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Determine the damping coefficient
Posted 30 ott 2014, 11:24 GMT-4 Version 5.2 14 Replies
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Hi,
I am designing a cantilever with specific dimensions in the micro scale, and using the electromechanics module in order to study the cantilevers behavior in the stationary and eigenfrequency cases. After getting the eigenmodes, I am interested in knowing how will my beam displace w.r.t. time (i.e. the transient analysis). Since there is no a transient analysis, I am planning to carry out the frequency domain analysis and then inverse Fourier transform the results to get the change in displacements w.r.t time. In the MEMS module, it mentions that in order to carry out the frequency analysis, I should define my damping coefficients alpha and beta. Can these coefficients be determined through comsol (although I don't think it is possible) or shall I determine them analytically?
I am designing a cantilever with specific dimensions in the micro scale, and using the electromechanics module in order to study the cantilevers behavior in the stationary and eigenfrequency cases. After getting the eigenmodes, I am interested in knowing how will my beam displace w.r.t. time (i.e. the transient analysis). Since there is no a transient analysis, I am planning to carry out the frequency domain analysis and then inverse Fourier transform the results to get the change in displacements w.r.t time. In the MEMS module, it mentions that in order to carry out the frequency analysis, I should define my damping coefficients alpha and beta. Can these coefficients be determined through comsol (although I don't think it is possible) or shall I determine them analytically?
14 Replies Last Post 1 feb 2017, 17:38 GMT-5
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Posted:
10 years ago
Hi Hossam,
Why can’t you do a transient analysis? Anyways, in the frequency domain you have more options for damping than you have in the time domain. I wouldn’t use the Rayleigh damping in the frequency domain. I prefer setting the damping loss factor as a function of frequency. That feature is not possible in a standard time domain analysis (that’s a theoretical limitation not a COMSOL one). In that case you can include damping either by using a viscoelastic material, or Rayleigh damping and selecting suitable values for alpha and beta coefficients as you noted. It is quite straightforward to calculate values for the two coefficients based on the material behavior and COMSOL provides guidelines in the documentation on how to do that.
Nagi Elabbasi
Veryst Engineering
Why can’t you do a transient analysis? Anyways, in the frequency domain you have more options for damping than you have in the time domain. I wouldn’t use the Rayleigh damping in the frequency domain. I prefer setting the damping loss factor as a function of frequency. That feature is not possible in a standard time domain analysis (that’s a theoretical limitation not a COMSOL one). In that case you can include damping either by using a viscoelastic material, or Rayleigh damping and selecting suitable values for alpha and beta coefficients as you noted. It is quite straightforward to calculate values for the two coefficients based on the material behavior and COMSOL provides guidelines in the documentation on how to do that.
Nagi Elabbasi
Veryst Engineering
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Posted:
10 years ago
Hi Nagi,
Thanks for your reply.
1. Regarding the transient analysis, the reason that it is not possible because by default, defining an elastic material in COMSOL without damping, treats the material as undamped, and hence in the time domain analysis, at the point where voltage is applied, the displacement appears across the beam abruptly, without any damping response, which contradicts what happens physically (due to damping).
More about this issue can be found in this thread:
www.comsol.com/community/forums/general/thread/13808/
2. Would you elaborate more please on how to determine these coefficients, because as far as the documentation explains, it mentions that these parameters (alpha and beta) shall be computed using two known frequencies as well as their damping factors. My question is how to determine these damping factors, is it done analytically or can they be extracted through another simulation from COMSOL?
-Hossam
Thanks for your reply.
1. Regarding the transient analysis, the reason that it is not possible because by default, defining an elastic material in COMSOL without damping, treats the material as undamped, and hence in the time domain analysis, at the point where voltage is applied, the displacement appears across the beam abruptly, without any damping response, which contradicts what happens physically (due to damping).
More about this issue can be found in this thread:
www.comsol.com/community/forums/general/thread/13808/
2. Would you elaborate more please on how to determine these coefficients, because as far as the documentation explains, it mentions that these parameters (alpha and beta) shall be computed using two known frequencies as well as their damping factors. My question is how to determine these damping factors, is it done analytically or can they be extracted through another simulation from COMSOL?
