用中心流形与形式级数法研究超音速流中带外挂二元翼的稳定性

基于超音速气动力活塞理论，采用第二类拉格朗日方程建立了带外挂二元翼系统在超音速和超高音速气流作用下的动力学方程。针对外挂上带有立方非线性刚度的系统，研究了刚心位置和等效线性刚度对颤振边界的影响。采用中心流形和形式级数方法研究了颤振系统平衡点的稳定性，并采用四阶龙格-库塔方法计算了非线性气动弹性系统的响应，验证了理论分析结果的正确性。

Stability Study of Two-dimension Airfoil with Store in the Supersonic Airflow Applying Central Manifold and Final Series Method

Based on the piston theory of supersonic flow, the second lagrange equation is used to set up the dynamic equations of an airfoil with store in the supersonic or hypersonic flow. In view of the airfoil-store system with cubic non-linearity, the effects of the location of elastic axis from the mid-chord point and the equivalent linearization stiffness on the flutter boundary are studied. The stabilities of flutter system are discussed by the central manifold and formal series. Finally, the 4th order Runge-Kutta method is used to calculate the responses of the nonlinear aero-elasticity system, which confirm the analytical results.