Effects of geometrical nonlinearities on the dynamic of a supercritical jeffcot rotor with internal damping
Résumé
This work is concerned with the stability of a nonlinear Jeffcott rotor. Geometrical nonlinearity (shaft with large flexural displacements) is considered as a Duffing oscillator type. Eigenvalues of the rotor show the existence of a supercritical Hopf bifurcation. Classical instabilities due to internal damping occurring in the supercritical range are modified. It is showed that previous instabilities become limit cycles with a relatively small radius. This results allow to preserve integrity of the machine if transverse displacement of the shaft is mechanically forbidden and will allow us to observe and to measure experimentally this modes.