BIFURCATION OF A SHAFT WITH HYSTERETIC-TYPE INTERNAL FRICTION FORCE OF MATERIAL

The bifurcation of a shaft with hysteretic internal friction of material was analysed. Firstly, the differential motion equation in complex form was deduced using Hamilton principle. Then averaged equations in primary resonances were obtained using the averaging method. The stability of steadystate responses was also determined.Lastly, the bifurcations of both normal motion （synchronous whirl） and selfexcited motion （nonsynchronous whirl） were investigated using the method of singularity. The study shows that by a rather large disturbance, the stability of the shaft can be lost through Hopf bifurcation in case the stability condition is not satisfied. The averaged selfexcited response appears as a type of unsymmetrical bifurcation with high orders of codimension. The second Hopf bifurcation, which corresponds to double amplitudemodulated response, can occur as the speed of the shaft increases. Balancing the shaft carefully to decrease its unbalance level and increasing the external damping are two effective methods to avoid the appearance of the selfsustained whirl induced by the hysteretic internal friction of material.