带集中非线性的机翼气动弹性问题研究进展

doi:10.7527/S1000-6893.2016.0140

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带集中非线性的机翼气动弹性问题研究进展

杨智春, 田玮, 谷迎松, 贺顺

西北工业大学航空学院, 西安 710072

收稿日期:2015-12-18 修回日期:2016-04-02 出版日期:2016-07-15 发布日期:2016-05-09
通讯作者: 杨智春男,博士,教授,博士生导师。主要研究方向:气动弹性力学、结构动力学与控制和结构健康监测。Tel:029-88460461,E-mail:yangzc@nwpu.edu.cn E-mail:yangzc@nwpu.edu.cn
作者简介:田玮男,博士研究生。主要研究方向:非线性气动弹性力学,E-mail:twtp100@163.com;谷迎松男,博士,副教授,硕士生导师。主要研究方向:非线性气动弹性力学和气动伺服弹性力学,E-mail:guyingsong@nwpu.edu.cn;贺顺男,博士研究生。主要研究方向:跨声速非线性气动弹性力学,E-mail:nwpuheshun@gmail.com
基金资助:
国家自然科学基金（11072198)；高等学校学科创新引智计划（B07050)

Advance in the study on wing aeroelasticity with concentrated nonlinearity

YANG Zhichun, TIAN Wei, GU Yingsong, HE Shun

School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China

Received:2015-12-18 Revised:2016-04-02 Online:2016-07-15 Published:2016-05-09
Supported by:
National Natural Science Foundation of China (11072198); the "111" Project of China (B07050)

摘要/Abstract

摘要：

带集中非线性环节的机翼非线性气动弹性问题是飞行器气动弹性研究领域的热点和难点。经过近几十年来的不断发展，这类机翼非线性气动弹性问题的研究已经取得了长足的进步，同时也面临着新的挑战。鉴于此，综述了近年来带集中非线性环节的机翼非线性气动弹性问题的研究进展，阐述了带集中非线性的机翼气动弹性分析的建模方法、分析方法及非线性气动弹性稳定性和响应行为的规律，并讨论和总结了相关的研究成果，对今后机翼非线性气动弹性问题的分析方法和研究内容提出了展望。

关键词: 非线性气动弹性, 非线性颤振, 集中非线性, 极限环振荡, 混沌, 主动控制

Abstract:

The nonlinear aeroelastic problem of wing with concentrated structural nonlinearity has become one of the hottest and also most challenging topics in the field of aircraft aeroelasticity. In recent decades, great progress has been made for wing nonlinear aeroelasticity, meanwhile new challenges have also emerged. In this paper, researches activities on wing nonlinear aeroelastic characteristics are reviewed. The key problems of the concentrated nonlinear aeroelasticity of wing are described, including the modeling for wing aeroelastic system with concentrated nonlinearity, analysis approaches and nonlinear aeroelastic behaviors. Moreover, the existing achievements of wing nonlinear aeroelasticity studies are summarized and discussed, the prospects of research topics and approaches of wing nonlinear aeroelasticity are proposed.

Key words: nonlinear aeroelasticity, nonlinear flutter, concentrated nonlinearity, limit cycle oscillation, chaos, active control

中图分类号:

V215.3

杨智春, 田玮, 谷迎松, 贺顺. 带集中非线性的机翼气动弹性问题研究进展[J]. 航空学报, 2016, 37(7): 2013-2044.

YANG Zhichun, TIAN Wei, GU Yingsong, HE Shun. Advance in the study on wing aeroelasticity with concentrated nonlinearity[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016, 37(7): 2013-2044.

