Stability investigation of rotors with periodic axial force

A vast amount of research has been conducted analyzing the destabilizing effect of an axial force acting on a rotor. In this study a harmonic axial force is used to stabilize a non-symmetric rotor driven at its critical speed. Both, the equation of motion of an inverted pendulum excited at the suspension point as well as the equations of motion of a non-symmetric rotor with periodic axial force, can be transformed into the Mathieu-equation. Since an inverted pendulum can be stabilized by periodic suspension point excitation, a periodic axial force stabilizes a non-symmetric rotor driven at its critical speeds. Additionally, similarities and differences between the stability of Jeffcott- and continuous rotors are pointed out. Furthermore, the influence of gyroscopic terms is investigated and illustrated with the help of stability cards.