Equivalence of three state space models for airfoil aeroelastic systems

HUANG Xiwen; CHEN Yanmao; LI Wenlong; LIU Guang

doi:10.13471/j.cnki.acta.snus.2020B155

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Equivalence of three state space models for airfoil aeroelastic systems

Research articles | 更新时间：2023-11-01

- Equivalence of three state space models for airfoil aeroelastic systems
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 61, Issue 3, Pages: 171-180(2022)
- 作者机构：
  
  中山大学航空航天学院，广东广州 510006
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2020B155
  CLC： V21
- Published：25 May 2022，
  
  Published Online：12 July 2021，
  
  Received：26 December 2020，
  
  Accepted：11 March 2020
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黄熙文,陈衍茂,李文龙等.翼型气动弹性系统的三种状态方程的等价性[J].中山大学学报(自然科学版),2022,61(03):171-180.

HUANG Xiwen,CHEN Yanmao,LI Wenlong,et al.Equivalence of three state space models for airfoil aeroelastic systems[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2022,61(03):171-180.
黄熙文,陈衍茂,李文龙等.翼型气动弹性系统的三种状态方程的等价性[J].中山大学学报(自然科学版),2022,61(03):171-180. DOI： 10.13471/j.cnki.acta.snus.2020B155.

HUANG Xiwen,CHEN Yanmao,LI Wenlong,et al.Equivalence of three state space models for airfoil aeroelastic systems[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2022,61(03):171-180. DOI： 10.13471/j.cnki.acta.snus.2020B155.

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。

Abstract

It is difficult to simulate the response of aeroelastic system directly because of the convolution 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， respectively. Numerical results show that these models exhibit exactly the same solutions for both transient and steady responses.

关键词

翼型气动弹性系统状态空间模型等效性

Keywords

airfoilaeroelastic systemstate space modelequivalence

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