参考文献

[1] 杨智春, 赵令诚. 飞行器气动弹性力学[M]. 西安:西北工业大学, 2009:1-3. YANG Z C, ZHAO L C. Flight vehicle aeroelasticity[M]. Xi'an:Northwestern Polytechnical University, 2009:1-3(in Chinese).
[2] DOWELL E H. A modern course in aeroelasticity[M]. 4th Revised and Enlarged Edition. New York:Kluwer Academic Publishers, 2004:1-3.
[3] 赵永辉. 气动弹性力学与控制[M]. 北京:科学出版社, 2007:7-10. ZHAO Y H. Aeroelasticity and control[M]. Beijing:Science Press, 2007:7-10(in Chinese).
[4] LEE B H K, PRICE S J, WONG Y S. Nonlinear aeroelastic analysis of airfoils:Bifurcation and chaos[J]. Progress in Aerospace Sciences, 1999, 35(3):205-334.
[5] DOWELL E H, TANG D. Nonlinear aeroelasticity and unsteady aerodynamics[J]. AIAA Journal, 2002, 40(9):l697-1707.
[6] 安效民, 徐敏, 陈士橹. 多场耦合求解非线性气动弹性的研究综述[J]. 力学进展, 2009, 39(3):284-298. AN X M, XU M, CHEN S L. An overview of CFD/CSD coupled solution for nonlinear aeroelasticity[J]. Advances in Mechanics, 2009, 39(3):284-298(in Chinese).
[7] DOWELL E H. Some recent advances in nonlinear aeroelasticity:Fluid-structure interaction in the 21st century[C]//Proceedings of 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference.[S.l.]:Springer International Publishing, 2010:1-23.
[8] 陈衍茂, 刘济科, 孟光. 二元机翼非线性颤振系统的若干分析方法[J]. 振动与冲击, 2011, 30(3):129-134. CHEN Y M, LIU J K, MENG G. Analysis methods for nonlinear flutter of a two-dimensional airfoil:A review[J]. Journal of Vibration and Shock, 2011, 30(3):129-134(in Chinese).
[9] XIANG J, YAN Y, LI D. Recent advance in nonlinear aeroelastic analysis and control of the aircraft[J]. Chinese Journal of Aeronautics, 2014, 27(1):12-22.
[10] TANG D, DOWELL E H, VIRGIN L N. Limit cycle behavior of an airfoil with a control surface[J]. Journal of Fluids and Structures, 1998, 12:839-858.
[11] TANG D, DOWELL E H. Aeroelastic airfoil with free play at angle of attack with gust excitation[J]. AIAA Journal, 2010, 48(2):427-442.
[12] LEE D, CHEN P, TANG D, et al. Nonlinear gust response of a control surface with free-play[C]//Proceedings of 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference.[S.l.]:Springer International Publishing, 2010:12-15.
[13] SCHLOMACH C, MARTIN L. All-movable control surface freeplay[C]//Presentation to the Aerospace Flutter and Dynamics Council. Hampton:NASA Langley Research Center, 2009:1-3.
[14] BEHAL A, RAO V M, MARZOCA P, et al. Adaptive control for a nonlinear wing section with multiple flaps[J]. Journal of Guidance, Control, and Dynamics, 2006, 29(3):744-749.
[15] BANSAL P, PITT D M. Uncertainties in control surface free-play and structural properties and their effect on flutter and LCO[C]//Proceedings of 55th AIAA/ASM/ASCE/AHS/SC Structures, Structural Dynamics, and Materials Conference.[S.l.]:Springer International Publishing, 2014:1-15.
[16] LEE I, KIM S H. Aeroelastic analysis of a flexible control surface with structural nonlinearity[J]. Journal of Aircraft, 1995, 32(4):868-874.
[17] LEE D H, CHEN P C. Nonlinear aeroelastic studies on a folding wing configuration with free-play hinge nonlinearity[C]//Proceedings of 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference.[S.l.]:Springer International Publishing, 2006:1-22.
[18] FIROUZ-ABADI R D, ALAVI S M, SALARIEH H. Analysis of non-linear aeroelastic response of a supersonic thick fin with plunging, pinching and flapping free-plays[J]. Journal of Fluids and Structures, 2013, 40:163-184.
[19] 杨翊仁, 赵令诚. 带外挂三角机翼极限环颤振的实验研究[J]. 应用力学学报, 1991, 8(3):38-43. YANG Y R, ZHAO L C. Experimental study of limit cycle flutter of a delta wing model with external store[J]. Chinese Journal of Applied Mechanics, 1991, 8(3):38-43(in Chinese).
