超声速流中壁板的颤振及其抑制
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摘要
壁板颤振是指壁板暴露在超声速气流中，由于惯性力、弹性力和流经壁板表面气流引发的气动力耦合作用下产生的一种自激振动现象。壁板颤振将引发壁板的大幅度横向振动，可能导致飞行器结构的疲劳失效。飞行过程中由于气动热效应引发的壁板温度的升高将在壁板面内产生热应力和力矩，降低壁板的弯曲刚度。另外，由于飞行器引擎和超声速气流产生的气动噪声对壁板的疲劳寿命也会带来很大的危害。为减小壁板颤振对飞行器结构带来的危害，通常研究者们采用不同的主、被动控制方法提高壁板的临界颤振动压或降低颤振时壁板的振动幅值。为此，本文主要针对以下几个问题展开研究：
采用von Karman大变形位移应变关系和三阶气动活塞理论描述壁板颤振模型中的几何非线性因素和气动非线性因素，利用Hamilton原理建立超声速流中壁板的非线性运动微分方程。采用伽辽金离散法对所得的壁板偏微分运动方程进行空间离散，得到壁板的常微分运动方程组，最后采用Runge-Kutta法对壁板的动力学响应进行数值模拟。采用非线性动力学理论求解了壁板的临界颤振动压，并对工程上出现的频率重合现象进行了解释。随后讨论了线性气动阻尼对壁板临界颤振动压、固有频率和振动频率的影响。
采用结构设计中常见的加肋方式对壁板实施被动颤振控制，研究超声速流中加肋壁板的动力学响应。为节约计算成本，摒弃了传统的有限元建模方法，在合理的假设条件下将加肋壁板等效为壁板子系统和肋条子系统，两个子系统间在接触面处满足力和位移的匹配条件。壁板子系统仍采用Hamilton原理进行建模，肋条子系统则采用Euler-Bernoulli梁理论进行建模。根据变形协调关系，导出壁板子系统和肋条子系统间作用力/反作用力表达式，最终建立加肋壁板的偏微分运动方程。对系统进行伽辽金离散，并采用Runge-Kutta法对加肋壁板的动力学响应进行模拟。随后讨论肋条高度、宽度和加肋方案对颤振抑制效果的影响。
采用在壁板背风面安装动态吸振器的方法对壁板颤振实施被动控制。建模时计及动态吸振器和壁板间的耦合效应，将二者间的作用力描述为其相对位移和相对速度的函数，分别采用Hamilton原理和牛顿第二定律对壁板和动态吸振器进行建模，并基于两者间的作用力关系建立壁板——动态吸振器系统的联立运动方程组。分别讨论动态吸振器质量、刚度系数、阻尼系数和安装位置对壁板颤振抑制效果的影响，最后根据动态吸振器对壁板颤振重合频率的影响规律对动态吸振器的安装位置进行优化设计。
研究声热联合激励下壁板的颤振特性。在壁板的几何关系中引入热应变，并采用有限带宽的零均值高斯白噪声模拟壁板表面所受的噪声激励，采用Hamilton原理建立声热联合激励下壁板的运动微分方程。分别研究铺设角、温度和声压级分贝数对壁板颤振的影响，最后对声热联合作用下壁板的动力学响应进行了数值模拟。
Panel flutter is a kind of self-excited oscillation resulting from the interactionof the inertial force, elastic force of the panel and the aerodynamic loads when thepanel is exposed to the supersonic flow. The flutter can cause the panel to vibratelaterally with high amplitude, which may lead to the fatigue failure of the flightvehicle. The growth of the temperature induced by the aerodynamic heating effectduring the flight may introduce in-plane thermal forces and bending moments to thepanel, which will decrease the bending stiffness of the panel. In addition, theaerodynamic noise caused by the engine of the fight vehicle and the supersonic flowis harmful to the fatigue life of the panel. In order to minish the damages caused bythe panel flutter, different passive and active control methods are adopted in theliteratures to enhance the critical flutter dynamic pressure or reduce the flutteramplitude of the panel. Thus, the present study devotes to investigate the panelflutter in the following aspects:
The von Karman nonlinear displacement-strain relationship and the third orderpiston theory are employed to describ the geometry and aerodynamic nonlinearities,respectively. The Hamilton principle is adopted to establish the equation of motionof the panel in the supersonic flow. The Galerkin discrete method is used to truncatethe partial differential equation of motion of the panel into a set of ordinarydifferential equations, which are then simulated by the fourth order Runge-Kuttamethod. The nonlinear dynamic theory is adopted to solve the critical flutterdynamic pressure of the panel and explain the frequencies superpositionphenomenon in the engineering. Then effect of the linear damping term on thecritical flutter dynamic pressure, the natural frequencies and the vibrationfrequencies are discussed, respectively.
