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Apply Floquet periodicity to weak form PDE

Posted Nov 10, 2017, 6:10 p.m. EST Structural & Acoustics, Acoustics & Vibrations, Structural Mechanics Version 5.3 2 Replies

Qianli Chen
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Hi all, I am new to Comsol and find it very convenient to use. I am now trying to do Bloch wave analysis to an cosserate medium. Since I am applying cosserate medium, I have to use the weak form PDE instead of solid mechanics. My next step is to apply Bloch/Floquet periodicity to the system. I know it is built-in for the solid mechanics but for weak form PDE, there is no such option in the periodic condition,

So can anyone tell me how I can apply this? PS, basically, what I need to do is to apply a displacement constrain like u_dst=u_src*exp(-ikd). where udst is the displacement in i.e. left boudnary and u_src is the displacement on i.e. right boudary and i is the imagiary number, k and d are all given constants.

2 Replies Last Post Nov 13, 2017, 7:24 p.m. EST
Henrik Sönnerlind COMSOL Employee

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Posted: 7 years ago Nov 11, 2017, 12:35 p.m. EST

Hi Qianli,

I think that the best idea is to look at the Floquet condition in Solid Mechanics, using Equation View. Pay particular attention to the reaction force term, which contains an 'unexpected' complex conjugate.

Another possibility is that you implement your Cosserat material inside Solid Mechanics. You would then need to replace the weak expression for the strain energy variation in Linear Elastic Material by your own. But you need to create your own stress and strain variables, since the built-in tensors are declared as symmetric. The advantage with this approach is that you have access to all built-in boundary conditions.

Note also that the Physics Builder is great tool for tasks like this, due to the possibility to form expressions using compact tensor notation.

Regards,

Henrik

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Henrik Sönnerlind
COMSOL
Hi Qianli, I think that the best idea is to look at the Floquet condition in Solid Mechanics, using **Equation View**. Pay particular attention to the reaction force term, which contains an 'unexpected' complex conjugate. Another possibility is that you implement your Cosserat material inside Solid Mechanics. You would then need to replace the weak expression for the strain energy variation in **Linear Elastic Material** by your own. But you need to create your own stress and strain variables, since the built-in tensors are declared as symmetric. The advantage with this approach is that you have access to all built-in boundary conditions. Note also that the Physics Builder is great tool for tasks like this, due to the possibility to form expressions using compact tensor notation. Regards, Henrik
Qianli Chen
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Posted: 7 years ago Nov 13, 2017, 7:24 p.m. EST

Thank you so much Henrik, I am processing with my work now.

Thank you so much Henrik, I am processing with my work now.

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