柔性翼型的气动弹性建模与颤振特性分析

Aeroelastic modeling and flutter characteristics of flexible aerofoil

运用Hamilton原理推导了柔性翼型的沉浮-俯仰-弦向弯曲三自由度运动方程,给出了考虑弦向弯曲变形的平板薄翼作简谐运动时非定常气动力的解析表达式,建立了柔性翼型的气动弹性模型.在此基础上,研究了柔性平板薄翼的颤振特性.结果表明:对于平板薄翼而言,单一的弦向弯曲运动是不稳定的.对于给定的沉浮和俯仰振动频率,平板薄翼的颤振速度和其弦向弯曲振动频率有着很大关系.当弦向弯曲振动频率小于俯仰振动频率时,发生颤振的是弦向弯曲分支,颤振速度远小于沉浮-俯仰经典模型的预测值;当弦向弯曲振动频率为俯仰的2.5倍时,弦向弯曲和俯仰分支同时发生颤振;当弦向弯曲振动频率大于俯仰的2.5倍时,发生颤振的分支转为俯仰;当弦向弯曲振动频率大于俯仰的5倍时,沉浮-俯仰-弦向弯曲模型与传统二自由度模型的预测值几乎相等.

The governing differential equations of motion for flexible aerofoil, which is coupled with plunge, pitch, and camber bending motions, were derived by using the Hamilton＇ s principle. The nonlinear aerody- namic forces of oscillating thin aerofoil were given with consideration of camber bending. The two-dimensional aeroelastic model of flexible aerofoil was presented and the flutter characteristics of flexible thin aerofoil were investigated. Numerical results show that the single camber bending motion is instability. When the character- istic frequencies of pitch and plunge modes are given, the flutter velocity is powerfully affected by the charac- teristic frequency of camber bending mode. When the characteristic frequency of camber bending mode is less than one of pitch mode, the flutter is dominated by the camber bending mode and the flutter velocity is much lower than one given by the classical pitch-plunge coupled model. When the ratio of characteristic frequencies of camber bending and plunge modes is 2.5, the flutter is dominated by the camber bending and plunge modes. When the ratio is greater than 2.5, it is dominated by the plunge mode. When the ratio is greater than 6.0, the pitch-plunge-camber bending coupled aeroelastic model is agreed with the pitch-plunge model.