-Hossam
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Posted:
10 years ago
Hi Hossam,
As I mentioned you can include damping in a transient analysis as Rayleigh damping or using a viscoelastic material instead of elastic.
Displacements never appear instantaneously in a transient analysis even when a force is applied instantaneously unless the mass is zero. It is probably occurring over a shorter time frame than your time steps. Adding damping increases the response time to an instantaneous load as you indicated, and it also gradually dissipates energy so that the structure doesn’t keep vibrating indefinitely.
The damping factor and its variation with frequency is a property of the material, just like say Young’s Modulus. You cannot determine it from simulation.
Nagi Elabbasi
Veryst Engineering
As I mentioned you can include damping in a transient analysis as Rayleigh damping or using a viscoelastic material instead of elastic.
Displacements never appear instantaneously in a transient analysis even when a force is applied instantaneously unless the mass is zero. It is probably occurring over a shorter time frame than your time steps. Adding damping increases the response time to an instantaneous load as you indicated, and it also gradually dissipates energy so that the structure doesn’t keep vibrating indefinitely.
The damping factor and its variation with frequency is a property of the material, just like say Young’s Modulus. You cannot determine it from simulation.
Nagi Elabbasi
Veryst Engineering
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Posted:
10 years ago
Hi Najy,
Thanks a lot for concerning my issue and replying promptly. I think that in order to carry the time-dependent study, some modifications in the solver shall be made as you've mentioned and couple my time dependence study to a stationary one as to get the initial conditions.
Thanks once again and will notify you once things work. Have a great day!
-Hossam
Thanks a lot for concerning my issue and replying promptly. I think that in order to carry the time-dependent study, some modifications in the solver shall be made as you've mentioned and couple my time dependence study to a stationary one as to get the initial conditions.
Thanks once again and will notify you once things work. Have a great day!
-Hossam
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Posted:
10 years ago
You may also get viscous and/or squeezed film damping from the air around your cantilever. They can be modelled through COMSOL but it will make your model a lot more complicated.
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Posted:
10 years ago
Hi Pieter,
Yes you are right, so far I used just the internal damping predefined in the material used (Silicon). No any external damping were concerned.
I actually successfully solved the problem by coupling the stationary study to a time dependent one, where I then added a rise time voltage and made my voltage source to be of a step function. Some changes in the solver methods were also changed to solve the problem efficiently.
Thanks Nagi as well as Pieter.
-Hossam
Yes you are right, so far I used just the internal damping predefined in the material used (Silicon). No any external damping were concerned.
I actually successfully solved the problem by coupling the stationary study to a time dependent one, where I then added a rise time voltage and made my voltage source to be of a step function. Some changes in the solver methods were also changed to solve the problem efficiently.
Thanks Nagi as well as Pieter.
-Hossam
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Posted:
10 years ago
I watched the following webinar
www.comsol.co.in/video/simulating-fluid-structure-interaction-comsol-multiphysics
, and was wondering how to use the linear extrusion (what shall i select for the source frame and destination geometry as well as the source vertices)? What are the implications of using the linear extrusion? I ran my study (damping without FSI), and did not get the expected results (got the transient response but with unrealistic displacements at some time steps). There is something wrong with my mesh. It seems that defining linear extrusion is necessary, but I am skeptical about how to move forward with it?
Can anyone help? I guess Nagi has used it and knows more about it, but of course anyone is welcome to help, and I would be grateful.
-Hossam
www.comsol.co.in/video/simulating-fluid-structure-interaction-comsol-multiphysics
, and was wondering how to use the linear extrusion (what shall i select for the source frame and destination geometry as well as the source vertices)? What are the implications of using the linear extrusion? I ran my study (damping without FSI), and did not get the expected results (got the transient response but with unrealistic displacements at some time steps). There is something wrong with my mesh. It seems that defining linear extrusion is necessary, but I am skeptical about how to move forward with it?
Can anyone help? I guess Nagi has used it and knows more about it, but of course anyone is welcome to help, and I would be grateful.
-Hossam
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Posted:
10 years ago
Hi Hossam,
In the webinar example I used the linear extrusion to map results from the beam to different regions of the fluid. I used that mapping to prescribe the fluid mesh in a way that would not make it fail given the excessive “squeezing” of the fluid below the beam. In this case the Source was the beam and the Destinations where the edges of the fluid.
