On the Discrete–Continuous Modeling of Rotor Systems forthe Analysis of Coupled Lateral Torsional Vibrations

Abstract

In the paper, dynamic investigations of the rotor shaft systems are performed by means of the discrete‐continuous mechanical models. In these models the rotor shaft segments are represented by the rotating cylindrical flexurally and torsionally deformable continuous viscoelastic elements. These elements are mutually connected according to the structure of the real system in the form of a stepped shaft which is suspended on concentrated inertial viscoelastic supports of linear or non‐linear characteristics. At appropriate shaft crosssections, by means of massless membranes, there are attached rigid rings representing rotors, disks, gears, flywheels and others. The proposed model enables us to investigate coupled linear or non‐linear lateral torsional Vibrations of the rotating systems in steady‐state and transient operating conditions. As demonstrative examples, for the steam turbo‐compressor under coupled lateral torsional vibrations, the transient response due to a blade falling out from the turbine rotor as well as the steady‐state response in the form of parametric resonance caused by residual unbalances are presented.