A passive control strategy is adopted to suppress the flutter of the panelaccording to a stiffened scheme, and the dynamic response of the stiffened panel inthe supersonic is investigated. In order to save the computational expense, thetransitional finite element method is abandoned in the modeling procedure. Thestiffened panel system is equivalent to a panel subsystem and a stiffener subsystemon the basis of two reasonable assumptions. The matching condition of the force andthe displacement is satisfied at the interface between the two subsystems. TheHamilton principle is adopted to establish the model of the panel subsystem, and theEuler-Bernoulli beam theory is adopted to establish the model of the stiffenersubsystem. On the basis of deformation compatibility, the acting and reacting forcesbetween the panel and the stiffener are deduced, and then the partial differential governing equation of motion of the stiffened panel is obtained. The Galerkinmethod is employed in the discrete process, and then a new method is established toanalysis the flutter of the stiffened panel based on the Galerkin method. Then theeffects of the height and width of the stiffener and the stiffened scheme on the effectof the flutter suppression of the panel are investigated, respectively.
A passive control strategy is adopted to suppress the flutter of the panel byinstalling a set of dynamic absorber on the backside of the panel. The couplinginduction between the dynamic absorber and the panel is considered in the modelingprocedure, and the acting and reacting forces between the dynamic absorber and thepanel are described as the function of their relative displacement and velocity. TheHamilton principle and Newton’s Second law of motion are used to establish themodels of the panel and the dynamic absorber, respectively. Based on the interactionforces between the dynamic absorber and the panel, the combined equations ofmotion of the panel-absorber system are obtained. The effects of the mass, stiffness,damping and installation position on the flutter suppression of the panel arediscussed, respectively. At last, the installation position of the absorber is optimizedon the basis of the influence law of the dynamic absorber on the flutter superpositionfrequency of the panel.
The flutter of the panel under thermal-acoustic combined excitation isinvestigated. The thermal strain induced by the temperature is introduced into thegeometry relationship of the panel, and the acoustic excitation is assumed as astationary white-Gaussian random pressure with zero mean, the Hamilton principleis employed to establish the equation of motion of the panel. The effects of the fiberangle, temperature difference and the SPL on the flutter of the panel are investigated,respectively. Then the dynamic response of the panel under the thermal-acousticcombined excitation is simulated.
