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Eigenfrequency Modeling of a Nanoresonator
Posted Dec 2, 2009, 3:23 p.m. EST 10 Replies
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We are currently attempting to design a nanoresonator of graphene. The graphene sheet is constrained at two ends, and is allowed to freely vibrate at its center. To achieve this, we are using the structural mechanics module of Comsol and applying boundary conditions to fix the motion of the membrane at its two ends.
We have run a simulation and found the eigenfrequencies.
Now we want to add some additional tension to the membrane, in the form of a tensile force applied at two ends. Then we want to re-run the simulation and hope to see the eigenfrequencies increase.
When we do this, we do not see the eigenfrequencies increase. Is this supposed to be the case?
Thanks!
We have run a simulation and found the eigenfrequencies.
Now we want to add some additional tension to the membrane, in the form of a tensile force applied at two ends. Then we want to re-run the simulation and hope to see the eigenfrequencies increase.
When we do this, we do not see the eigenfrequencies increase. Is this supposed to be the case?
Thanks!
10 Replies Last Post Oct 26, 2010, 3:35 a.m. EDT
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Posted:
1 decade ago
We are currently attempting to design a nanoresonator of graphene. The graphene sheet is constrained at two ends, and is allowed to freely vibrate at its center. To achieve this, we are using the structural mechanics module of Comsol and applying boundary conditions to fix the motion of the membrane at its two ends.
We have run a simulation and found the eigenfrequencies.
Now we want to add some additional tension to the membrane, in the form of a tensile force applied at two ends. Then we want to re-run the simulation and hope to see the eigenfrequencies increase.
When we do this, we do not see the eigenfrequencies increase. Is this supposed to be the case?
Thanks!
it's normal if you want to see the impact of prestress on resonance frequency you must first run a static analysis with the load and then use this analysis as a linearisation point in the eigenfrequency analysis
but all this two step with the large deformation option. The procedure is entirely described in the comsol model 'residual stress in a thin film' (attached file).One other thing , with this procedure you take into account of the non linear geometric effect of prestress, so check if the graphene has third order coefficent of stiffness.in this case you have to take into account the non linear material effect ; i know how to do it and i would describe how to do in this forum if you ask for....
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Posted:
1 decade ago
We are currently attempting to design a nanoresonator of graphene. The graphene sheet is constrained at two ends, and is allowed to freely vibrate at its center. To achieve this, we are using the structural mechanics module of Comsol and applying boundary conditions to fix the motion of the membrane at its two ends.
We have run a simulation and found the eigenfrequencies.
Now we want to add some additional tension to the membrane, in the form of a tensile force applied at two ends. Then we want to re-run the simulation and hope to see the eigenfrequencies increase.
When we do this, we do not see the eigenfrequencies increase. Is this supposed to be the case?
Thanks!
it's normal if you want to see the impact of prestress on resonance frequency you must first run a static analysis with the load and then use this analysis as a linearisation point in the eigenfrequency analysis
but all this two step with the large deformation option. The procedure is entirely described in the comsol model 'residual stress in a thin film' (attached file).One other thing , with this procedure you take into account of the non linear geometric effect of prestress, so check if the graphene has third order coefficent of stiffness.in this case you have to take into account the non linear material effect ; i know how to do it and i would describe how to do in this forum if you ask for....
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Posted:
1 decade ago
Thanks a lot.
The suggestion is helpful. But I have some problem in implementing your method. Can we talk about the details?
The suggestion is helpful. But I have some problem in implementing your method. Can we talk about the details?
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Posted:
1 decade ago
Hi, I'm trying to build a similar thing with a silicon thin beam; fixed at both ends and freely vibrating at the center. But somehow I can't get the simulation to show me the exact eigenfrequency values; it just says 0(1), 0(2) and so forth, instead of showing me frequency values in Hz. How do I get it to show me the frequency values?
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Posted:
1 decade ago
Hi
if you have frequencies set to "0" Hz it means that you have not correctly fixed your beam, these are the free-free modes, and the (1) (2) are the moe muliplicity when you get the same frequency for degenerated modes.
Try it out, make a beam i.e. 1x0.1x0.01[m] aside, with no restrictive BC's and do an eigenfrequency analysis of it, but ask to solve for 9 first modes.
You will see that you get 0(1) 0(2) 0(3) the free tree translations and then three free modes (the rotations) very close, but not necesarily exactly set to 0 Hz
This is a good indication that you are not well attached.
furthermore, many modes whenyou part is symmetric, are decomposed into to or more of same frequency, as they are mirtror image of each others.
could it be that you are using "assembly" mode and that you then have NOT attached the pairs together, for parts tightly attached together, you should rather use "non-assembly" mode, which gives you more correct in ternal "continuous" internal boundaries.
Hope this help
Good luck
Ivar
if you have frequencies set to "0" Hz it means that you have not correctly fixed your beam, these are the free-free modes, and the (1) (2) are the moe muliplicity when you get the same frequency for degenerated modes.
Try it out, make a beam i.e. 1x0.1x0.01[m] aside, with no restrictive BC's and do an eigenfrequency analysis of it, but ask to solve for 9 first modes.
You will see that you get 0(1) 0(2) 0(3) the free tree translations and then three free modes (the rotations) very close, but not necesarily exactly set to 0 Hz
This is a good indication that you are not well attached.
furthermore, many modes whenyou part is symmetric, are decomposed into to or more of same frequency, as they are mirtror image of each others.
could it be that you are using "assembly" mode and that you then have NOT attached the pairs together, for parts tightly attached together, you should rather use "non-assembly" mode, which gives you more correct in ternal "continuous" internal boundaries.
