Nicely explained @ggiraldo!
@Schtig, you can also try doing the frequency analysis with a second order mesh. You can see a mesh study on frequency analysis here: Beam Natural Frequencies - Mesh Study
Doing this can also help you to get more accurate results. Although your geometrical case is quite simple but it might be possible that it leads you to the non-positive Jacobian since solver used for Frequency analysis is quite sensitive on mesh quality. Nevertheless its worth a try 
I hope this helps.
Best,
Ahmed