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The higher modal spring constant calculation
Posted 5 ago 2010, 16:59 GMT-4 4 Replies
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I have a question about how to use COMSOL to calculate the higher mode spring constant of beam. Thanks
4 Replies Last Post 23 ott 2010, 17:50 GMT-4
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Posted:
1 decade ago
Hi
what exactly are you referring to as "higher modes"?
If you define a geometry and a material constant, as well as a mesh that is sufficiently fine (at least >> 3-10 elements per mode wavelength) you should be able to get all eigenmodes up to this limit.
Nevertheless, I do seldom use any mode much higher than the first dozen (after the 6 rigid body modes in 3D). Their shape and frequency depends als on the way you fix the parts.
Note that the eigenvalues are normalysed and that displacement are to be use only relative w.r.t their shapes, in no way to interprete as absolute values
COMSOL does NOT normalise the mode shapes to allow easily the extraction of the effective masses (or mass participation factors of the eigenmodes), this could be easily implemented as a postprocessing function but COMSOL here is the only FEM software I know about NOT proposing this type of eigenvector normalisation. I hope they will soon implement it ;)
It is possible, check the forum, to extract these values for simple cases via a matlab script. But this is too heavy for any true engineering model
--
Good luck
Ivar
what exactly are you referring to as "higher modes"?
If you define a geometry and a material constant, as well as a mesh that is sufficiently fine (at least >> 3-10 elements per mode wavelength) you should be able to get all eigenmodes up to this limit.
Nevertheless, I do seldom use any mode much higher than the first dozen (after the 6 rigid body modes in 3D). Their shape and frequency depends als on the way you fix the parts.
Note that the eigenvalues are normalysed and that displacement are to be use only relative w.r.t their shapes, in no way to interprete as absolute values
COMSOL does NOT normalise the mode shapes to allow easily the extraction of the effective masses (or mass participation factors of the eigenmodes), this could be easily implemented as a postprocessing function but COMSOL here is the only FEM software I know about NOT proposing this type of eigenvector normalisation. I hope they will soon implement it ;)
It is possible, check the forum, to extract these values for simple cases via a matlab script. But this is too heavy for any true engineering model
--
Good luck
Ivar
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Posted:
1 decade ago
Thanks. Actually, I want to calculate the spring constant for the fourth flexural modal of doubly-clamped silicon beam. How can I use the COMSOL to do that? Thanks.
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Posted:
1 decade ago
Hi
I'm not sure how you define the stiffness for a mode, in rigid body one would write
2*pi*freq[Hz]=k[N/m] / (m[kg])
but you have a distributed system, one way is to say we use the modal effective mass, but this is not calculated by default in COSMOL (they use another normalisation of the eigenmodes) which means that you must use Matlab to renormalise the modes. There are a few threads discussiong this (+code). Try a search on the forum with "mass participation factor" "modal mass" "effetive mass"
For a simple model the matlab code is OK (it's an issue of RAM and extraction of the sparse model structure and stiffness matrices to Matlab).
with this mass and the frequency, you can get a distributed stiffness value for each mode. If this is what you are looking for, then you have a work-around.
It would be good to check it out against a simple beam, from known stiffness values from the litterature
--
Good luck
Ivar
I'm not sure how you define the stiffness for a mode, in rigid body one would write
2*pi*freq[Hz]=k[N/m] / (m[kg])
but you have a distributed system, one way is to say we use the modal effective mass, but this is not calculated by default in COSMOL (they use another normalisation of the eigenmodes) which means that you must use Matlab to renormalise the modes. There are a few threads discussiong this (+code). Try a search on the forum with "mass participation factor" "modal mass" "effetive mass"
For a simple model the matlab code is OK (it's an issue of RAM and extraction of the sparse model structure and stiffness matrices to Matlab).
with this mass and the frequency, you can get a distributed stiffness value for each mode. If this is what you are looking for, then you have a work-around.
It would be good to check it out against a simple beam, from known stiffness values from the litterature
--
Good luck
Ivar
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Posted:
1 decade ago
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