Has anyone tried something like this in calculix?
In CalculiX, you can perform both regular and complex eigenfrequency extraction analysis. The latter is meant specifically for rotordynamics as it accounts for Coriolis forces. Then you may carry out a steady-state dynamics analysis (frequency-domain response to harmonic loads) but keep in mind that it can’t account for nonlinearities. To include those, you would need a nonlinear time-domain simulation (implicit dynamics).
I guess you have to analyse one speed at a time, extract frequencies and run the SSD; given that frequency and out of balance loading are both changing with rotational speed.
Yes, you can start by creating a Campbell diagram (eigenfrequency vs rotational speed).