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Explicit specification of damping constant
Posted Mar 21, 2020, 3:19 p.m. EDT Structural & Acoustics, MEMS & Piezoelectric Devices 4 Replies
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I am modeling a MEMS resonator in 3D using the structural mechanics physics interface.
Experimentally, the response of the resonator closely follows the classical model of a 1D damped, driven harmonic oscillator. Based on experimental data and physical dimensions, I know the 1D model parameters m, k, and b (mass, spring constant and damping constant).
It was straightforward enough to set up my 3D model in COMSOL to match m and k from experimental data.
Where I am struggling, however, is the damping constant b. For now, I am not interested in calculating b from "first principles": e.g., by adding a physically representative squeeze-film damping condition or considering viscous/thermal losses to the surrounding air.
Rather, I already know b, and I'm looking for a simple way to make my 3D model exhibit the same b that I measure. Is there a surface or volume condition I can apply, or material property I can manipulate, that would make my 3D model exhibit the b that I want? I'm not going for strict physical relevance here, I'm looking for a straightforward and computationally 'easy' way to make my 3D model behave with the b that I specify.
Can this be done? Thank you.
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Hi Brian,
As long as you are interested in one natural frequency only, there are several ways to do it.
If you use mode superposition, you can directly presribe the modal damping. If not, you can use for example Rayleigh damping or loss factor damping.
See also https://www.comsol.com/blogs/how-to-model-different-types-of-damping-in-comsol-multiphysics
-------------------Henrik Sönnerlind
COMSOL
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Hi Henrik,
Thanks for your response.
The lowest natural frequency 
of my system is the only one that matters; all other resonances are 
. I want to be able to model its response to a driving force with frequency between 
and 
.
I want to model a constant damping factor 
that behaves just like in the case of a 1D SHO 
.
I don't think mode superposition will work in my case, because I'm interested in a range of driving frequencies from to .
I don't think Rayleigh damping will work, because it introduces a frequency-dependent damping term. I'm only interested in modeling a constant damping term as in the SHO equation.
I don't think Loss factor damping will work, because it acts on the displacement amplitude term (
) and not on the velocity term (
).
Did I misunderstand anything? Thanks for your advice.
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If you are not concerned about being physically correct, you could impose a force on an appropriate boundary that is proportional to its velocity. (Make sure you get the sign right).
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You also have the option to add viscous damping in the Damping node.
Rayleigh damping is velocity proportional (just as viscous damping). If you use only the 
part, Rayleigh damping is equivalent to viscous damping (the relation is given in the blog post I linked above). The frequency dependence you are referring is present also in viscous damping. This effect is however only important for modes other than the one for which you tuned the damping. The concept of a single relative damping value is only meaningful for a one DOF problem.
Why do you consider mode superposition unsuitable? As long as you include all modes up to say 
it seems like a good choice.
Henrik Sönnerlind
COMSOL