The invariant manifold approach applied to nonlinear dynamics of a rotor-bearing system

TL;DR

This paper applies the invariant manifold approach to nonlinear rotor-bearing systems, developing a reduced order model that captures speed-dependent effects without extensive eigenvalue computations, enhancing analysis efficiency.

Contribution

It introduces a strategy to approximate invariant manifolds for nonlinear rotors, accounting for spin speed effects efficiently without solving eigenvalue problems at each speed.

Findings

Reduced order model accurately predicts rotor dynamics across speeds.

Invariant manifold approximation captures nonlinear normal modes effectively.

Speed-dependent effects are incorporated without extensive computations.

Abstract

The invariant manifold approach is used to explore the dynamics of a nonlinear rotor, by determining the nonlinear normal modes, constructing a reduced order model and evaluating its performance in the case of response to an initial condition. The procedure to determine the approximation of the invariant manifolds is discussed and a strategy to retain the speed dependent effects on the manifolds without solving the eigenvalue problem for each spin speed is presented. The performance of the reduced system is analysed in function of the spin speed.