used joule heating and thermal expansion. i increased the temperature but the resonance frequency remains same. can anyone tell me why the frequency is not changing? or how can i make the elasticity coefficient temperature dependent?
Hi Ivar I am doing Piezo electric simulation. I want to see the effect of the varying temperature on the output piezoelectric open circuit voltage. I thought it will be better to start observing the resonance frequency with changing temperature. i used joule heating and thermal expansion. i increased the temperature but the resonance frequency remains same. can anyone tell me why the frequency is not changing? or how can i make the elasticity coefficient temperature dependent?

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