采用von Karman大变形位移应变关系和三阶气动活塞理论描述壁板颤振模型中的几何非线性因素和气动非线性因素，利用Hamilton原理建立超声速流中壁板的非线性运动微分方程。采用伽辽金离散法对所得的壁板偏微分运动方程进行空间离散，得到壁板的常微分运动方程组，最后采用Runge-Kutta法对壁板的动力学响应进行数值模拟。采用非线性动力学理论求解了壁板的临界颤振动压，并对工程上出现的频率重合现象进行了解释。随后讨论了线性气动阻尼对壁板临界颤振动压、固有频率和振动频率的影响。
采用结构设计中常见的加肋方式对壁板实施被动颤振控制，研究超声速流中加肋壁板的动力学响应。为节约计算成本，摒弃了传统的有限元建模方法，在合理的假设条件下将加肋壁板等效为壁板子系统和肋条子系统，两个子系统间在接触面处满足力和位移的匹配条件。壁板子系统仍采用Hamilton原理进行建模，肋条子系统则采用Euler-Bernoulli梁理论进行建模。根据变形协调关系，导出壁板子系统和肋条子系统间作用力/反作用力表达式，最终建立加肋壁板的偏微分运动方程。对系统进行伽辽金离散，并采用Runge-Kutta法对加肋壁板的动力学响应进行模拟。随后讨论肋条高度、宽度和加肋方案对颤振抑制效果的影响。
采用在壁板背风面安装动态吸振器的方法对壁板颤振实施被动控制。建模时计及动态吸振器和壁板间的耦合效应，将二者间的作用力描述为其相对位移和相对速度的函数，分别采用Hamilton原理和牛顿第二定律对壁板和动态吸振器进行建模，并基于两者间的作用力关系建立壁板——动态吸振器系统的联立运动方程组。分别讨论动态吸振器质量、刚度系数、阻尼系数和安装位置对壁板颤振抑制效果的影响，最后根据动态吸振器对壁板颤振重合频率的影响规律对动态吸振器的安装位置进行优化设计。
研究声热联合激励下壁板的颤振特性。在壁板的几何关系中引入热应变，并采用有限带宽的零均值高斯白噪声模拟壁板表面所受的噪声激励，采用Hamilton原理建立声热联合激励下壁板的运动微分方程。分别研究铺设角、温度和声压级分贝数对壁板颤振的影响，最后对声热联合作用下壁板的动力学响应进行了数值模拟。
Panel flutter is a kind of self-excited oscillation resulting from the interactionof the inertial force, elastic force of the panel and the aerodynamic loads when thepanel is exposed to the supersonic flow. The flutter can cause the panel to vibratelaterally with high amplitude, which may lead to the fatigue failure of the flightvehicle. The growth of the temperature induced by the aerodynamic heating effectduring the flight may introduce in-plane thermal forces and bending moments to thepanel, which will decrease the bending stiffness of the panel. In addition, theaerodynamic noise caused by the engine of the fight vehicle and the supersonic flowis harmful to the fatigue life of the panel. In order to minish the damages caused bythe panel flutter, different passive and active control methods are adopted in theliteratures to enhance the critical flutter dynamic pressure or reduce the flutteramplitude of the panel. Thus, the present study devotes to investigate the panelflutter in the following aspects:
The von Karman nonlinear displacement-strain relationship and the third orderpiston theory are employed to describ the geometry and aerodynamic nonlinearities,respectively. The Hamilton principle is adopted to establish the equation of motionof the panel in the supersonic flow. The Galerkin discrete method is used to truncatethe partial differential equation of motion of the panel into a set of ordinarydifferential equations, which are then simulated by the fourth order Runge-Kuttamethod. The nonlinear dynamic theory is adopted to solve the critical flutterdynamic pressure of the panel and explain the frequencies superpositionphenomenon in the engineering. Then effect of the linear damping term on thecritical flutter dynamic pressure, the natural frequencies and the vibrationfrequencies are discussed, respectively.
A passive control strategy is adopted to suppress the flutter of the panelaccording to a stiffened scheme, and the dynamic response of the stiffened panel inthe supersonic is investigated. In order to save the computational expense, thetransitional finite element method is abandoned in the modeling procedure. Thestiffened panel system is equivalent to a panel subsystem and a stiffener subsystemon the basis of two reasonable assumptions. The matching condition of the force andthe displacement is satisfied at the interface between the two subsystems. TheHamilton principle is adopted to establish the model of the panel subsystem, and theEuler-Bernoulli beam theory is adopted to establish the model of the stiffenersubsystem. On the basis of deformation compatibility, the acting and reacting forcesbetween the panel and the stiffener are deduced, and then the partial differential governing equation of motion of the stiffened panel is obtained. The Galerkinmethod is employed in the discrete process, and then a new method is established toanalysis the flutter of the stiffened panel based on the Galerkin method. Then theeffects of the height and width of the stiffener and the stiffened scheme on the effectof the flutter suppression of the panel are investigated, respectively.
