Note: This discussion is about an older version of the COMSOL Multiphysics® software. The information provided may be out of date.

Discussion Closed This discussion was created more than 6 months ago and has been closed. To start a new discussion with a link back to this one, click here.

Cantilever Beam under Electrostatic Step Load

Please login with a confirmed email address before reporting spam

Hello,
I am a new user of comsol and need your expert help in the following matter,

I wish to perform a transient dynamic analysis of a 3D microcantilever model excited by a Heaviside Step electrostatic voltage. I have followed the instructions given in 3D_ALE_Cantilever model in help section in order to solve the static system.

Can anybody suggest what changes I will have to incorporate (in the same model) to analyze the dynamic response. The first eigenfrequency of the model is f1=265429.04167060566 Hz.

In Solver Parameters I changed the analysis to Time-Dependent Analysis and then analyzed the system from t=0:1/(100*f1):10e-6. But the response of the free end of the cantilever is obtained as constant with respect to time.

Can anybody help me to resolve this issue?
Thanks in advance.

Dekar


5 Replies Last Post Mar 13, 2012, 11:46 a.m. EDT
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

Please login with a confirmed email address before reporting spam

Posted: 1 decade ago Feb 28, 2010, 7:51 a.m. EST
Hi

I'm not fully understanding what you want to do, but here are already some comments:

If youre eigenfrequency value is a truely measured value with so many digits (you must have a H maser reference or something like that ;) then dO not exepct mUch more than 5-10% correspondance with the FEM, except if you start to tune the materials, then you might end up somewhat below 1%

Now if you have a static response, and you want the eigenfrequency you change that in the physics view from static to eigenfrequency, and check your boundary conditions, that no unwanted prescribed displacements remain (normally force loads are ignored if not used for prestress buildup, in which case always check from which initial conditions you start)

If you want the transient response then teak well your excitation step, as in my opinion it should be some 100 times more rapid than the 1/f1 to excite the mode and you need to step carefully around this step to allow the solver to follow, and with such high frequencies and short times there might be some numerical scaling issues that could (not sure) show up due to the numerics, do one really have more than 8-9 digits resolution ?

Hope this helps on the way

Good luck
Ivar
Hi I'm not fully understanding what you want to do, but here are already some comments: If youre eigenfrequency value is a truely measured value with so many digits (you must have a H maser reference or something like that ;) then dO not exepct mUch more than 5-10% correspondance with the FEM, except if you start to tune the materials, then you might end up somewhat below 1% Now if you have a static response, and you want the eigenfrequency you change that in the physics view from static to eigenfrequency, and check your boundary conditions, that no unwanted prescribed displacements remain (normally force loads are ignored if not used for prestress buildup, in which case always check from which initial conditions you start) If you want the transient response then teak well your excitation step, as in my opinion it should be some 100 times more rapid than the 1/f1 to excite the mode and you need to step carefully around this step to allow the solver to follow, and with such high frequencies and short times there might be some numerical scaling issues that could (not sure) show up due to the numerics, do one really have more than 8-9 digits resolution ? Hope this helps on the way Good luck Ivar

Please login with a confirmed email address before reporting spam

Posted: 1 decade ago Mar 1, 2010, 10:41 a.m. EST
Hi Ivar,

Thank you for your response.
Sorry for being a bit obscure while posing the question. Here is what I want to simulate:

I am solving the problem of electrostatic actuation of a microcantilever in which, the electrostatic load (voltage) is applied in the Heaviside step manner. The anticipated response is periodic up to a critical value of the applied voltage (popularly known as the pull-in voltage) and non-periodic for voltages higher than this critical value.

I have the COMSOL model for static analysis (in which the voltage is applied slowly such that the equilibrium exists at every step). This is the same model, which has been explained in the 3D_ALE_Cantilever beam tutorial. I wish to know what changes I will have to make in order to get a transient dynamic response. This is like answering the question: what would be the response of the cantilever beam if some particular voltage is suddenly applied.

In physics menu, I have boundary forces given by dnTx_emes, dnTy_emes, dnTz_emes.
In solver parameters, I changed the analysis to Time-Dependent Analysis instead of static.
I selected the time step as 1/(100*f1), in which f1 was obtained from the eigenvalue analysis run previously (I just copy-pasted the frequency value obtained from the analysis, that value is not measured ;)).
All other settings, including the meshing is same as explained in 3D_ALE_Cantilever beam tutorial.

I run the simulation from t=0 to t=10e-6, in which I expect around 3 oscillations of the beam, but I have not been able to obtain the oscillatory response.

Where exactly I am going wrong? It will be helpful if somebody can throw some light on this issue.

