Numerical Tracking of Limit Points for Direct Parametric Analysis in Nonlinear Rotordynamics

Abstract

A frequencydomain approach for direct parametric analysis of limit points (LPs) of nonlinear dynamical systems is presented in this paper. Instead of computing responses curves for several values of a given system parameter, the direct tracking of LPs is performed. The whole numerical procedure is based on the harmonic balance method (HBM) and can be decomposed in three distinct steps. First, a response curve is calculated by HBM combined with a continuation technique until an LP is detected. Then this starting LP is used to initialize the direct tracking of LPs which is based on the combination of a socalled extended system and a continuation technique. With only one computation, a complete branch of LPs is obtained, which provides the stability boundary with respect to system parameters such as nonlinearity or excitation level. Several numerical examples demonstrate the capabilities and the performance of the proposed method.