Stability analysis of rotating shafts under axial and torsional periodic loads

A contribution is given to clarify gyroscopic effects on stability of parametrically excited rotor systems, highlighting the role played by stabilizing damping distributions. As case–study of general interest, giving rise to a set of coupled differential Mathieu–Hill equations with both gyroscopic and damping terms, a continuous perfectly balanced shaft is considered, modelled as a spinning Timoshenko beam loaded by oscillating axial end thrust and twisting moment. After discretization of the equations of motion into a set of coupled ordinary differential Mathieu–Hill equations, stability of Floquet solutions is studied via eigenproblem formulation, obtained by applying the harmonic balance method. A numerical algorithm is then developed for computing global stability thresholds in presence of both gyroscopic and damping terms, aimed at reducing the computational load. Finally, the influence on stability of the main characteristic parameters of the shaft is analyzed with respect to frequency and amplitude of the external loads on stability charts in the form of Ince–Strutt diagrams.