大展弦比机翼气动颤振的有限元分析

Flutter analysis for a high-aspect ratio wing with finite element method

在Theodorsen二元气动力的基础上,建立非定常气动力时域内积分形式的表达式或者等价的频域表达式,利用粘弹性结构振动分析中对积分方程的等价变换将其写成与结构动力学方程一致的二阶常微分方程,将气动力的影响作为对结构有限元模型质量阵、刚度阵和阻尼阵的补充,保留了结构原有的所有动力学特性,并且能够直接用计算结构动力学的通用有限元软件进行空气-结构耦合的整体动力学分析,适合应用于具有复杂结构的气弹问题。气动力模型的建立可以利用各种试验及数值方法得到的气动力数据,适用性强。算例给出了大展弦比机翼的颤振边界计算结果。

Expressions for unsteady aerodynamics in time domain or frequency domain were established based on Theodorsen theory.The expressions with integration were converted into second order ordinary differential equations.The effects of unsteady aerodynamic force on a structure were regarded as comlements of mass matrix,stiffness one and damping one of finite element model of a structure.The whole dynamic characteristics were retained.General finite element software could be used to calculate the flutter boundary of an air-structure coupled model.The method was suitable for solving aeroelastic problems of complex structures.The unsteady aerodynamic data obtained with any numerical method or test could be used to establish an unsteady aerodynamic model.The proposed method was applicable to different cases.The flutter boundary of a high-aspect ratio wing was calculated.