[20] TANG D, DOWELL E H. Flutter and limit-cycle oscillations for a wing-store model with freeplay[J]. Journal of Aircraft, 2006, 43(2):487-503.
[21] FICHERA S, QUARANTE G, RICCI S. Experimental and numerical investigation of the behaviour of a T-tail with control surface freeplay[C]//Proceedings of 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference.[S.l.]:Springer International Publishing, 2012:1-14.
[22] FICHERA S, QUARANTA G, RICCI S. Behaviour of an aeroelastic T-tail model with rudders freeplay experimental and numerical investigation[J]. The Journal of Aerospace Science, Technology and Systems, 2012, 91(3):86-97.
[23] NI K, HU P, ZHAO H W. Flutter and LCO of an all-movable horizontal tail with freeplay[C]//Proceedings of 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference.[S.l.]:Springer International Publishing, 2012:1-9.
[24] HU P, ZHAO H W, XUE L P, et al. High-fidelity modeling and simulation of flutter/LCO for all-movable horizontal tail with freeplay[C]//Proceedings of AIAA Atmospheric Flight Mechanics Conference. Reston:AIAA, 2011:1-13.
[25] TANG D, DOWELL E H. Computational/experimental aeroelastic study for a horizontal-tail model with free play[J]. AIAA Journal, 2012, 51(2):341-352.
[26] SEO Y J, LEE S J, BAE J S, et al. Effects of multiple structural nonlinearities on limit cycle oscillation of missile control fin[J]. Journal of Fluids and Structures, 2011, 27(4):623-635.
[27] BAE J S, LEE I. Limit cycle oscillation of missile control fin with structural non-linearity[J]. Journal of Sound and Vibration, 2004, 269(3):669-687.
[28] THEODORSEN T. General theory of aerodynamic instability and the mechanism of flutter:REPORT NO. 496[R]. US Government Printing Office, Washington, D.C.:Report National Advisory Committee for Aerodynamics, 1949:413-433.
[29] LEE B H K, GONG L, WONG Y S. Analysis and computation of nonlinear dynamic response of a two-degree-of-freedom system and its application in aeroelasticity[J]. Journal of Fluids and Structures, 1997, 11(3):225-246.
[30] PETERS D A, JOHNSON M J. Finite-state airloads for deformable airfoils on fixed and rotating wings[C]//Symposium on Aeroelasticity and Fluid/Structure Interaction, ASME Winter Annual Meeting. New York:American Society of Mechanical Engineers, 1994:6-11.
[31] ALIGHANBARI H, PRICE S J. The post-Hopf-bifurcation response of an airfoil in incompressible two-dimensional flow[J]. Nonlinear Dynamics, 1996, 10(4):381-400.
[32] 谷迎松, 杨智春. 带迟滞非线性环节二元机翼的气动弹性响应分析[J]. 机械科学与技术, 2006, 25(8):900-904. GU Y S, YANG Z C. Aeroelastic response analysis of an airfoil with hysteresis nonlinearity[J]. Mechanical Science and Technology, 2006, 25(8):900-904(in Chinese).
[33] KHOLODAR D B, DOWELL E H. Behavior of airfoil with control surface freeplay for nonzero angles of attack[J]. AIAA Journal, 1999, 37(5):651-653.
[34] GORDON J T, MEYER E E, MINOGUE R L. Nonlinear stability analysis of control surface flutter with freeplay effects[J]. Journal of Aircraft, 2008, 45(6):1906-1916.
[35] 李道春, 向锦武. 控制面间隙对非线性二元机翼气动弹性响应的影响[J]. 航空学报, 2009, 30(8):1385-1391. LI D C, XIANG J W. Effect of control surface freeplay on nonlinear aeroelastic responses of an airfoil[J]. Acta Aeronautica et Astronautica Sinica, 2009, 30(8):1385-1391(in Chinese).
[36] LIU L, WONG Y S. Non-linear aeroelastic analysis using the point transformation method, Part 2:Hystersis model[J]. Journal of Sound and Vibration, 2002, 253(2):471-483
