A GEOMETRICALLY NON-LINEAR MODEL OF ROTATING SHAFTS WITH INTERNAL RESONANCE AND SELF-EXCITED VIBRATION

A geometrically non-linear model of the rotating shaft is introduced, which includes Kلrman non-linearity, non-linear curvature effects, large displacements and rotations as well as gyroscopic effects. Through applying Timoshenko-type assumptions, the shear effects are also included in the model. Convenient matrix descriptions are used in order to facilitate the analysis based on Galerkin and continuation methods. The model is used to analyze the phenomenon of internal resonance. The influence of some of the systemʹs parameters on the amplitude and frequency of self-excited vibration is investigated.