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Eigenfrequency Analysis of a Stepped Beam with Clamped Ends
Posted Jul 11, 2023, 4:40 p.m. EDT General, MEMS & Piezoelectric Devices Version 6.1 4 Replies
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I am currently investigating the eigenfrequencies of a stepped beam that is clamped at both ends using COMSOL. The beam is made of silicon and is in a vacuum environment, with heat transfer occurring solely through radiation (emissivity set to 0.8). I am applying a voltage of 10V on one end and grounding the other end, utilizing Joule Heating for tuning.
I anticipate the second bending mode to be approximately 1MHz and the third bending mode to be around 2MHz. However, I am encountering complex eigenfrequencies in my analysis. I would greatly appreciate any guidance regarding potential inaccuracies in my setup. I have attached my .mph model for reference.
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If there are no losses in the problem the eigenvalue solver usually comes up with very small imaginary parts for the eigenfrequencies. When a loss mechanism is present (fluid damping or friction or whatever) the imaginary part represents an actual physical loss leading to a finite quality factor.
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You should only solve for structural mechanics in the eigenfrequency study. If not, you will see the very small imaginary eigenvalues of the diffusion type equations, like thermal eigenmodes.
-------------------Henrik Sönnerlind
COMSOL
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You should only solve for structural mechanics in the eigenfrequency study. If not, you will see the very small imaginary eigenvalues of the diffusion type equations, like thermal eigenmodes.
If there are no losses in the problem the eigenvalue solver usually comes up with very small imaginary parts for the eigenfrequencies. When a loss mechanism is present (fluid damping or friction or whatever) the imaginary part represents an actual physical loss leading to a finite quality factor.
Thank you, Dave and Heinrik, for your insightful replies.
I wish to elaborate more on the goal of this simulation.
I have a stepped microbeam, which I am heating up by applying a voltage across it. I want to know how the eigenmode frequencies vary as I change the voltage across the beam.
The beam is made from Silicon and is inside a vacuum. It is also anchored on both ends, and these ends act as the electrodes as well. The only energy loss can be considered to be the heat radiating out from the beam. The vacuum is in the 10milliTorr range, so the air damping can be neglected.
How can I achieve this multiphysics simulation?
Appreciate your insight!
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There are three important contributions to the temperature dependence of the eigenfrequencies:
- The stress induced by inhibited thermal expansion
- The change in geometry due to thermal expansion
- Temperature dependence of Young's modulus
This is discussed in detail in https://www.comsol.com/blogs/how-to-analyze-eigenfrequencies-that-change-with-temperature
At microscale, you can have a significant damping contribution from thermoelastic damping. See also
https://www.comsol.com/blogs/damping-in-structural-dynamics-theory-and-sources and https://www.comsol.com/blogs/how-to-model-different-types-of-damping-in-comsol-multiphysics
-------------------Henrik Sönnerlind
COMSOL