If you want to calculate the electronic band structure, then density functional theory (Vasp, quantum espresso, fhi-aims...) is what you need. FEM codes are not able to do this kind of calculation. IN theory, you could set up an fem calculation of the wave function structure, but localized FE base functions are not really suitable for the task.

Dear Martin, thank You for the answer. I want to do structural vibrations. Are there some free or open source packages?

It was possible to implement the Floquet-BC into ANSYS with APDL

Dear all, thank you for the interest on this question.

Finally, here is a brief description how to do it with ANSYS.

Conference Paper Dispersion Curves of Elastic Metamaterials and Sonic Crystal...