Nonlinear Dynamics, Continuation, and Stability Analysis of a Shaft-Bearing Assembly

In this work, the frequency response of a simplified shaft-bearing assembly is studied using numerical continuation. Roller-bearing clearances give rise to contact behavior in the system, and past research has focused on the nonlinear normal modes of the system and its response to shock-type loads. A harmonic balance method (HBM) solver is applied instead of a time integration solver, and numerical continuation is used to map out the system’s solution branches in response to a harmonic excitation. Stability analysis is used to understand the bifurcation behavior and possibly identify numerical or system-inherent anomalies seen in past research. Continuation is also performed with respect to the forcing magnitude, resulting in what are known as S-curves, in an effort to detect isolated solution branches in the system response.