I'm working on a vibration combined simulation, and I need the different modes of vibration formulation, I've been using harmonic mode but I need further formulation like that.
don't trust formulas for modelizing the vibration of industrial structures! The reason relate to the fact that what matters are your assumptions on the "boundary conditions": formulas work perfectly for a beam in really free (or perfectly clamped) conditions, but you have nothing like that in reality...
So my recommendation is to start with EXPERIMENTAL modal analysis then try to learn how this behaviour can be approached by simple formulas if any. Then you can safer try to modelize other structures of similar construction... The same if you uses FEM. Stuctural dynamics remain an art more than a science!