考虑弯扭耦合运动的旋转带冠叶片非线性气动弹性分析

本文针对旋转叶片的气动弹性问题，将带叶冠的叶片简化为末端加质量块的均质悬臂梁。悬臂梁受到离心力和气动力作用，发生弯曲和扭转耦合振动变形。利用Hamilton原理建立了叶片的偏微分运动方程。对方程无量纲化，运用Galerkin方法对其离散，得到两自由度的非线性常微分方程。通过数值求解叶片颤振速度和极限环响应，并用谐波平衡法求解极限环响应与数值解进行对比。最后，讨论了结构参数对颤振速度和极限环响应幅值的影响。
Abstract：In order to deal with the aerodynamic elasticity of rotating blades,a shrouded blade was simplified as a homogeneous cantilever beam with end mass.The cantilever beam was subjected to centrifugal force and aerodynamic force,and coupled bending and torsion vibration occured.The partial differential motion equation of the blade was established by using the Hamiltonian principle.After making the equation dimensionless,nonlinear ordinary differential equations with two degrees of freedom were obtained by using the Galerkin method.The flutter velocity and limit cycle oscillation response of the blade were solved by numerical method.The harmonic balance method was utilized to analyze the limit cycle oscillation responses,and the results were compared with the numerical solutions.The influences of structural parameters on the flutter velocity and limit cycle oscillation amplitudes were discussed.