Abstract
The purpose of this work is to explore the nonlinear vibration of a rub-impact Jeffcott rotor. In the first stage, the motion is not affected by the friction force, but in the second stage, the motion is influenced by the normal force and the friction force. The governing equations of the rotor of this model are derived in this paper. In consequence, there appears a difference between the two stages. We establish an approximate analytical solution for nonlinear vibrations corresponding to two stages with the mention of the location of jumps. The obtained results are compared with the numerical integration results. The steady-state response and the stability of the solutions are analytically determined for the two stages. The stability of a full annular rub solution is studied with the help of the Routh−Hurwitz criterion. Effects of different parameters of the system, the saddle-node bifurcation (turning points) and the Hopf bifurcation are presented. The main contribution lies in the analytical approximation solution based on the Optimal Auxiliary Functions Method.