可折叠机翼气动弹性研究
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摘要
可折叠机翼作为未来飞行器智能变形的重要设计方案,其气动弹性问题正在得到学者们的极大关注。本文以可折叠机翼为研究对象,在深入分析其结构动力学特性基础上,对折叠翼的气动弹性稳定性问题进行了较为深入的研究,同时还开展了折叠过程动力学的仿真研究。
首先通过有限元分析技术,建立可折叠机翼各个翼段的子结构模型。通过分析和定义铰链约束的类型,模拟真实铰链连接,按照模态综合理论建立了可折叠机翼的有限元模型。
引入机翼折叠角和铰链刚度作为研究参数,通过研究可折叠机翼的不同折叠工况和铰链特性,分析了可折叠机翼结构与传统固定翼相比不同的动力学特性,尤其是折叠过程中结构刚度和质量重新分配所引起的新的结构特性变化。
利用偶极格子网法计算空气动力影响系数矩阵,采用子空间法将空气动力影响系数矩阵拟合成时域有理函数形式,建立了可折叠机翼的状态空间颤振方程,并进行数值计算获得其线性颤振特性。
可折叠机翼包含有两个铰链,采用分段线化的方法,研究了间隙引起的双铰链非线性可折叠机翼的气动弹性响应问题。分析了其气动弹性响应和发生极限环振荡的条件。
在ADAMS平台上,应用虚拟样机技术,对可折叠机翼的折叠过程进行了气动弹性动力学仿真研究。其中重点研究了非定常气动力的实时计算和耦合问题。通过一典型算例,初步探讨了结构响应以及作动器施加在铰链上的力矩变化规律。
The aeroelastic problems of folding wing, which is an important design configuration for future intelligent morphing aircraft, have gained significant attention in the aeroelastic community. In this thesis, the folding wing is taken as the research object. Based on the thorough analysis of its structural dynamic properties, a profound study of the aeroelastic stability problems of folding wing is performed and the simulation of the folding process dynamics is also investigated.
The sub-structure models of each wing section of the folding wing are constructed by finite element analysis technique. In order to simulate the connection of the actual hinges, the types of the hinge constraints are analyzed and defined and the finite element model of the folding wing is constructed according to modal synthesis theory.
The folding angle and hinge stiffness are considered as the research parameters. By studying the different folding sub-cases and hinge properties of the folding wing, the different dynamic characteristics between traditional wing and the folding wing are investigated and particularly, the variations of structure properties which are caused by re-distribution of the structure stiffness and mass in the folding process are highly concerned.
The aerodynamic influencing coefficients matrices which are obtained by doublet lattice method are approximated as rational functions via subspace method, and then the state-space equations of the folding wing are formulated. The numerical simulations are performed and the linear aeroelastic characteristics are obtained.
Folding wing includes two hinge free-plays, which is a double hinge nonlinear problem. The aeroelastic response problems of the folding wing with double hinges nonlinearity caused by freeplay are investigated by piecewise linearization method. The aeroelastic response and the excitation conditions of limit oscillation cycle are also analyzed.
Based on ADAMS platform, the folding processes of the folding wing are simulated and the aeroelastic problems of in the folding process are investigated. Particularly, the real time computation of the unsteady aerodynamics and interaction problems are emphatically studied. By a typical study case, the structural responses and the varying rule of hinge moment imposed by actuators are discussed preliminarily.
