Influence of fluid induced tangential forces, nonlinear stiffness, and internal damping on the vibration response of a Jeffcott Rotor System

This study investigates horizontal and vertical oscillations of a horizontally supported Jeffcott Rotor System (JRS), emphasizing the impact of key dynamic parameters. These include the eccentricity ratio, fluid induced tangential forces, nonlinear restoring forces due to large shaft deformations, and internal shaft damping. Under simultaneous resonance, the nonlinear amplitude–phase modulation equations are formulated using the analytical technique of the Method of Multiple Scales (MMS). A detailed analysis of both localized and non-localized oscillations is performed. Numerical simulations comprising time responses, phase portraits, amplitude frequency responses, backbone curves, and phase angle diagrams demonstrate complex dynamic phenomena such as the jump phenomenon, multi-valued solutions, and multiple loops. The analytical results are compared through numerical simulations, and the stability of the steady-state solutions is assessed using linear stability analysis (LSA). Furthermore, analytical expressions are derived to identify critical parameter thresholds corresponding to initiating turning points in localized oscillations. The findings provide valuable insights into the nonlinear dynamics and stability characteristics of rotor systems operating under multi-parameter excitation. The findings demonstrate that key parameters related to lubricant viscosity, geometry, and material properties of the rotor play a crucial role in control or mitigating the vibration amplitudes and unwanted jump phenomena.