Bifurcation analysis of fan casing under rotating air flow excitation

A fan casing model of cantilever circular thin shell is constructed based on the geometric characteristics of the thin-walled structure of aero-engine fan casing. According to Donnelly＇s shell theory and Hamilton＇s principle, the dynamic equations axe established. The dynamic behaviors are investigated by a multiple-scale method. The effects of casing geometric parameters and motion parameters on the natural frequency of the system are studied. The transition sets and bifurcation diagrams of the system are obtained through a singularity analysis of the bifurcation equation, showing that various modes of the system such as the bifurcation and hysteresis will appear in different parameter regions. In accordance with the multiple relationship of the fan speed and stator vibration frequency, the fan speed interval with the casing vibration sudden jump is calculated. The dynamic reasons of casing cracks are investigated. The possibility of casing cracking hysteresis interval is analyzed. The results show that cracking is more likely to appear in the hysteresis interval. The research of this paper provides a theoretical basis for fan casing design and system parameter optimization.