首先通过有限元分析技术,建立可折叠机翼各个翼段的子结构模型。通过分析和定义铰链约束的类型,模拟真实铰链连接,按照模态综合理论建立了可折叠机翼的有限元模型。
引入机翼折叠角和铰链刚度作为研究参数,通过研究可折叠机翼的不同折叠工况和铰链特性,分析了可折叠机翼结构与传统固定翼相比不同的动力学特性,尤其是折叠过程中结构刚度和质量重新分配所引起的新的结构特性变化。
利用偶极格子网法计算空气动力影响系数矩阵,采用子空间法将空气动力影响系数矩阵拟合成时域有理函数形式,建立了可折叠机翼的状态空间颤振方程,并进行数值计算获得其线性颤振特性。
可折叠机翼包含有两个铰链,采用分段线化的方法,研究了间隙引起的双铰链非线性可折叠机翼的气动弹性响应问题。分析了其气动弹性响应和发生极限环振荡的条件。
在ADAMS平台上,应用虚拟样机技术,对可折叠机翼的折叠过程进行了气动弹性动力学仿真研究。其中重点研究了非定常气动力的实时计算和耦合问题。通过一典型算例,初步探讨了结构响应以及作动器施加在铰链上的力矩变化规律。
The aeroelastic problems of folding wing, which is an important design configuration for future intelligent morphing aircraft, have gained significant attention in the aeroelastic community. In this thesis, the folding wing is taken as the research object. Based on the thorough analysis of its structural dynamic properties, a profound study of the aeroelastic stability problems of folding wing is performed and the simulation of the folding process dynamics is also investigated.
The sub-structure models of each wing section of the folding wing are constructed by finite element analysis technique. In order to simulate the connection of the actual hinges, the types of the hinge constraints are analyzed and defined and the finite element model of the folding wing is constructed according to modal synthesis theory.
The folding angle and hinge stiffness are considered as the research parameters. By studying the different folding sub-cases and hinge properties of the folding wing, the different dynamic characteristics between traditional wing and the folding wing are investigated and particularly, the variations of structure properties which are caused by re-distribution of the structure stiffness and mass in the folding process are highly concerned.
The aerodynamic influencing coefficients matrices which are obtained by doublet lattice method are approximated as rational functions via subspace method, and then the state-space equations of the folding wing are formulated. The numerical simulations are performed and the linear aeroelastic characteristics are obtained.
Folding wing includes two hinge free-plays, which is a double hinge nonlinear problem. The aeroelastic response problems of the folding wing with double hinges nonlinearity caused by freeplay are investigated by piecewise linearization method. The aeroelastic response and the excitation conditions of limit oscillation cycle are also analyzed.
Based on ADAMS platform, the folding processes of the folding wing are simulated and the aeroelastic problems of in the folding process are investigated. Particularly, the real time computation of the unsteady aerodynamics and interaction problems are emphatically studied. By a typical study case, the structural responses and the varying rule of hinge moment imposed by actuators are discussed preliminarily.
引文
[1]崔尔杰,白鹏,杨基明.智能变形飞行器的发展道路.航空制造技术,2007(8).
[2] Rrank.H.Gern, AMIR,H.Naghshineh-Pour,etl, Flexible Wing Model for Structureal Wing Sizing and Multidiscdiplinary Design Optization of a Strut-Braced Wing, 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA-2000-1327.
[3] Pendleton, Ed‘Miller, etl, The Active Aeroelastic Wing Flight Research Program-Technicai Program and Model Analytical Development, 39th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, p2518-2531.
[4] Florance, Jenifer P., Contributions of the NASA Langley Research Center to the DARPA/AFRL/NASA/Northrop Grumman Smart Wing Program, 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 18-21 April ,2003,p19.
[5] R.W.Wlezien,G.C.Horner, The Aircraft Morphing Program,AIAA 98-1927.
[6]丛敏.美国研究变形结构飞行器.飞航导弹, 2005 (3)
[7]马洪忠,彭建平,吴维,等.智能变形飞行器的研究与发展.飞航导弹, 2006 (5)
[8] Armando R. Rodriguez, Morphing Aircraft Technology Survey, 45th AIAA Aerospace Sciences Meeting and Exhibit 8-11 January 2007, Reno, Nevada.
[9] Snyder, M. P., Sanders, B., Eastep, F. E., Frank, G. J.,“Vibration and Flutter Characteristics of a Folding Wing,”46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference 18-21 April 2005,Austin, Texas.
