Continuation analysis of a nonlinear rotor system

Abstract

Nonlinearities in rotating systems have been seen to cause a wide variety of rich phenomena; however, the understanding of these phenomena has been limited because numerical approaches typically rely on “brute force” time simulation, which is slow due to issues of step size and settling time, cannot locate unstable solution families, and may miss key responses if the correct initial conditions are not used. This work uses numerical continuation to explore the responses of such systems in a more systematic way. A simple isotropic rotor system with a smooth nonlinearity is studied, and the rotating frame is used to obtain periodic solutions. Asynchronous responses with oscillating amplitude are seen to initiate at certain drive speeds due to internal resonance, in a manner similar to that observed for nonsmooth rotor–stator contact systems in the previous literature. These responses are isolated, in the sense that they will only meet the more trivial synchronous responses in the limit of zero damping and out of balance forcing. In addition to increasing our understanding of the responses of these systems, the work establishes the potential of numerical continuation as a tool to systematically explore the responses of nonlinear rotor systems.