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Eigenfrequency of CCbeam Vs temperature
Posted 02.08.2021, 03:05 GMT-4 MEMS & Nanotechnology, Structural & Acoustics, Structural Mechanics Version 4.3 5 Replies
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I have a silicon based CCbeam built in comsol, when I only consider the thermal expansion coefficient as 2.3e-6, a constant, then at different temperature, get the eigen frequency of the CCbeam to derive the TCF of the beam. but the TCF is in the order of arround 1000ppm/K, which is 10^3 times higher than the theory analysis results. I wander of there is any setting that I need consider when I did the solid mechanical analysis with temperature effects of the CCbeam, also I tried the thermal stess analysis, it almost give the similiar results as the solid mechanical module.
I am confused about the simulation results have a large mismatch with the theory results.
Thanks if you could share any suggestion or guidence.
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This is probably due to the fact that you are using a very old version (4.3). From version 5.3, this should work out of the box (see https://www.comsol.com/release/5.3/structural-mechanics-module and https://www.comsol.se/blogs/how-to-analyze-eigenfrequencies-that-change-with-temperature )
In version 4.3, you should be able to obtain the same effect using a Saint-Venant Kirchhoff hyperelastic material.
-------------------Henrik Sönnerlind
COMSOL
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This is probably due to the fact that you are using a very old version (4.3). From version 5.3, this should work out of the box (see and )
In version 4.3, you should be able to obtain the same effect using a Saint-Venant Kirchhoff hyperelastic material.
Hello! Henrik, thanks for your reply. I also had the access to version 5.4 comsol, also I learned the case in the link. the point is when I calculate the numbers [50713(first mode freq)-50425(first mode freq_10K)]/10K=28.8 Hz/K, then 28.8/50713=5.68*10^-4(1/K)=568ppm(1/K), but in the material base that you used the thermal expansion is arround 1^(-5)(1/k) (x direction) so the value should be arround 10-100ppm and less than 100ppm in analytically if we only consider the thermal expansion coefficient. also I would like ask you another problem, when in the practical cases, the two ends in fixed constraint of double clamped beam is not exist, right? so if we cansider the perfect double clamped beam in comsol, we will see no expansion in the two ends of the beam which cause a ultra-high stress in the beam, but this case will loss some accuracy with experimental results, right?I wish if you could give me any views about my thoughts.
thanks for your time and wait for your reply. Xuecui
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in the practical cases, the two ends in fixed constraint of double clamped beam is not exist, right? so if we cansider the perfect double clamped beam in comsol, we will see no expansion in the two ends of the beam which cause a ultra-high stress in the beam,
In a practical case buckling would occur if the ends were absolutely fixed. And they are not- in a practical case you would have to also simulate the supporting structure.
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In a practical case buckling would occur if the ends were absolutely fixed. And they are not- in a practical case you would have to also simulate the supporting structure.
**Thanks for your reply! So if we consider this case, the anchors of resonator are fixed on the thin silicon oxide layer, then fixed on the handle wafer. if the handle wafer is the similiar material like the resonator, this one should be different with the one with perfect fixed contraints of the ends of resonator, right?
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The silicon dioxide + substrate alone would have some minor amount of bending due to the different thermal expansion. Some stress would be transferred to anything built on the substrate.
It's not clear whether your resonator is single crystal silicon or polysilicon. Polysilicon would have a bit different thermal expansion coefficient than single crystal (and the single crystal thermal expansion coefficient would presumably be anisotropic).