[10] Thomas G. Ivanco, Robert C. Scott, Michael H. Love, et al. Validation of the Lockheed Martin morphing concept with wind tunnel testing [C]// 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. AIAA, 2007: 1-10
[11] M.H. Love, P.S. Zink, R.L. Stroud, et al. Demonstration of morphing technology through ground and wind tunnel tests [C]// 48th AIAA/ASME/ASCE/AHS/ASC Structures, Struc-tural Dynamics, and Materials Conference. AIAA, 2007: 1-10
[12] M.H. Love, P.S. Zink,etc, Impact of Actuation Concepts on Morphing Aircraft Structures, 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Confer 19-22 April 2004, Palm Springs, California
[13] Lee, D.H., Weisshaar, T. A.,“Aeroelastic Studies on a Folding Wing Configuration,”46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference 18-21 April 2005, Austin, Texas.
[14] John N.Scarlett, Robert A. Canfield,etc,Multibody Dynamic Aeroelastic Simulation of a Folding Wing Aircraft, 46thAIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference 18-21,2005.
[15] Gregory W. Reich, Brian Sanders,etc, Development of an Integrated Aeroelastic Multibody Morphing Simulation Tool, 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference 1-4 May 2006, Newport, Rhode Island
[16] Earl H. Dowell, Deman Tang , Theoretical and Experimental Aeroelastic Study for Folding Wing Structures, JOURNAL OF AIRCRAFT Vol. 45, No. 4, July–August 2008.
[17]李毅,王生楠.变体飞行器结构振动特性研究.航空计算技术, Vol.36 No.6, 2006.
[18]赵育善,余旭东等,折叠翼展开过程仿真研究,弹箭与制导学报,2007(6),19-23
[19]谭湘霞,余旭东等,用弹性动力学基本分析方法求解导弹折叠翼展开的动响应,,现代防御技术,2001-29(3),27-30
[20]易龙,彭云,孙秦,折叠机构弹性动力学数值分析,机械设计与制造,2007(7),12-13
[21]李莉,任茶仙,张铎,折叠翼机构展开动力学仿真及优化,强度与环境,2007, 34(1),
[22]郭小良,裴锦华,杨忠清,朱剑峰,王永刚,无人机折叠机翼展开运动特性研究,南京航空航天大学学报,Vol 38, No.4, August. 2006
[23] Price S J . The aeroelastic response of a two-dimensional airfoil with bilinear and cubic structural nonlinearities [J] . Journal of Fluids and Structures , 1995 , 9 (2) :175 - 193.
[24] Deman Tang, Denis Kholodar and Earl H.dowell,Nolinear Aeroelastic Response of a Typical Airfoil Section with Control Surface Freeplay, AIAA-2000-1621
[25] Liu L , Wong Y S. Nonlinear aeroelastic analysis using the point transformation method , Part I : freeplay models [J] .Journal of Sound and Vibration , 2002 , 253 (2) : 447 - 469.
[26] Tang, D. M. and Dowell, E. H.,“Experimental and Theoretical Study on Aeroelastic Response of High-Aspect-Ratio Wings,”AIAA Journal, Vol. 39, No. 8, August 2001, P:1430-1441
[27] L. Tang and R.E. Bartels, etal , Simulation of Transonic Limit Cycle Oscillations Using a CFD Time-Marching Method - 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference & Exhibit -16–19 April 2001 - Seattle, WA
[28] LIU JIKE, ZHAO LINGCHENG. Bifurcation analysis of airfoil in incompressible flow [J] . Journal of Sound and Vibration,1992 ,154 (1) :117-124.
