Numerical Tracking of Limit Points for Direct Parametric Analysis in Nonlinear Rotordynamics
Abstract
A frequency-domain approach for direct parametric analysis of limit points 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 limit points is performed. The whole numerical procedure is based on the Harmonic Balance Method and can be decomposed in three distinct steps. Firstly, a response curve is calculated by HBM combined with a continuation technique until a limit point is detected. Then this starting limit point is used to initialize the direct tracking of limit points which is based on the combination of a so-called extended system and a continuation technique. With only one computation, a complete branch of limit points 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.
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