On the dynamic behaviour of rotating shafts under combined axial and torsional loads

A comprehensive dynamic study on a distributed parameter model of a straight uniform rotating shaft is developed, aimed at presenting some clarifications and corrections to published results, together with novel contributions. The model includes the effects of transverse shear, rotatory inertia and gyroscopic moments with additional combined end thrust and twisting moment. The equations of motion are derived in both Newtonian and Lagrangian formulations according to the Timoshenko beam theory. A novel contribution is given in the development of complete modal analysis of the model under study, highlighting the properties of the operators involved and the relations among eigenfunctions represented in complex and real variables. The influence of the main governing parameters (slenderness ratio, angular velocity, external axial end thrust and twisting moment) is studied on natural frequencies, modal shapes and critical speeds of the rotor. New evidence of existence of a second frequency spectrum in the Timoshenko beam theory is presented, together with a novel definition for its identification, only possible if considering gyroscopic effects.