Consider a system made of a cylindrical column (fixed on the ground) with a mass attached on top of it (B). Both the mass of the column and the mass are not negligible. Depending on the value of the mass I could have self-buckling of the column. What I would like to compare is the natural frequency at the top of the column as a function of mass and presence of self-buckling.
1) If there isn't self buckling, then I can compute the natural frequency of the column+mass system as a cylindrical cantilever (still don't know how, but it seems standard).
2) If I have self-buckling, the column bends and I expect the system to have a natural frequency around the z-axis due to system symmetry (in red). Is that true? How can I compute that frequency?
I need help especially for "2)". Any reference/help for "1)" is appreciated.