Overview

As already stated, in many cases rotors are modeled as one-dimensional bodies, made basically of beam-like shafts with rigid bodies attached to them. This approach is typical of rotordynamics, both analytical and numerical, and several rotordynamic codes, either based on the transfer matrices approach or on the finite element method, follow this trend.

The one-dimensional mathematical models usually yield results that are accurate enough for most practical purposes while simple enough to allow relatively straightforward computations to be performed. However, rotors are intrinsically more complicated than assemblies of slender shafts and rigid bodies, and there are cases in which true three-dimensional modelling is required. There are cases in which the shafts are very stub or have a thin-walled tubular cross section, and neither the Euler-Bernoulli nor the Timoshenko beam theory is adequate to model their behavior in detail or thin bladed discs do not behave as rigid bodies. The effects linked with these deviation from the classic shafts-rigid-bodies models are usually felt more strongly on the high-frequency modes, and the very reason for which they are usually neglected is that the first critical speed and the lowest vibration frequency (or, better, the low-frequency part of the Campbell diagram) are little affected by them.

There are, however, cases in which the search for a better agreement between simulation and experimental results; the presence of high-frequency excitation that compels us to take into account also the high-frequency response, the presence of very compliant parts like thin discs or long, slender blades,...