[37] LI D C, GUO S J, XIANG J W. Modeling and nonlinear aeroelastic analysis of a wing with morphing trailing[J]. Aerospace Engineering, 2012, 227(4):619-631.
[38] FICHERA S, RICCI S. High order harmonic balance applied to an aeroelastic T-tail model with a control surface freeplay[C]//Proceedings of 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference.[S.l.]:Springer International Publishing, 2013:1-11.
[39] KHOLODAR D B. Nature of freeplay-induced aeroelastic oscillations[J]. Journal of Aircraft, 2014, 51(2):1-13.
[40] HALL K C. Eigen analysis of unsteady flows about airfoils, cascades, and wings[J]. AIAA Journal, 1994, 32(12):2426-2432.
[41] TANG D, KHOLODAR D, DOWELL E H. Nonlinear response of airfoil section with control surface freeplay to gust loads[J]. AIAA Journal, 2000, 38(9):1543-1557.
[42] TANG D, KHOLODAR D, DOWELL E H. Nonlinear aeroelastic response of a typical airfoil section with control surface freeplay[C]//Proceedings of 41th AIAA/ASME/ASCE/AHS/ASC, Structures, Structural Dynamics, and Materials Conference.[S.l.]:Springer International Publishing, 2000:1-10.
[43] 郑国勇, 杨翊仁. 超音速流中结构非线性二元机翼的复杂响应研究[J]. 振动与冲击, 2007, 26(12):96-100. ZHENG G Y, YANG Y R. Complicated response of a 2-D wing structural nonlinearity in supersonic flow[J]. Journal of Vibration and Shock, 2007, 26(12):96-100(in Chinese).
[44] 郭虎伦, 陈予恕. 超声速流中含间隙和立方非线性二元机翼的动力学分析[J]. 应用数学和力学, 2012, 33(1):1-13. GUO H L, CHEN Y S. Dynamic analysis of a two-degree-of-freedom airfoil with freeplay and cubic nonlinearities in supersonic flow[J]. Applied Mathematics and Mechanics, 2012, 33(1):1-13(in Chinese).
[45] 陈香, 杨志军, 范志强, 等. 超音速二元翼极限环颤振的高次线化分析[J]. 科学技术与工程, 2009, 9(1):175-179. CHEN X, YANG Z J, FAN Z Q, et al. High order linearization analyze of limit cycle flutter of a supersonic dualistic airfoil[J]. Science Technology and Engineering, 2009, 9(1):175-179(in Chinese).
[46] ABBAS L K, CHEN Q, DOWELL K, et al. Numerical studies of a non-linear aeroelastic system with plunging and pitching freeplays in supersonic/hypersonic regimes[J]. Aerospace Science and Technology, 2007, 11(5):405-418.
[47] ZHAO H, CAO D, ZHU X. Aerodynamic flutter and limit cycle analysis for a 2-D wing with pitching freeplay in the supersonic flow[C]//Systems and Control in Aeronautics and Astronautics (ISSCAA), 20103rd International Symposium on. Piscataway, N J:IEEE, 2010:1105-1109.
[48] ABBAS L K, CHEN Q. Bifurcations and chaotic behavior of hypersonic lifting surfaces with freeplay including the stiffness and damping nonlinearities[C]//Proceedings of 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference.[S.l.]:Springer International Publishing, 2007:1-24.
[49] PARK Y K, YOO J H, LEE I. Effects of angle-of-attack on the aeroelastic characteristics of a wing with freeplay[J]. Journal of Spacecraft and Rockets, 2006, 43(6):1419-1422.
[50] DOWELL E H, UEDA T. Flutter analysis using nonlinear aerodynamic forces[J]. Journal of Aircraft, 1984, 21(2):101-109
[51] BADCOCK K J, WOODGATE M A, RICHARDS B E. Hopf bifurcation calculations for a symmetric airfoil in transonic flow[J]. AIAA Journal, 2004, 42(5):883-892.
[52] KIM D H, LEE I. Transonic and low-supersonic aeroelastic analysis of a two-degree-of-freedom airfoil with a freeplay non-linearity[J]. Journal of Sound and Vibration, 2000, 234(5):859-880.
[53] VASCONCALLOS R, ABDELKEFI A, MARQUES F D, et al. Control surface freeplay nonlinearity modeling and experimental validation[C]//Proceedings of 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference.[S.l.]:Springer International Publishing, 2012:1-12.
