Parametric analysis of the nonlinear behavior of rotating structures

Lihan Xie (1) , Sébastien Baguet (1) , Benoit Prabel (2) , Régis Dufour (1)

1 DCS - Dynamique et Contrôle des Structures
2 DYN - Laboratoire d'études de DYNamique

An efficient frequency-domain method is presented for the rapid parametric analysis of stability changes in nonlinear rotating systems which are modeled by three-dimensional finite elements. This method provides directly the stability boundary with respect to parameters such as the system nonlinearity or excitation level. Firstly, the response curve is calculated by combining Harmonic Balance Method (HBM) and continuation. Then stability of equilibrium solutions is determined by Floquet theory. The singular points where a stability change often arises are detected with the sign change of the Jacobian determinant and then located through a penalty method that increases the solving equation system by a completing constraint. Tracking these points, which provides an efficient way to analyze parametrically the nonlinear behavior of a system, can be fulfilled, once again, by the continuation technique.

Mots clés: Bifurcations; Nonlinear dynamics; Harmonic Balance Method; Rotordynamics; Bifurcation tracking

Domaines: Vibrations [physics.class-ph]

Lihan Xie, Sébastien Baguet, Benoit Prabel, Régis Dufour. Parametric analysis of the nonlinear behavior of rotating structures. EUROMECH-Colloquium 573 Coupling and non-linearities in rotating machinery, Aug 2015, Lyon, France. ⟨hal-01192957⟩