翼型气动弹性系统的三种状态方程的等价性  

Equivalence of three state space models for airfoil aeroelastic systems

作　　者：黄熙文 陈衍茂 李文龙 刘广 HUANG Xiwen;CHEN Yanmao;LI Wenlong;LIU Guang(School of Aeronautics and Astronautics,Sun Yat-sen University,Guangzhou 510006,China)

机构地区：[1]中山大学航空航天学院,广东广州510006

出　　处：《中山大学学报（自然科学版）（中英文）》2022年第3期171-180,共10页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金(11272361,11972380)。

摘　　要：作用于翼型气动弹性系统上的非定常Theodorsen空气动力中含有卷积积分,此积分算子的存在使得直接模拟气动弹性系统的响应是一项困难的工作。目前,已有三种不同的方式可以处理方程中的积分算子,使得化简后的方程仅含微分算子,但三种模型之间的等价关系仍然研究较少。文章将从数学上证明这三种化简后的模型是等价的,且分别采用龙格-库塔法和精细积分法对其进行验证。数值结果表明,三种模型无论是瞬态还是稳态响应,都是完全相同的。It is difficult to simulate the response of aeroelastic system directly because of the convolu‐tion integral in the unsteady Theodorsen aerodynamic force.To the best of our knowledge,there are three different ways to deal with the integral operator,so that the simplified equation only contains the differential operators.Despite huge applications of these models,the equivalence relationship among them is still less studied.In this paper,we will prove mathematically proved that the three simplified models are equivalent,and verify them by Runge-Kutta method and precise integration method,re‐spectively.Numerical results show that these models exhibit exactly the same solutions for both tran‐sient and steady responses.

关 键 词：翼型 气动弹性系统 状态空间模型 等效性 

分 类 号：V21[航空宇航科学与技术—航空宇航推进理论与工程]