[54] 胡巍, 杨智春, 谷迎松. 带操纵面机翼气动弹性地面试验仿真系统中的气动力降阶方法[J]. 西北工业大学学报, 2013, 31(5):810-815. HU W, YANG Z C, GU Y S. A new and effective method for reducing order of aerodynamics of a wing with control surface for ground flutter test[J]. Journal of Northwestern Polytechnical University, 2013, 31(5):810-815(in Chinese).
[55] ABBAS L K, QIAN C, MARZOCCA P, et al. Active aerothermoelastic control of hypersonic double-wedge lifting surface[J]. Chinese Journal of Aeronautics, 2008, 21(1):8-18.
[56] DAI H, YUE X, XIE D, et al. Chaos and chaotic transients in an aeroelastic system[J]. Journal of Sound and Vibration, 2014, 333(26):7267-7285.
[57] ZHAO D M, ZHANG Q C. Bifurcation and chaos analysis for aeroelastic airfoil with freeplay structural nonlinearity in pitch[J]. Chinese Physical Society and IOP Publishing Ltd., 2010, 19(3):030518-1-10.
[58] CHEN F X, LIU J K, CHEN Y M. Flutter analysis of an airfoil with nonlinear damping using equivalent linearization[J]. Chinese Journal of Aeronautics, 2014, 27(1):59-64.
[59] 陈科文, 赵海, 周立杰, 等. 超声速流中二元机翼的颤振与极限环[J]. 动力学与控制学报, 2012, 10(1):62-66. CHEN K W, ZHAO H, ZHOU L J, et al. Aerodynamic flutter and limited cycle of a 2-D wing in the hypersonic flow field[J]. Journal of Dynamic and Control, 2012, 10(1):62-66(in Chinese).
[60] DING Q, WANG D L. Flutter control of a two-dimensional airfoil using wash-out filter technique[J]. Chinese Journal of Aeronautics, 2005, 8(2):131-137
[61] 刘延柱, 陈立群. 非线性振动[M]. 北京:高等教育出版社, 2001:250-320. LIU Y Z, CHEN L Q. Nonlinear vibration[M]. Beijing:Higher Education, 2001:250-320(in Chinese).
[62] CASTRAVETE S C, IBRAHIM R A. Effect of stiffness uncertainties on the flutter of a cantilever wing[J]. AIAA Journal, 2008, 46(4):925-935.
[63] LI Y, YANG Z C. Probabilistic flutter analysis and risk assessment of an airfoil[C]//27th Congress of International Congress of Aeronautical Sciences. Nice, France:[s.n.], 2010:1-6.
[64] LI Y, YANG Z C. Uncertainty quantification in flutter analysis for an airfoil with preloaded freeplay[J]. Journal of Aircraft, 2010, 47(4):1454-1457.
[65] MUKHOPADHYAY V. Historical perspective on analysis and control of aeroelastic responses[J]. Journal of Guidance, Control, and Dynamics, 2003, 26(5):673-684.
[66] 刘菲, 杨翊仁. 不可压缩流中二元翼运动的分支问题[J]. 西南交通大学学报, 2002, 37(B11):95-97. LIU F, YANG Y R. Bifurcation of motions of an airfoil in in incompressible flow[J]. Journal of Southwest Jiaotong University, 2002, 37(B11):95-97(in Chinese).
[67] 刘菲, 杨翊仁. 不可压缩流中二元翼运动的余维二分叉[J]. 振动与冲击, 2006, 24(4):18-19. LIU F, YANG Y R. Codimension-two bifurcation of motions of an airfoil in incompressible flow[J]. Journal of Vibration and Shock, 2006, 24(4):18-19(in Chinese).
[68] 郑国勇, 杨翊仁. 不可压缩流中机翼外挂系统的分叉分析[J]. 科学技术与工程, 2006, 6(8):1018-1021. ZHENG G Y, YANG Y R. Analysis of bifurcation of an airfoil with an external store in incompressible flow[J]. Science Technology and Engineering, 2006, 6(8):1018-1021(in Chinese).
[69] LIU L, WONG Y S, LEE B H K. Application of the center manifold theory in nonlinear aeroelasticity[J]. Journal of Sound and Vibration, 2000, 234(4):641-659.
[70] SHAHRZAD P, MAHZOON M. Limit cycle flutter of airfoils in steady and unsteady flows[J]. Journal of Sound and Vibration, 2002, 256(2):213-225.
[71] DING Q, WANG D L. The flutter of an airfoil with cubic structural and aerodynamic nonlinearities[J]. Aerospace Science and Technology, 2006, 10(5):427-434.