[29]赵永辉,胡海岩,具有操纵面间隙非线性二维翼段的气动弹性分析,航空学报,Vol 21,No.6,Nov. 2003,P521-525
[30]冉玉国,韩景龙,间隙非线性结构气弹响应分析程序的DMAP开发,南京航空航天大学学报,Vol 39, No 1, Feb.2007
[31] M.H. Sadr Lahidjani, H.R.Ovesy, etal, Aeroelastic and Flutter Analysis of a Flexible wing, AIAA Paper 2003-1492, 44th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Confere, Norfolk, Virginia, April 7-10, 2003
[32] Guclu Seber and Oddvar O.Bendiksen, Nonlinear Flutter Calculations Using Finite Elements in a Large Deformation Direct Eulerian-Lagrangian Formulation, AIAA Paper 2005-1856, 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, Austin, Texas, April 18-21, 2005
[33] Dong-Hyun Kim, In Lee, etal, Transonic/Supersonic Aeroelastic Instability of an All Movable Wing with Structural Nonlinearity, AIAA Paper 2003-1412, 44th AIAA/ASME /ASCE/AHS Structures, Structural Dynamics, and Materials Conference, Norfolk, Virginia , April 7-10, 2003
[34] Guclu Seber and Oddvar O.Bendiksen, Nonlinear Flutter Calculations Using Finite Elements in a Large Deformation Direct Eulerian-Lagrangian Formulation, AIAA Paper 2005-1856, 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Confer, Austin, Texas, April 18-21, 2005
[35] Lee, D. H. and Weisshaar, T. A., Aeroelastic Studies on a Folding Wing Configuration, AIAA-2005-1996, 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Austin, TX, April 18-21, 2005.
[36]张亮、韩景龙,大展弦比机翼的非线性颤振计算,[南京航空航天大学硕士学位论文],南京,南京航空航天大学,2003年
[37] Radcliffe,T.O.and Cesnik,C.E., Aeroelastic Response of Multi-Segmented Hinged Wings, AIAA-2001-1371,42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, Seattle, WA, April 16-19, 2001.
[38] Pitt, D. M.,“Static and Dynamic Aeroelastic Analysis of Structural Wing Fold Hinges That are Employed as an Aeroelastic Tailoring Tool,”AIAA-2004-1754, 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Palm Spring, CA, April.
[39] D.H. Lee, P.C. Chen, Nonlinear Aeroelastic Studies on a Folding Wing Configuration with Freeplay Hinge Nonlinearity 47th AIAA/ASME/ASCE/AHS/ASC Structures, StructuralDynamics, and Materials Conference, 2006, 19-22
[40]卢叔全,气动弹性讲义,南京,南京航空航天大学,1991。
[41]陈桂彬,邹丛青,杨超,气动弹性设计基础,北京,北京航空航天大学出版社,2004。
[42]赵永辉,气动弹性力学与控制,北京,科学出版社,2007。
[43] Tang, D., Conner, M. D., and Dowell, E. H.“Reduced-Order Aerodynamic Model and Its Application to a Nonlinear Aeroelastic System,”Journal of Aircraft, Vol. 35, No. 2, 1998, P:332-338
[44] Tang, D. M. and Dowell, E. H.“Flutter and Stall Response of Helicopter Blade with Structural Nonlinearity”, Journal of Aircraft, Vol. 29, 1992, P:953-960
[45] Tang, D. M. and Dowell, E. H.“Comparison of Theory and Experiment for Nonlinear Flutter and Stall Response of a Helicopter Blade”, Journal of Sound and Vibration, Vol. 165, No. 2, 1993, P:251-276
[46] Dunn, P. and Dugundji, J.,“Nonlinear Stall Flutter and Divergence Analysis of Cantilevered Graphite/Epoxy Wings," AIAA Journal, Vol. 30, No. 1, Jan. 1992, P: 153-162
[47] O’Neil, T. and Strganac, T. W.,“Nonlinear Aeroelastic Response-Analysis and Experiments,”AIAA Paer, 96-0014, Proceeding of the 43th Aerospace Sciences Meeting and Exhibit, Reno, Nevada, Jan 1996
[48] Gilliatt, H. C., Strganac, T. W. and Kurdila, A. J.,“On the Presence of Internal Resonances in Aeroelastic System”, In Proceedings of the 39th Structures, Structural Dynamics, and Materials Conference, Long Beanch, California, April 1998, P:2045-2055
[49] S. J. Price, Lee, An Analysis of the Post-Instability Behaviour of a two-dimensional Airfoil with Structural Nonlinearity, AIAA-93-1474-CP, P:1452-1460
[2] Rrank.H.Gern, AMIR,H.Naghshineh-Pour,etl, Flexible Wing Model for Structureal Wing Sizing and Multidiscdiplinary Design Optization of a Strut-Braced Wing, 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA-2000-1327.