Hope this help
Good luck
Ivar
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Posted:
1 decade ago
I have a similar model of a nanoresonator which is a ZnO nanorod fixed at 2 ends. I am able to see the modes in eigen frequency analysis but when I do the harmonic analysis, the deformation of my beam at the resonant frequencies is different from that seen in eigen frequency analysis. In both the cases I actuate the resonator by applying a voltage at the ends which causes deformation due to piezoelectric property of ZnO. Shouldn't I be expecting to see the similar distortion shape in both the cases although the magnitude of distortion will be different? It would be great if anyone could help me understand this!
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Posted:
1 decade ago
Hi
There are different things you must be aware of. In an eigenfrequency analyisis it is only the relative mode shape that is relevant, total amplitude is normalised by convention (and there are several, COMSOL has a diffeent on than ANSYS and NASTRAN, all are mathematically correct, it depends on wich referential you end up in) as you do not limit the energy input to the system.
While in harmonic load you come with a given load or displacement that gives you a bounded energy into the system, when you the have some damping (there are always if not some "numeric" for the solver stability) then these will give the limits of the absolute deformation values.
The shape and frequency of the two results (eigenfrequency and harmonic) will also depend somewhat on the electrode shapes, the applied impedance (open or short or...) and the type of harmonic load, so they might be different.
So far, my simulations, when I refer to examples in the books of Pr. Preumont on piezo systems and structural damping, are rather coherent, and I trust COMSOL, provided I have got the correct BC's
Good luck
Ivar
There are different things you must be aware of. In an eigenfrequency analyisis it is only the relative mode shape that is relevant, total amplitude is normalised by convention (and there are several, COMSOL has a diffeent on than ANSYS and NASTRAN, all are mathematically correct, it depends on wich referential you end up in) as you do not limit the energy input to the system.
While in harmonic load you come with a given load or displacement that gives you a bounded energy into the system, when you the have some damping (there are always if not some "numeric" for the solver stability) then these will give the limits of the absolute deformation values.
The shape and frequency of the two results (eigenfrequency and harmonic) will also depend somewhat on the electrode shapes, the applied impedance (open or short or...) and the type of harmonic load, so they might be different.
So far, my simulations, when I refer to examples in the books of Pr. Preumont on piezo systems and structural damping, are rather coherent, and I trust COMSOL, provided I have got the correct BC's
Good luck
Ivar
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Posted:
1 decade ago
Hello Mr KJELBERG,
I was looking for any help related to eigenfrequencies and a saw your comments. I got a piezoelectric (quartz) disk and I want to obtain it resonant frequency. I tryed to do it with an eigenfrequency analysis but I just obtain some values very close together around de analytical value (near to 5MHz). I finally obtain this value doing the frecuency response analysis.
I have not put constrains in the BCs and I followed the COMSOL example "Composite Piezoelectric Transducer". In this example ocurred the same if I look for eigenfrecuencies near a higher resonance value (in the order of MHz instead of 43KHz).
I very much appreciate if I you or someone could help me with this topic.
Kind regards
Martín
I was looking for any help related to eigenfrequencies and a saw your comments. I got a piezoelectric (quartz) disk and I want to obtain it resonant frequency. I tryed to do it with an eigenfrequency analysis but I just obtain some values very close together around de analytical value (near to 5MHz). I finally obtain this value doing the frecuency response analysis.
I have not put constrains in the BCs and I followed the COMSOL example "Composite Piezoelectric Transducer". In this example ocurred the same if I look for eigenfrecuencies near a higher resonance value (in the order of MHz instead of 43KHz).
I very much appreciate if I you or someone could help me with this topic.
Kind regards
Martín
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Posted:
1 decade ago
Hi
do not forget that a PZT stiffness depends on the electric impedance you put across the electrodes, hence, as the mass/density remains constant, your frequency changes too with the impedance, so define your BC's accordingly, the difference is not that important though.
But then, if you are in free-free mode, or in a fixed free mode, the eigenfrequency calculations should be correct (w.r.t BC's set-up), and the impedance scan (harmonic) have alsays been correct for my models so far (i.e. good match with the measurements).
One other difficulty with the PZT is to orient the PZT tensors correctly, note that the notation is different from the structural order. This is by convention IEEE one. Read carefully through the doc to clarify these points, and/or try it out on a simple beam, define a local coordinate system (unfortunately these are not easy to visualise) to orient the tensor accordingly. (if I remeember correctly the MEMS guide has the most complete PZT description).
Finally there are a few good examples in the doc, as ususal, but mostly I have to repeat them a couple of times, with some months intervalle, to get most of the info out, it is to dense for just one run.
good luck
Ivar
do not forget that a PZT stiffness depends on the electric impedance you put across the electrodes, hence, as the mass/density remains constant, your frequency changes too with the impedance, so define your BC's accordingly, the difference is not that important though.
But then, if you are in free-free mode, or in a fixed free mode, the eigenfrequency calculations should be correct (w.r.t BC's set-up), and the impedance scan (harmonic) have alsays been correct for my models so far (i.e. good match with the measurements).
One other difficulty with the PZT is to orient the PZT tensors correctly, note that the notation is different from the structural order. This is by convention IEEE one. Read carefully through the doc to clarify these points, and/or try it out on a simple beam, define a local coordinate system (unfortunately these are not easy to visualise) to orient the tensor accordingly. (if I remeember correctly the MEMS guide has the most complete PZT description).
Finally there are a few good examples in the doc, as ususal, but mostly I have to repeat them a couple of times, with some months intervalle, to get most of the info out, it is to dense for just one run.
good luck
Ivar
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Posted:
1 decade ago
Maybe this free to download book about Modeling and simulation help someone with research or just for better understanding. This is link: www.intechopen.com/books/show/title/modelling_and_simulation