[72] 吴志强. 多自由度非线性系统的非线性模态及Normal Form直接方法[D]. 天津:天津大学, 1996. WU Z Q. Nonlinear normal modes and Normal Form direct method for multi-degrees of freedom of nonlinear systems[D]. Tianjin:Tianjin University, 1996(in Chinese).
[73] LIU J K, ZHAO L C, FANG T. Bifurcation point analysis of airfoil flutter with structural nonlinearity:Chapter 3, advances in nonlinear dynamics in China-theory and practice. Lisse[M].The Netherland:Swets & Zeitlinger Publishers, 2002:1-6.
[74] SADAGHAT A, COPPER J E. Limit cycle oscillation prediction for aeroelastic systems with continuous nonlinearities:AIAA-2000-1397[R]. Reston:AIAA, 2000.
[75] 张琪昌, 刘海英, 任爱娣. 具有立方非线性机翼颤振的局部分岔[J]. 天津大学学报, 2004, 37(11):970-974. ZHANG Q C, LIU H Y, REN A D. Local bifurcation for airfoil with cubic nonlinearities[J]. Journal of Tianjin University, 2004, 37(11):970-974(in Chinese).
[76] 陈衍茂, 刘济科. 非线性颤振极限环稳定性判别的复数正规形法[J]. 航空动力学报, 2007, 22(4):614-618. CHEN Y M, LIU J K. Application of complex normal form method for stability judgement of limit cycle of nonlinear flutter[J]. Journal of Aerospace Power,, 2007, 22(4):614-618(in Chinese).
[77] CHEN Y M, LIU J K. Supercritical as well as subcritical Hopf bifurcation in nonlinear flutter systems[J]. Applied Mathematics and Mechanics, 2008, 29(2):199-206.
[78] LIU J K, ZHAO L C. Bifurcation analysis of airfoils in incompressible flow[J]. Journal of Sound and Vibration, 1992,154(1):117-124.
[79] 刘菲, 杨翊仁. 立方非线性机翼的二重半稳定极限环分叉[J]. 西南交通大学学报, 2004, 39(5):638-640. LIU F, YANG Y R. Bifurcation s of 2-multiple semistable limit cycles of airfoils with cubic nonlinearity[J]. Journal of Southwest Jiaotong University, 2004, 39(5):638-640(in Chinese).
[80] GUO H L, CHEN Y S. Dynamic analysis of two-degree-of-freedom airfoil with freeplay and cubic nonlinearities in supersonic flow[J]. Applied Mathematics and Mechanics, 2012, 33(1):1-14.
[81] LIM C W, WU B S. A new analytical approach to the duffing-harmonic oscillator[J]. Physics Letters A, 2003, 311(4-5), 365-373.
[82] CHEN Y M, LIU J K. On the limit cycles of aeroelastic systems with quadratic nonlinearities[J]. Structural Engineering and Mechanics, 2008, 30(1):67-76.
[83] CHEN Y M, LIU J K. Elliptic harmonic balance method for two degree-of-freedom self-excited oscillators[J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(3):916-922.
[84] YANG Y R. KBM method of analyzing limit cycle flutter of a wing with an external store and comparison with a wind-tunnel test[J]. Journal of Sound and Vibration, 1995, 187(2):271-280.
[85] LEE C L. An iterative procedure for nonlinear flutter analysis[J]. AIAA Journal, 1986, 24(5):833-840.
[86] 李道春, 向锦武. 非线性二元机翼气动弹性近似解析研究[J]. 航空学报, 2007, 28(5):1080-1084. LI D C, XIANG J W. Nonlinear aeroelastic analysis of airfoil using quasi-analytical approach[J]. Acta Aeronautica et Astronautica Sinica, 2007, 28(5):1080-1084(in Chinese).
[87] LEE B H K, LIU L, CHUNG K W. Airfoil motion in subsonic flow with strong cubic nonlinear restoring forces[J]. Journal of Sound and Vibration, 2005, 281(3):699-717.
[88] GHADIRI B, RAZI M. Limit cycle oscillations of rectangular cantilever wings containing cubic nonlinearity in an incompressible flow[J]. Journal of Fluids and Structures, 2007, 23(4):665-680
[89] LIU L P, DOWELL E H. The secondary bifurcation of an aeroelastic airfoil motion effect of high harmonics[J]. Nonlinear Dynamics, 2004, 37(1):31-49.
[90] LIU L, DOWELL E H. Higher order harmonic balance analysis of an airfoil with a freeplay control surface[J]. AIAA Journal,2005, 43(4):802-815.
[91] AMUYEDO N, COOPER J E. A higher order harmonic balance approach for an aeroelastic airfoil with a freeplay control Surface[C]//ISMA 2006 Conference Proceedings.[S.l.]:ISMA, 2006:1-5.
