A colleague of mine wrote a critical speed computer program based on the transfer matrix method. I checked his results and found they were no different from mine (within the engineering accuracy) using the beam theory. With the rotor's weight as the known mass, elastic modulus and second moments of area of the shaft cross sections to obtain the stiffness and the bearings as the pinned or spring supports in a multispan beam system the natural frequencies can be determined very quickly by simple calculation. With the ability to compute it from first principle you could at least do a sanity check if you do get numerical answers from the readers.
Any commercial structural analysis software can be used to analyse a beam and none of them can sell without the ability to do some basic dynamic analyses. The simple modelling is within the capability of a engineering graduate.
Our original software was written in Fortran and are no long needed when the commercial software becomes available. I use mainly Staadpro.
Typically the shaft can be modelled as one-dimension line elements with nodal points at least at the ends of shaft and bearing points. The commercial software needs information on the material properties like elastic modulus and density (Poisson ratio may be asked) and the element properties like areas and I-values. For a quick answer the bearings can be assumed rigid first and then later refined according to their actual vertical stiffness. By instructing a modal analysis all the natural frequencies and mode shapes will out.
I haven't got myself into the theory and computation of critical speed but can confirm that the solution appears to differ very little from that obtainable by the beam theory. The critical speed transfer matrix algorithms had many refinements like gyroscopic effect but the dominant terms are the mass and the structural profile of the rotor. I remember the difference of the two approaches was no more than a few percent for all the modes I investigated.
If the natural frequencies of a rotor analysed as a beam supported on bearing points are not essentially similar to the critical speeds of the rotating shaft I would like the experts here help to correct it. I always think it is one of those funny things in life that a mechanical and a civil engineer walk adifferent paths but arrive at the same destination.
Thanks everyone. We eventually got the manual. For everyone's learning the gas producer design speed is 15 015 rpm. The 1st critical occurs at 6000 rpm. The 2nd at 8200 rpm. The powerturbine design speed is 15 700. The 1st critical is at 5140 and the 2nd. at 12690.
