非线性飞行稳定性研究的新综合方法

A NOVEL SYNTHETICAL METHOD FOR STUDYING NONLINEAR FLIGHT STABILITY

本文提出“分歧和突变理论-时间历程-龙格库塔灵敏度分析”的综合方法,用其研究作为非线性系统的飞机稳定性。该方法利用分歧理论来确定飞机的全局稳定性,并由平衡面找出应予检验的平衡点,对这些平衡点,计算状态参数的时间历程,由此确定飞机运动的性质。最后,利用龙格-库塔灵敏度分析方法来研究动稳定性随时间的变化,由此可以解析地求得任意瞬间影响飞行稳定性的空气动力项,结构项及组合项。 利用上述方法所得到的有关稳定性的信息是全面的,它对飞机的操稳设计有重要参考价值。

A novel synthetical method called BACTM-TH-RK ( Bifurcation Analysis and Catastrophe Theory Methodology-Time History-Runge Kutta Sensitivity Analysis) is introduced that results in generalized nonlinear stability criterion. The basic concept of the present methodology is by use of the BACTM to dertermine the global stability and choose the points to be checked from the equilibrium surface, to calculate the time history of the state parameters to know the aircraft motion, and to use the Runge-Kutta Sensitivity Analysis to study the dynamic stability which varies with time.Two examples for two typical aeroplanes are given from which we can see the whole process of solving the problem and the complete information on flight stability obtained from the present method. The information includes the equilibrium surface of the state vectors, the time histories of the state parameters, the time variation of the dynamic stability, the sensitivity of the nonlinear system stability to aerodynamic, structural and combination parameters, and the linear and nonlinear analytical terms which have strong effects on the stability. The information has proved to be useful for aeroplane design.