[92] AMUYEDO N, COOPER J E. Higher order harmonic balance analysis of an airfoil with a hysteretic non-linearity[C]//48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference.[S.l.]:Springer International Publishing, 2007:23-26.
[93] HALL K C, THOMAS J P, CLARK W S. Computation of unsteady nonlinear flows in cascades using a harmonic balance technique[J]. AIAA Journal, 2002, 40(5):879-886.
[94] LIU L, DOWELL E H, THOMAS J. Higher order harmonic balance analysis for limit cycle oscillations in an airfoil with cubic restoring forces[C]//Proceedings of the 46th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics & materials conference.[S.l.]:Springer International Publishing, 2005:1-10.
[95] LIU L, THOMAS J P, DOWELL E H, et al. A comparison of classical and high dimensional harmonic balance approaches for a Duffing oscillator[J]. Journal of Computational Physics, 2006, 215(1):298-320.
[96] LIU L, DOWELL E H, THOMAS J P. A high dimensional harmonic balance approach for an aeroelastic airfoil with cubic restoring forces[J]. Journal of Fluids and Structures, 2007, 23(3):351-363.
[97] DAI H, YUE X, YUAN J, et al. A time domain collocation method for studying the aeroelasticity of a two dimensional airfoil with a structural nonlinearity[J]. Journal of Computational Physics, 2014, 270(1):214-237.
[98] RAGHOTHAMA A, NARAYANAN S. Non-linear dynamics of a two-dimensional airfoil by incremental harmonic balance method[J]. Journal of Sound and Vibration, 1999, 226(3):493-517.
[99] 蔡铭, 刘济科, 杨怡. 强非线性颤振分析的增量谐波平衡法[J]. 机械科学与技术, 2004, 23(6):742-744. CAI M, LIU J K, YANG Y. Incremental harmonic balance method for strongly nonlinear flutter of airfoils[J]. Mechanical Science and Technology, 2004, 23(6):742-744(in Chinese).
[100] 蔡铭, 刘济科, 李军. 多自由度强非线性颤振分析的增量谐波平衡法[J]. 应用数学和力学, 2006, 27(7):833-838. CAI M, LIU J K, LI J. Incremental harmonic balance method for airfoil flutter with multiple strong nonlinearities[J]. Applied Mathematics and Mechanics, 2006, 27(7):833-838(in Chinese).
[101] CAI M, LIU J, LI J. Incremental harmonic balance method for airfoil flutter with multiple strong nonlinearities[J]. Applied Mathematics and Mechanics, 2006, 27(7):953-958.
[102] LIU J K, CHEN F X, CHEN Y M. Bifurcation analysis of aeroelastic systems with hysteresis by incremental harmonic balance method[J]. Applied Mathematics and Computation, 2012, 219(5):2398-2411.
[103] CHEN Y M, LIU J K, MENG G. Incremental harmonic balance method for nonlinear flutter of an airfoil with uncertain-but-bounded parameters[J]. Applied Mathematical Modeling, 2012, 36(2):657-667.
[104] CHAN H S Y, CHUNG K W, XU Z. A perturbation-incremental method for strongly non-linear oscillators[J]. International Journal of Non-Linear Mechanics, 1996, 31(1):59-72.
[105] CHUNG K W, CHAN C L, LEE B H K. Bifurcation analysis of a two-degree-of-freedom aeroelastic system with freeplay structural nonlinearity by a perturbation-incremental method[J]. Journal of Sound and Vibration, 2007, 299(3):520-539.
[106] CHUNG K W, HE Y B, LEE B H K. Bifurcation analysis of a two-degree-of-freedom aeroelastic system with hysteresis structural nonlinearity by a perturbation-incremental method[J]. Journal of Sound and Vibration, 2009, 320(1):163-183.

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

带集中非线性的机翼气动弹性问题研究进展

Advance in the study on wing aeroelasticity with concentrated nonlinearity

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