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This paper describes a step forward in calculating the nonlinear frequencies and resultant dynamic behavior of high speed rotor bearing system with mass unbalance. Nonlinear strongly coupled equations of motion has been formulated based on strain energy and kinetic energy equations for shaft, disk and unbalance mass with shaft undergoing large bending deformations. Here gyroscopic effects of disk as well as mass unbalance are also considered while vibration effect along the shaft axis is ignored. Time history and FFT analysis for finding the fundamental frequencies for the rotating are portrayed under variation of shaft diameter, frequency of the shaft speed, geometric nonlinearity and disk location. The present research shows an interesting development that the initial conditions are playing an important role in finding the nonlinear frequencies and this variation is strongly due to the presence of nonlinear geometric coupling. In addition, response analysis of the system has been developed due to mass unbalanced using time history. This paper enables an understanding and realization of operating zones of rotational speed of the shaft by which the excessive vibration can easily be avoided due to the resonant conditions occurred as the natural frequencies come closer to the frequency of the rotational speed.

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The present research studies the vibration and bifurcation analysis of a spinning rotor-disk-bearing system to carefully scrutinize the dynamic stability under extrinsic mass unbalance and pulsating axial load. The shaft is flexible and taken into account the geometrical nonlinearities due to large elastic deformation in bending. The rotor is supported by flexible bearings, which are modeled as an equivalent spring-damper system having linear and nonlinear stiffness elements. Equation of motion of the rotating system, which includes flexible shaft, rigid disk, and flexible bearing, is derived using extended Hamilton principle with the assumption of the Euler's beam theory. We studied initially the modal analysis to determine the modal parameters, i.e. natural frequency and mode shapes prior to the investigation of the dynamics of the system. Further, we developed the bifurcation diagram for steady-state solutions and to study the subsequent dynamic stability and verify with the findings solved numerically. The interactive behavior among the nonlinear shaft-bearing, axial load and an unbalance has been analyzed. Numerical simulation tools, i.e. frequency–response characteristics, time history, phase trajectories, and Poincaré map have been used to highlight the presence of nonlinear phenomena and its important role towards evaluating the system dynamics and subsequent stability. This current research showed that flexible bearings stabilize the system as a result of increasing the restoring force. Analyzing the bifurcation diagrams of pulsating axial load, we found that the system exhibits complex phenomena as multiple but stable periodic orbits leading to period doubling. The present system is highly vulnerable to catastrophic failure due to the S–N and Pitchfork bifurcation. The present research enables the notability of axial load and mechanical unbalance on the overall system behavior and stability in real working conditions.