航空发动机压气机叶片的非线性振动问题

本文研究了航空发动机压气机叶片的非线性振动问题．将叶片简化为功能梯度材料的悬臂薄壁梁，因为是稳态气流，利用一阶活塞理论来计算气动力．考虑几何大变形的影响，利用Hamilton原理建立了叶片的非线性偏微分运动方程．运用Galerkin方法对方程进行一阶离散得到常微分控制方程．考虑1：1：1内共振情况，利用高阶多尺度法对控制方程进行摄动分析．基于平均方程，通过数值仿真模拟不同气流流速下旋转叶片的动态响应，得到相图、波形图和频谱图．结果表明：气流流速对系统动力学特性有重要影响，随着气流流速的增加，系统会呈现倍周期运动、周期运动、混沌运动等多种复杂动力学行为．

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.