[3] Pendleton, Ed‘Miller, etl, The Active Aeroelastic Wing Flight Research Program-Technicai Program and Model Analytical Development, 39th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, p2518-2531.
[4] Florance, Jenifer P., Contributions of the NASA Langley Research Center to the DARPA/AFRL/NASA/Northrop Grumman Smart Wing Program, 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 18-21 April ,2003,p19.
[5] R.W.Wlezien,G.C.Horner, The Aircraft Morphing Program,AIAA 98-1927.
[6]丛敏.美国研究变形结构飞行器.飞航导弹, 2005 (3)
[7]马洪忠,彭建平,吴维,等.智能变形飞行器的研究与发展.飞航导弹, 2006 (5)
[8] Armando R. Rodriguez, Morphing Aircraft Technology Survey, 45th AIAA Aerospace Sciences Meeting and Exhibit 8-11 January 2007, Reno, Nevada.
[9] Snyder, M. P., Sanders, B., Eastep, F. E., Frank, G. J.,“Vibration and Flutter Characteristics of a Folding Wing,”46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference 18-21 April 2005,Austin, Texas.
[10] Thomas G. Ivanco, Robert C. Scott, Michael H. Love, et al. Validation of the Lockheed Martin morphing concept with wind tunnel testing [C]// 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. AIAA, 2007: 1-10
[11] M.H. Love, P.S. Zink, R.L. Stroud, et al. Demonstration of morphing technology through ground and wind tunnel tests [C]// 48th AIAA/ASME/ASCE/AHS/ASC Structures, Struc-tural Dynamics, and Materials Conference. AIAA, 2007: 1-10
[12] M.H. Love, P.S. Zink,etc, Impact of Actuation Concepts on Morphing Aircraft Structures, 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Confer 19-22 April 2004, Palm Springs, California
[13] Lee, D.H., Weisshaar, T. A.,“Aeroelastic Studies on a Folding Wing Configuration,”46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference 18-21 April 2005, Austin, Texas.
[14] John N.Scarlett, Robert A. Canfield,etc,Multibody Dynamic Aeroelastic Simulation of a Folding Wing Aircraft, 46thAIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference 18-21,2005.
[15] Gregory W. Reich, Brian Sanders,etc, Development of an Integrated Aeroelastic Multibody Morphing Simulation Tool, 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference 1-4 May 2006, Newport, Rhode Island
[16] Earl H. Dowell, Deman Tang , Theoretical and Experimental Aeroelastic Study for Folding Wing Structures, JOURNAL OF AIRCRAFT Vol. 45, No. 4, July–August 2008.
[17]李毅,王生楠.变体飞行器结构振动特性研究.航空计算技术, Vol.36 No.6, 2006.
[18]赵育善,余旭东等,折叠翼展开过程仿真研究,弹箭与制导学报,2007(6),19-23
[19]谭湘霞,余旭东等,用弹性动力学基本分析方法求解导弹折叠翼展开的动响应,,现代防御技术,2001-29(3),27-30
[20]易龙,彭云,孙秦,折叠机构弹性动力学数值分析,机械设计与制造,2007(7),12-13
[21]李莉,任茶仙,张铎,折叠翼机构展开动力学仿真及优化,强度与环境,2007, 34(1),
[22]郭小良,裴锦华,杨忠清,朱剑峰,王永刚,无人机折叠机翼展开运动特性研究,南京航空航天大学学报,Vol 38, No.4, August. 2006
[23] Price S J . The aeroelastic response of a two-dimensional airfoil with bilinear and cubic structural nonlinearities [J] . Journal of Fluids and Structures , 1995 , 9 (2) :175 - 193.