A passive control strategy is adopted to suppress the flutter of the panel byinstalling a set of dynamic absorber on the backside of the panel. The couplinginduction between the dynamic absorber and the panel is considered in the modelingprocedure, and the acting and reacting forces between the dynamic absorber and thepanel are described as the function of their relative displacement and velocity. TheHamilton principle and Newton’s Second law of motion are used to establish themodels of the panel and the dynamic absorber, respectively. Based on the interactionforces between the dynamic absorber and the panel, the combined equations ofmotion of the panel-absorber system are obtained. The effects of the mass, stiffness,damping and installation position on the flutter suppression of the panel arediscussed, respectively. At last, the installation position of the absorber is optimizedon the basis of the influence law of the dynamic absorber on the flutter superpositionfrequency of the panel.
The flutter of the panel under thermal-acoustic combined excitation isinvestigated. The thermal strain induced by the temperature is introduced into thegeometry relationship of the panel, and the acoustic excitation is assumed as astationary white-Gaussian random pressure with zero mean, the Hamilton principleis employed to establish the equation of motion of the panel. The effects of the fiberangle, temperature difference and the SPL on the flutter of the panel are investigated,respectively. Then the dynamic response of the panel under the thermal-acousticcombined excitation is simulated.
引文
[1]曹秀云.近空间飞行器成为各国近期研究的热点（上）[J].中国航天,2006,6:32-35.
[2]曹秀云.近空间飞行器成为各国近期研究的热点（下）[J].中国航天,2006,7:30-32.
[3]蒋持平,柴慧,严鹏.近空间高超声速飞行器防热隔热与热力耦合研究进展[J].力学与实践,2011,33(1):1-9.
[4]陈予恕,郭虎伦,钟顺.高超声速飞行器若干问题研究进展[J].飞航导弹.2009,8:26-33.
[5]蔡亚梅,汪丽萍.美国的高超声速飞行器发展计划及关键技术分析[J].航天制造技术.2012,12(6):4-7.
[6]沈海军,程凯,杨莉.近空间飞行器[M].北京:航空工业出版社,2012：1-25
[7]李建林.临近空间高超声速飞行器发展研究[M].北京:中国宇航出版社,2012：1-4.
[8]孟凡颢,钟腾育.用壁板颤振理论解决某系列飞机的方向舵蒙皮裂纹故障[J].飞机设计2000,4:1-6
[9] Park J S, Kim J H, Moon S H. Thermal post-bulking and flutter characteristicsof composite plates embebded with shape memory alloy fibers[J]. CompositePart B: Engineering,2005,36:627-636.
[10]杨智春,夏巍,孙浩.高速飞行器壁板颤振的分析模型和分析方法[J].应用力学学报,2006,23(4):537-542.
[11] Garrick I E, Reed W H. Historical development of aircraft flutter[J]. Journal ofAircraft,1981,18(11):897-912.
[12]杨超,许赟,谢长川.高超声速飞行器气动弹性力学研究综述[J].航空学报,2010,31(1):1-11.
[13] Zhou R C, Xue D Y, Mei C. Finite element time domain modal formulation fornonlinear flutter of composite panels [J]. AIAA Journal,1994,32(10):2044-2052.
[14]王渤成,邵敏.有限单元法基本原理和数值方法[M].北京：清华大学出版社，1997：15-20.
[15] Cheng G F, Mei C. Finite element modal formulation for hypersonic panelflutter analysis with thermal effects[J]. AIAA,2004,42(4):687-695.
[16] Eastep F E, McIntosh S C. Analysis of nonliearn panel flutter and responseunder random excitation or nonlinear aerodynamic loading[J]. AIAA Journal,1971,9(3):411-418.
[17]黄琳,段志生,杨剑影.近空间高超声速飞行器对控制科学的挑战[J].控制理论与应用.2011,28(10):1496-1505.