PS: The aforementioned problem of pull-in instability is very popular in the field of electrostatic MEMS and I hope, a few of the users here should have tackled his problem earlier.
Hi Ivar, Thank you for your response. Sorry for being a bit obscure while posing the question. Here is what I want to simulate: I am solving the problem of electrostatic actuation of a microcantilever in which, the electrostatic load (voltage) is applied in the Heaviside step manner. The anticipated response is periodic up to a critical value of the applied voltage (popularly known as the pull-in voltage) and non-periodic for voltages higher than this critical value. I have the COMSOL model for static analysis (in which the voltage is applied slowly such that the equilibrium exists at every step). This is the same model, which has been explained in the 3D_ALE_Cantilever beam tutorial. I wish to know what changes I will have to make in order to get a transient dynamic response. This is like answering the question: what would be the response of the cantilever beam if some particular voltage is suddenly applied. In physics menu, I have boundary forces given by dnTx_emes, dnTy_emes, dnTz_emes. In solver parameters, I changed the analysis to Time-Dependent Analysis instead of static. I selected the time step as 1/(100*f1), in which f1 was obtained from the eigenvalue analysis run previously (I just copy-pasted the frequency value obtained from the analysis, that value is not measured ;)). All other settings, including the meshing is same as explained in 3D_ALE_Cantilever beam tutorial. I run the simulation from t=0 to t=10e-6, in which I expect around 3 oscillations of the beam, but I have not been able to obtain the oscillatory response. Where exactly I am going wrong? It will be helpful if somebody can throw some light on this issue. PS: The aforementioned problem of pull-in instability is very popular in the field of electrostatic MEMS and I hope, a few of the users here should have tackled his problem earlier.

Please login with a confirmed email address before reporting spam

Posted: 1 decade ago Mar 7, 2011, 4:49 p.m. EST
Hey what's up,

Did you manage to solve your problem?
i'm trying to do something similar, but the results I'm getting are not coherent. I actuate the cantilever with a voltage step function, but the deformation depends on the amount of time that the final value of step remains applied, which in reality is not true, once you reach a final value the cantilever shouldn't continue to deflect. This is really giving me a headache, cause I'm precisely working on the switching properties of the cantilever. If you or someone could shed some light on this topic I'd be very grateful.

Regards

Hey what's up, Did you manage to solve your problem? i'm trying to do something similar, but the results I'm getting are not coherent. I actuate the cantilever with a voltage step function, but the deformation depends on the amount of time that the final value of step remains applied, which in reality is not true, once you reach a final value the cantilever shouldn't continue to deflect. This is really giving me a headache, cause I'm precisely working on the switching properties of the cantilever. If you or someone could shed some light on this topic I'd be very grateful. Regards

Please login with a confirmed email address before reporting spam

Posted: 1 decade ago Mar 11, 2011, 1:08 p.m. EST
Hi Dekar,

I'm currently solving the same problem although I'm more interested in time rather than frecuency. Here's what you have to do to solve your problem:

In Electric potential, multiply your voltage Vin with a step function (which you should adecuate according to your needs of simulation time, time step, etc...). Leave everything identical and be sure to have your moving mesh activated to be able to see the pull in effects. It is critical that you pay attention to simulation time and time step so you can see meaningful results, if your response is not reaching a maximum value and then descending, be sure to to add more simulation time. Another factor for you may be the fact that you probably haven't added a boundary restoring force -K*v, which is the one that restores the cantilever to its initial position in the non-pullin regions. At the pull in region your going to observe a huge increase in electrostatic force, which will deflect the cantilever far beyond the limits of your geometry.

Hope this helps.
Hi Dekar, I'm currently solving the same problem although I'm more interested in time rather than frecuency. Here's what you have to do to solve your problem: In Electric potential, multiply your voltage Vin with a step function (which you should adecuate according to your needs of simulation time, time step, etc...). Leave everything identical and be sure to have your moving mesh activated to be able to see the pull in effects. It is critical that you pay attention to simulation time and time step so you can see meaningful results, if your response is not reaching a maximum value and then descending, be sure to to add more simulation time. Another factor for you may be the fact that you probably haven't added a boundary restoring force -K*v, which is the one that restores the cantilever to its initial position in the non-pullin regions. At the pull in region your going to observe a huge increase in electrostatic force, which will deflect the cantilever far beyond the limits of your geometry. Hope this helps.

Please login with a confirmed email address before reporting spam

Posted: 1 decade ago Mar 13, 2012, 11:46 a.m. EDT
Hi All,

I see that this thread is a bit outdated, but I'm looking for the 3D_ALE_Cantilever beam tutorial, and cannot seem to find it anywhere. Could someone post the pdf file, or the mph file for that tutorial?

Thanks!

- Jason
Hi All, I see that this thread is a bit outdated, but I'm looking for the 3D_ALE_Cantilever beam tutorial, and cannot seem to find it anywhere. Could someone post the pdf file, or the mph file for that tutorial? Thanks! - Jason

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.