I would like to analyze a machine I'm designing for the natural frequencies of all the rotating shafts and inertias. We used to do this with the Holzer Tabulation method with many hand calculated iterations to achieve a result. I'm sure there is software available today to do this. Does anyone know from experience what software that would be?
Programming the holzer method is fairly straightforward though most commercial software using the method actually use transfer matrices. Probably the single most serious (but overstated) limitation to the holzer method (transfer matrices) is that it is said to be unsuited to systems with closely spaced natural freuencies ... in my experience however it hasn't been a real problem.
Newer software (developed since the mid-'70's) use what is called an FEA method, however it bears a striking resemblance to the holzer method. In any case google Dyrobes, ARMD and XLrotor for a quick survey of software packages. Also a visit to Texas A&M's Turbomachinery Lab website and Virginia Tech's website should turn you on to current research and software developments in the area of rotordynamics.
If you are short of budget then one low-budget way of 'programming' the holzer method is to build a spreadsheet to compute a holzer table and then use a 'goal seeking' function to find the 1st root. Then repeat (with suitable constraints) to find higher roots.