Conjectural bifurcation analysis of the contact-induced vibratory response of an aircraft engine blade

This paper deals with the numerical investigation of the unilateral contact-induced dynamics of a turbomachine blade rotating within a perfectly rigid yet distorted casing. This investigation is motivated by unelucidated vibratory behaviours observed experimentally. The simulations are based on an in-house time-marching strategy incorporating Lagrange multipliers for the unilateral contact treatment, as well as centrifugal stiffening and abradable coating removal. Significant extensions are proposed through the implementation of (1) aerodynamic loading on the blade and (2) post-processing techniques involving the empirical mode decomposition which provides fruitful insights on important transient phenomena. A thorough bifurcation analysis with and without aerodynamic loading highlights the existence of flip bifurcations with period-doubling and period-halving sequences over a broad angular speed range. Numerical simulations with external aerodynamic loading yield quasi-periodic and likely to be chaotic motions that could not be observed under vacuum. The proposed numerical investigations underline the key role of the aerodynamic loading in the blade dynamics and suggest that unexplained experimental vibratory behaviours are related to the vacuum conditions of the experiment.