The Turbulent Backstep model in the COMSOL Gallery is a good example that uses the Linear Extrusion operator.
Nagi Elabbasi
Veryst Engineering
In the webinar example I used the linear extrusion to map results from the beam to different regions of the fluid. I used that mapping to prescribe the fluid mesh in a way that would not make it fail given the excessive “squeezing” of the fluid below the beam. In this case the Source was the beam and the Destinations where the edges of the fluid.
The Turbulent Backstep model in the COMSOL Gallery is a good example that uses the Linear Extrusion operator.
Nagi Elabbasi
Veryst Engineering
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Posted:
10 years ago
Hi Nagi,
I am sorry regarding the very late reply. I actually got the simulation results, however without the FSI. For some reason, I get awkward (incorrect) results once I use the linear extrusion operator. I will look more into it and get back to you, and mention what I did wrong once I figure out.
Many thanks Nagi for the prompt replies. Have a good day.
-Hossam
I am sorry regarding the very late reply. I actually got the simulation results, however without the FSI. For some reason, I get awkward (incorrect) results once I use the linear extrusion operator. I will look more into it and get back to you, and mention what I did wrong once I figure out.
Many thanks Nagi for the prompt replies. Have a good day.
-Hossam
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Posted:
9 years ago
Hi Hossam,
What module did you use?
Thank you. Have a good day.
What module did you use?
Thank you. Have a good day.
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Posted:
9 years ago
Hello Trieu,
I used the FSI module. I got my simulation working and I reran the same simulation but using the laminar flow under solid mechanics instead and got the same results. Thanks for your reply.
In case you're wondering what was stopping me earlier, it was an error in the boundary conditions while using the symmetry boundaries. I tried finding what the problem was, but I then decided to avoid symmetry and got the simulation working correctly.
Thanks and let me know if you face problems in the same module (hopefully not).
I used the FSI module. I got my simulation working and I reran the same simulation but using the laminar flow under solid mechanics instead and got the same results. Thanks for your reply.
In case you're wondering what was stopping me earlier, it was an error in the boundary conditions while using the symmetry boundaries. I tried finding what the problem was, but I then decided to avoid symmetry and got the simulation working correctly.
Thanks and let me know if you face problems in the same module (hopefully not).
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Posted:
9 years ago
Hi Hossam,
Thank you very much for your reply.
That is a very good experience, I will note it.
I started a 2D model (a cantilever which is immersed in a fluid) a few days ago.
I will start a 3D model soon.
Hope to have your help then (if there are troubles).
Wish you have a good weekend.
Trieu.
Thank you very much for your reply.
That is a very good experience, I will note it.
I started a 2D model (a cantilever which is immersed in a fluid) a few days ago.
I will start a 3D model soon.
Hope to have your help then (if there are troubles).
Wish you have a good weekend.
Trieu.
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Posted:
7 years ago
Hi Hossam,
Could you please tell me how did you get the alpha and beta value of Rayleigh damping? I want to include the effect of piezoelectric damping in my model. However, I am not able to find the right way to determine these values using numerical simulation. I appreciate your help.
Thanks,
Sajiree
Could you please tell me how did you get the alpha and beta value of Rayleigh damping? I want to include the effect of piezoelectric damping in my model. However, I am not able to find the right way to determine these values using numerical simulation. I appreciate your help.
Thanks,
Sajiree
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Posted:
7 years ago
Hi Sajiree,
Check this module users guide:
lost-contact.mit.edu/afs/enea.it/user/e/ebolese/StructuralMechanicsModuleUsersGuide.pdf
Page 77. Solve the system of two equations using two known resonant frequencies and damping ratios. There is an example shown in the MEMS module library module as well, you can have a look at it.
-Hossam
Check this module users guide:
lost-contact.mit.edu/afs/enea.it/user/e/ebolese/StructuralMechanicsModuleUsersGuide.pdf
Page 77. Solve the system of two equations using two known resonant frequencies and damping ratios. There is an example shown in the MEMS module library module as well, you can have a look at it.
-Hossam