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How to localize the mode in the cantilever beam attached to a substrate and PML layer?

Posted 11 sept. 2024, 10:07 UTC−4 Structural & Acoustics, Geometry, Modeling Workflow Version 6.2 0 Replies

Mohit Kumar

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Hi all,

I am trying to benchmark the anchor loss in cantilever beam attached to a substrate and also has a PML. The beam is Depth (D) > Width (W) > Height (H) and, is attached to a substrate which is quarter sphere and also the outer layer has PML and also outer surface boundries (opposite side to the beam) is fixed constrained. The problem I am facing while trying to benchmark is the following:

first, let's call the radius of substrate to be "r_sub" and length (or rather, radius) of PML to be "r_pml"

and everything here is 'Polycrystalline Silicone'

I was simulating this cantilever beam ~ (50 um, 30 um, 5 um) and I was taking r_sub ~ 90 um and r_pml ~ 40 um and it seemed to be working well: high enough of Quality factor, mode shape looking good and everything. Later, I learned that the size of both r_sub and r_pml should be at least one wavelength bigger which, in this case comes about to be 900 um, if not bigger.
Here's the catch, the quality factor changes as I increase the r_sub and as I reach to the suggested size of the substrate, the quality factor just goes down and also the size difference between beam and the substrate now is quite significant.

I have tried number of things, which doesn't seem to be working either.

Playing with mesh, since there's a size difference. I have tried taking several combination of meshes, making beam finer and making both beam and substrate finer
playing with the size of r_pml
since there seems to be some sort of mode coupling happening between beam and substrate, I tried to change substrate to a stiffer material, read diamond. doesn't work
fixing more surfaces including the whole substrate and PML ridden surfaces to be fixed constraints. (Which I think was a little absurd to do, even to begin with)

I am mainly looking for suggestions on how to make this system work where the beam is significantly smaller to the size of substrate. the mode is not localizing just to the beam, rather the whole substrate seems to be involved in it too, which makes the quality factor seemingly worst. Please find attached the pictures of the geometry and mode shape.

many thanks, Mohit

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