Modal analysis using cylindrical coordinates


I’m trying to find the natural frequencies of a structure that is an axisymmetric cut of a circular disc. I wrote the FreeFem code using cylindrical coordinates, but the results are different compared to the full disc configuration. I suspect that i need to specifiy periodic boundary conditions on theta, how can i implement it in the code?

Thank you in advance

By Theta, I understand you mean the polar angle?
If so, it is not periodic, but 2 pi periodic, and thus discontinuous…
what kind of periodicity do you have in mind?

If the structure is axisymmetric and your problem is linear, I would suggest you keep your problem in a 2D framework and expand along theta in a Fourier series of integer azimuthal wavenumbers.

Otherwise, you can try what @frederichecht suggests here: Cylindrical coordinate for flow simulation

Yes theta is the polar angle. I’m solving only a 1 degree cut of the full disc and i want to impose a rotational periodicity on the lateral faces to make it seem like it’s the full geometry

i’m solving the problem in a 3D framework (r,theta,z). This is why i need to impose a rotational periodicity