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Purely real eigenvalue
Posted Apr 20, 2010, 11:53 a.m. EDT 1 Reply
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I am trying to model a fairly simple MEMS structure: a small cantilever of InP with a thin film of gold layered on top of each end. Specifically, I am doing eigenvalue simulations to try and find the mechanical modes of the structure. Due to the nature of the gold deposition there should be some initial in-plane tensile stress in the gold layer.
If I put no stress or a small amount of initial stress in the gold, everything proceeds as I would expect and COMSOL successfully finds the modes. If I increase the stress too much, however, a very peculiar thing happens. The lowest order mode found by COMSOL still has the same mode shape as the fundamental mode found in previous simulations, but now the eigenvalue returned by COMSOL is purely real (i.e. the eigenfrequency of the mode is pure imaginary). I am used to associating the real portion of the eigenvalue with losses, but I don't know what to make of a purely real eigenvalue. Moreover, I am not doing a damped eigenfrequency analysis, so there shouldn't be any losses in the system.
What is the physical interpretation of a purely real eigenvalue (if indeed there is any)?
If I put no stress or a small amount of initial stress in the gold, everything proceeds as I would expect and COMSOL successfully finds the modes. If I increase the stress too much, however, a very peculiar thing happens. The lowest order mode found by COMSOL still has the same mode shape as the fundamental mode found in previous simulations, but now the eigenvalue returned by COMSOL is purely real (i.e. the eigenfrequency of the mode is pure imaginary). I am used to associating the real portion of the eigenvalue with losses, but I don't know what to make of a purely real eigenvalue. Moreover, I am not doing a damped eigenfrequency analysis, so there shouldn't be any losses in the system.
What is the physical interpretation of a purely real eigenvalue (if indeed there is any)?
1 Reply Last Post Apr 21, 2010, 10:00 a.m. EDT
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Posted:
1 decade ago
Hi
Normally the "eigenfrequency" is defined as 1/2/pi*abs(imag(lambda)) with "lambda" being the complex eigenvalue, therefore I would expect a real eigenfrequency and a complex eigenvalue, note "eiglambda" being -2*i*pi*eigenfrequency. But the internals of COMSOL uses "lambda" called "complex angular frequency".
these variablesare defined in the "scalar Variables" tab when you apply eigenfrequency/eigenvalue, and are further defined in the doc.
it could be that COMSOl uses a sign convention that is slightly different from yours to be globally coherent for all its physics, this would not be the only place. And be sure you mention clearly which one you refer too
This does not change the isue about the change from real to imaginary that should be linked to some damping I agree, remains to know if there are some "numerical damping" in there to assure convergence.
hope this helps on the way
Ivar
Normally the "eigenfrequency" is defined as 1/2/pi*abs(imag(lambda)) with "lambda" being the complex eigenvalue, therefore I would expect a real eigenfrequency and a complex eigenvalue, note "eiglambda" being -2*i*pi*eigenfrequency. But the internals of COMSOL uses "lambda" called "complex angular frequency".
these variablesare defined in the "scalar Variables" tab when you apply eigenfrequency/eigenvalue, and are further defined in the doc.
it could be that COMSOl uses a sign convention that is slightly different from yours to be globally coherent for all its physics, this would not be the only place. And be sure you mention clearly which one you refer too
This does not change the isue about the change from real to imaginary that should be linked to some damping I agree, remains to know if there are some "numerical damping" in there to assure convergence.
hope this helps on the way
Ivar