[18] Dowell E H. A review of the aeroelastic stability of plates and shells[J]. AIAAJournal,1970,8(3):385-399.
[19] Bendiksen O O. Review of unsteady transonic aerodynamics: Theory andapplications. Progress in Aerospace Sciences,2011,47:135-167.
[20] Lighthill M J. Oscillating airfoils at high mach number[J]. Journal ofAeornautical Science,1953,20(6):402-406.
[21] Ashely H, Zartarian G. Piston theory-a new aerodynamic tool foraeroelastician[J]. Journal of Aeornautical Science,1956,23(10):1109-1118.
[22]陈劲松,曹军.超声速和高超声速翼型非定常气动力的一种近似计算方法[J].空气动力学报,1990,8(3):339-344.
[23]杨炳渊,宋伟力.用当地流活塞理论计算大攻角翼面超音速颤振[J].振动与冲击,1995,15(2):60-63
[24]王乐,王毅,南宫自军.活塞理论及其改进方法在超声速翼面颤振分析中的应用[J].导弹与航天运载技术.2011,4:13-17.
[25] Selvam R Qu P, Z Q, Zhen Q. Three-dimensional nonlinear panel flutter atsupersonic euler flow[C].43rd AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics, and Materials Conference, Denver, Colorado,2002.
[26] Dowell E H. Nonlinear oscillations of a fluttering plate. I[J]. AIAA Journal,1966,4(7):1267-1275.
[27] Scott R C, Weisshaar T A. Panel flutter suppression using adaptive materialactuators[J]. Journal of Aircraft,1994,31(1):213-222.
[28]张晓梅,任勇生,李磊.埋入SMA纤维的复合材料壁板的气弹稳定性研究[J].太原科技大学学报,2010,31(6):497-501.
[29] Olson M D. Finite elements applied to panel flutter[J]. AIAA Journal,1967,5(12):2267-2270.
[30] Rao K S, Rao G V. Large amplitude supersonic flutter of panels with endselastically restrained against rotation[J]. Computers and Structures,1980,11(3):197-201.
[31] Sarma B S, Varadan T K. Nonlinear panel flutter by finite element method.AIAA Journal,1988,26:566-574.
[32] Olson M D. Some flutter solutions using finite elements[J]. AIAA Journal,1970,8(4):747-752.
[33] Yuan K H, Qiu Z P. Nonlinear flutter analysis of stiffened composite panels insupersonic flow[J]. Science China Physics, Mechanics&Astronomy,53(2):336-344.
[34] Mei C, Rogers J L. Application of NASTRAN to large deflection supersonicflutter of panels. NASA TM X-3428,1976:67-97.
[35] Mei C. A finite element approach for nonlinear panel flutter. AIAA Journal,1977,15:1107-1110.
[36] Han A D, Yang T Y. Nonlinear panel flutter using high order triangular finiteelements[J]. AIAA Journal,1983,21:1453-1461.
[37] Jameson A, Schmidt W, Turkel E. Numerical solution of the euler equation byfinite volume methods using Runge-Kutta time stepping schemes[C].14thFluid and Plasma Dynamics Conference, California,1981.
[38] Atsushi H, Igor M, and Yoshiaki N. Panel Flutter Analysis with aFluid-Structure Coupled Scheme[C].33rd AIAA Fluid Dynamics Conferenceand Exhibit, Florida,2003.
[39] Epureanu B I, Tang L S, Paidousis M P. Coherent structures and their influenceon the dynamics of aeroelastic panels[J]. International Journal of Non-linearMechanics,2004,39:977-991.
[40] Selvam R P, Qu Z Q, Zheng Q. Efficient Method for Dynamic Condensation ofNonclassically Damped Vibration Systems[J]. AIAA Journal,2002,40(2):368-375.
[41]陈予恕.非线性振动[M].北京：高等教育出版社,2002:259-260.
[42] Morino L. A perturbation method for treating nonlinear panel flutterproblems[J]. AIAA Journal,1969,7(3):405-411.
