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3D Membrane Structural Mechanics Question
Posted Nov 20, 2009, 3:30 p.m. EST 1 Reply
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Hello,
We are working on making a model which can measure the resonant frequency of a membrane of graphene. Our plan is to (1) model the membrane (2) apply boundary conditions so the membrane can only deflect in one direction (3) apply a load so that we can measure the frequency (point or distributed and possibly time varying).
We are having trouble creating the mesh, despite the fact that the membrane is extremely small (microscale), and can not seem to apply the load in such a way that when we solve the problem, we can measure the frequency.
Any help would be extremely appreciated!
We are working on making a model which can measure the resonant frequency of a membrane of graphene. Our plan is to (1) model the membrane (2) apply boundary conditions so the membrane can only deflect in one direction (3) apply a load so that we can measure the frequency (point or distributed and possibly time varying).
We are having trouble creating the mesh, despite the fact that the membrane is extremely small (microscale), and can not seem to apply the load in such a way that when we solve the problem, we can measure the frequency.
Any help would be extremely appreciated!
1 Reply Last Post Nov 21, 2009, 3:24 a.m. EST
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Posted:
2 decades ago
Hi
normally you should use shell items for thin memebranes in structural, but as discussed on another topic herer, large deformations are no well simulated with shells (not with the ones curently in COMSOL), but still therer is quite some analysis that can be done, we have survived the last 30 years with those in FEM programmes.
Now normally a membrane with or without load will have the same freuqency, except if you introduce non linear effects. For linear theory in fact any surface/volume load will be ignored in the eigenfrequency analysis, its just a static offset.
Do not forget that for larger structures there is a simple "rule of thumb" relation useful for checking maximum gravity deformation and the first eigenfrequency:
(2*pi*f)^2 = k/m = G/dz
where f is the first mode, k is the stiffness, m the mass, G the gravity acceleration and dz the maximum deflextion. it's mosty valid within some 10% if your model (meshing) is valid
But I havnt checked it for small items (MEMS) as often additional effects related to the surface to volume ratios changes the rules, that is to be more precise for some of you: if you assume the same model, you can use this rule, but if you compare with measurements on small items it might be wrong, as other physics must be added and cannot be ignord in the smal scale worlds.
So back to meshing thin structures, particularly if the geometry is not too complex, you have on the manual interactive meshing window, under "advanced" tab a geometric scale factor, I would suggest to learn how to use this feature, it is very useful for meshing thin features with large dimension dfferences
Good luck
Ivar
normally you should use shell items for thin memebranes in structural, but as discussed on another topic herer, large deformations are no well simulated with shells (not with the ones curently in COMSOL), but still therer is quite some analysis that can be done, we have survived the last 30 years with those in FEM programmes.
Now normally a membrane with or without load will have the same freuqency, except if you introduce non linear effects. For linear theory in fact any surface/volume load will be ignored in the eigenfrequency analysis, its just a static offset.
Do not forget that for larger structures there is a simple "rule of thumb" relation useful for checking maximum gravity deformation and the first eigenfrequency:
(2*pi*f)^2 = k/m = G/dz
where f is the first mode, k is the stiffness, m the mass, G the gravity acceleration and dz the maximum deflextion. it's mosty valid within some 10% if your model (meshing) is valid
But I havnt checked it for small items (MEMS) as often additional effects related to the surface to volume ratios changes the rules, that is to be more precise for some of you: if you assume the same model, you can use this rule, but if you compare with measurements on small items it might be wrong, as other physics must be added and cannot be ignord in the smal scale worlds.
So back to meshing thin structures, particularly if the geometry is not too complex, you have on the manual interactive meshing window, under "advanced" tab a geometric scale factor, I would suggest to learn how to use this feature, it is very useful for meshing thin features with large dimension dfferences
Good luck
Ivar