Analysis on nonlinear dynamics of the aero-engine compressor blade

In this paper, the nonlinear dynamic behaviors of thin-walled beams made of functionally graded materials, which is used as rotating blades in turbomachinery under aerodynamic pressure loadings, are investigated. The quasi-steady aerodynamic pressure loadings are determined by using the first-order piston theory. The nonlinear factors are involved in displacement-strain relationships. The nonlinear governing partial differential equations of motion for the blade are established by using the Hamiltonian Principle. Using the Galerkin approach, the ordinary differential equation of motion is derived with three-degree-of-freedom. The method of multiple scales is used to obtain a six-dimensional nonlinear averaged equation. The case of 1:1:1 internal resonance is considered. The results of numerical simulation show that there exist the complicated nonlinear behaviors of the rotating blade with different air flow velocities, such as the periodic, period-n and chaotic motions.