Effect of internal damping on the stability of a non-linear continuous rotor system

Accurate prediction of nonlinear vibration behavior in rotor systems is essential for the safe and efficient operation of high-speed rotating machinery. This paper performs a nonlinear continuous rotor system (CRS) analysis. The CRS model is derived by including some important factors, like the gyroscopic effect, the rotary inertia of the disc and shaft, internal damping, large shaft deformation, and constraint to the axial motion of the shaft at the bearing ends. Unlike existing studies these effects considered independently, the proposed formulation captures their combined influence within a continuous model. The method of multiple scales is applied to obtain the autonomous amplitude and phase equations for simultaneous resonance conditions. A comparison of the analytical and numerical results yields a close match. Localized and nonlocalized oscillations are examined. Linear stability analysis is performed to assess the stability of steady-state solutions. Expressions for the critical value of a parameter along both directions are derived to determine the emergence of limit points (LPs). A comprehensive parametric analysis is conducted to investigate the impact of various system parameters on the system dynamics. The results demonstrate complex nonlinear behavior characterized by multivalued solutions, jump phenomena, and the onset of instability through limit point bifurcations. These findings provide critical insight into nonlinear rotor behavior, improving the understanding, design, and prediction of instability in systems operating under nonlinear and resonance conditions.