This dissertation forms part of a research project assigned to the University of Pretoria by Eskom (the primary electricity utility in South Africa). The project aims to address, amongst others, the limitations imposed by shaft runout on the usable frequency range of diagnostic data measured by eddy current proximity probes on turbogenerator shafts. This research includes an experimental investigation into the effects of artificially induced faults on a laboratory-scale rotor system, the development and analysis of a mathematical (numerical) model of this rotor system and the development of data processing techniques (including artificial intelligence) to determine the rotor’s condition, faults and diagnostic signal parameters from both the experimental and numerical results. Furthermore, a methodology is to be developed to perform runout compensation in an unsupervised manner. These techniques are then to be implemented for proximity probe vibration data measured on turbogenerators. As part of the research project, this dissertation specifically focuses on the development and rotor dynamic analysis of numerical (finite element) models of the experimental (laboratory-scale) rotor system (using finite element software MSC.Nastran), including gyroscopic effects, a nonlinear force model for the hydrodynamic journal bearing of the rotor system (capable of capturing oil whirl and oil whip instabilities) as well as simulated faults (such as unbalance and rotor-stator rubbing). Since MSC.Nastran does not have a built-in nonlinear hydrodynamic journal bearing model, a custom model of such a bearing was developed and incorporated into the finite element solver, further expanding its already powerful rotor dynamic modelling capabilities. Rotor dynamic analyses performed include the calculation of critical speeds (synchronous complex modes analysis), Campbell diagrams (asynchronous complex modes analysis), steady state frequency response due to unbalance (synchronous frequency response analysis) and nonlinear transient response during rotor run-up. Amongst others, this dissertation explores the seemingly largely unexplored/undocumented capability of finite element software MSC.Nastran to perform rotor dynamic analyses using rotor models constructed with three-dimensional elements. Software (MATLAB code) was also developed to perform post-processing of the simulation results as well as signal processing for investigating the spectral content of transient results. The support structure of the laboratory-scale rotor system was experimentally characterised and an experimental modal analysis was performed on the rotor (excluding its support structure) and its results used to update the finite element rotor models. The transient dynamic response of the experimental rotor system during run-up due to unbalance and rubbing was also analysed in order to validate the developed numerical rotor system models. The numerical results are found to be in good agreement with the experimental results.