First-order approximate rigid-flexible coupled dynamics analysis of a simple aero-engine blade model with dynamic stiffening effect

Aero-engine blades often fracture failed due to resonance. In order to analyze the vibration characteristics of high-speed rotating blades of aero-engine more accurately, not only the out-of-plane deformation and in-plane deformation, but also the in-plane deformation caused by out-of-plane deformation are taken into account in the process of research on the rigid-flexible coupling dynamics of blade. The study using the hypothetical modal method to describe the deformation of the blade and using the Lagrangian dynamics equation to establish the first-order approximation coupled dynamics equation of the flexible blade with three-dimensional large displacement motion. The simulation results show that the theoretical results of the first approximation coupling model are consistent with the actual results, but the zero-order approximation coupling model is flawed when the blade speed is high. Based on the first-order approximation coupling model, the vibration frequency, frequency-steering and mode-switching problems of the blade are analyzed, and the feasibility of the proposed method is verified.