[24] Deman Tang, Denis Kholodar and Earl H.dowell,Nolinear Aeroelastic Response of a Typical Airfoil Section with Control Surface Freeplay, AIAA-2000-1621
[25] Liu L , Wong Y S. Nonlinear aeroelastic analysis using the point transformation method , Part I : freeplay models [J] .Journal of Sound and Vibration , 2002 , 253 (2) : 447 - 469.
[26] Tang, D. M. and Dowell, E. H.,“Experimental and Theoretical Study on Aeroelastic Response of High-Aspect-Ratio Wings,”AIAA Journal, Vol. 39, No. 8, August 2001, P:1430-1441
[27] L. Tang and R.E. Bartels, etal , Simulation of Transonic Limit Cycle Oscillations Using a CFD Time-Marching Method - 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference & Exhibit -16–19 April 2001 - Seattle, WA
[28] LIU JIKE, ZHAO LINGCHENG. Bifurcation analysis of airfoil in incompressible flow [J] . Journal of Sound and Vibration,1992 ,154 (1) :117-124.
[29]赵永辉,胡海岩,具有操纵面间隙非线性二维翼段的气动弹性分析,航空学报,Vol 21,No.6,Nov. 2003,P521-525
[30]冉玉国,韩景龙,间隙非线性结构气弹响应分析程序的DMAP开发,南京航空航天大学学报,Vol 39, No 1, Feb.2007
[31] M.H. Sadr Lahidjani, H.R.Ovesy, etal, Aeroelastic and Flutter Analysis of a Flexible wing, AIAA Paper 2003-1492, 44th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Confere, Norfolk, Virginia, April 7-10, 2003
[32] Guclu Seber and Oddvar O.Bendiksen, Nonlinear Flutter Calculations Using Finite Elements in a Large Deformation Direct Eulerian-Lagrangian Formulation, AIAA Paper 2005-1856, 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, Austin, Texas, April 18-21, 2005
[33] Dong-Hyun Kim, In Lee, etal, Transonic/Supersonic Aeroelastic Instability of an All Movable Wing with Structural Nonlinearity, AIAA Paper 2003-1412, 44th AIAA/ASME /ASCE/AHS Structures, Structural Dynamics, and Materials Conference, Norfolk, Virginia , April 7-10, 2003
[34] Guclu Seber and Oddvar O.Bendiksen, Nonlinear Flutter Calculations Using Finite Elements in a Large Deformation Direct Eulerian-Lagrangian Formulation, AIAA Paper 2005-1856, 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Confer, Austin, Texas, April 18-21, 2005
[35] Lee, D. H. and Weisshaar, T. A., Aeroelastic Studies on a Folding Wing Configuration, AIAA-2005-1996, 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Austin, TX, April 18-21, 2005.
[36]张亮、韩景龙,大展弦比机翼的非线性颤振计算,[南京航空航天大学硕士学位论文],南京,南京航空航天大学,2003年
[37] Radcliffe,T.O.and Cesnik,C.E., Aeroelastic Response of Multi-Segmented Hinged Wings, AIAA-2001-1371,42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, Seattle, WA, April 16-19, 2001.
[38] Pitt, D. M.,“Static and Dynamic Aeroelastic Analysis of Structural Wing Fold Hinges That are Employed as an Aeroelastic Tailoring Tool,”AIAA-2004-1754, 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Palm Spring, CA, April.
[39] D.H. Lee, P.C. Chen, Nonlinear Aeroelastic Studies on a Folding Wing Configuration with Freeplay Hinge Nonlinearity 47th AIAA/ASME/ASCE/AHS/ASC Structures, StructuralDynamics, and Materials Conference, 2006, 19-22
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[41]陈桂彬,邹丛青,杨超,气动弹性设计基础,北京,北京航空航天大学出版社,2004。
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