International audienceThe safety of turbomachines requires controlling the risks caused by contacts occurring between fixed and rotating parts. Undesirable phenomena induced by bladed wheel/casing interactions are caused by the forced excitation of the natural modes of a blade leading to its damage or by potentially dangerous couplings between the modes of the casing and those of the wheel. Rotor-stator contacts may also lead to various types of dangerous behavior, including the well known configurations of dry whirl and dry whip. The paper proposes a large-scale literature review and examines existing numerical models and experimental setups used for highlighting the phenomenology involved in different rotor to stator contacts configurations. It confirms the great complexity of the problems which, by nature, are considerably nonlinear and involve multiphysics and multiscale coupled behaviors

The aim of this paper is to provide an efficient frequency-domain method for bifurcation analysis of nonlinear dynamical systems. The proposed method consists in directly tracking the bifurcation points when a system parameter such as the excitation or nonlinearity level is varied. To this end, a so-called extended system comprising the equation of motion and an additional equation characterizing the bifurcation of interest is solved by means of the Harmonic Balance Method coupled with an arc-length continuation technique. In particular, an original extended system for the detection and tracking of Neimark-Sacker (secondary Hopf) bifurcations is introduced. By applying the methodology to a nonlinear energy sink and to a rotor-stator rubbing system, it is shown that the bifurcation tracking can be used to efficiently compute the boundaries of stability and/or dynamical regimes, i.e., safe operating zones.