[43] Kuo C C, Morino L, Dugundji L. Perturbation and harmonic balance fortreating nonlinear panel flutter[J]. AIAA Journal,1972,10:1479-1484.
[44] Kobayashi S. Flutter of a simply supported rectangular plates in a supersonicflow-two dimensional panel flutter, I simply supported, II clamped panels[J].Trans Japan Soc of Aeron and Space Sci1962,5,79-118.
[45] Bolotin V V, Grishke A A, Kounadis A N, Gantes C J. Nonlinear panel flutter inremote post-critical Domains[J]. International Journal of Nonlinear Mechanics,1998,33(5):753-764.
[46]胡海岩.应用非线性动力学[M].北京：航空工业出版社,2000:60-62.
[47] Bolotin V V. Nonconservative problems of the theory of elastic stability[M].New York: McMilian,1963:199-312.
[48] Eastep F E, McIntosh S C. Analysis of nonlinear panel flutter and responseunder random excitation or nonlinear aerodynamic loading. AIAA Journal,1971,9(3):411-418.
[49] Kuo C C, Morino L, Dugunji L. Perturbation and harmonic balance for tratingnonlinear panel flutter[J]. AIAA Journal,1972,10:1479-1484.
[50] Lau S L, Cheung Y K. Amplitude incremental variational principle fornonlinear vibration of elastic system[J]. Journal of Applied Mechanics,1981,48(4):959-964.
[51] Yuen S W, Lau S L. Effects of inplane load on nonlinear panel flutter byincremental harmonic balance method[J]. AIAA Journal,1991,29:1472-1479.
[52]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.
[53]陈大林,杨翊仁,胡绍全等.二维薄板在超音速气流作用下的热弹性颤振[J].西南交通大学学报,2007,42(6):691-694.
[54] Bolovin V V, Petrosky A V. Secondary bifurcation and global instability of anaeroelastic non-linear system in the divergence domain[J]. Journal of Soundand vibration,1996,191(3):431-451.
[55] Gray C E, Mei C. Finite element method for large-amplitude Two-Dimensionalpanel flutter at hypersonic speeds[J]. AIAA Journal,29(2):290-298.
[56] Xue D Y, Mei C. Finite element nonlinear panel flutter with arbitrarytemperatures in supersonic flow[J]. AIAA Journal,1993,31(1):154-162.
[57]范晨光.薄壳气动弹性非线性响应研究[D].成都，西南交通大学学位论文.2010:52-55.
[58]陈大林,杨翊仁,范晨光.用微分求积法计算二维薄板在超音速流中的非线性颤振[J].固体力学学报,2007,28(4):399-405.
[59]李鹏,杨翊仁,鲁丽.微分求积法分析二维亚音速壁板的失稳问题[J].动力学与控制学报.2012,10(1):11-14.
[60]梅冠华,张家忠.时滞惯性流形在三维壁板颤振数值分析中的应用[J].西安交通大学学报,2011,45(9):40-46.
[61] M R Brake, D J Segalman. Nonlinear model reduction of von Karman plateunder quasi-steady fluid flow[J]. AIAA Jounral,2010,48(10):2339-2347.
[62] Guo X Y, Mei C. Application of aeroelastic modes on nonlinear supersonicpanel flutter at elecated temperatures[J]. Computers and Sturctures,2006,84:1619-1628.
[63]赵秀芳，曹树谦.用Normal Form直接法研究壁板的热颤振与控制.振动与冲击[J].2012,13(11)：54-56
[64]丁千,陈予恕．机翼颤振的非线性动力学和控制研究[J]．科技导报，2009，27(2):53-61．
[65]丁千,王冬立.用规范型直接法研究立方非线性机翼的颤振[J].飞行力学,2005,23(3):85-88.
[66]丁然.气动力及热载荷作用下功能梯度材料矩形板的非线性动力学[D].天津，天津大学博士学位论文:1-7.
[67] Sohn K J, Kim J H. Nonlinear thermal flutter of functionally graded panelsunder a supersonic flow[J]. Composite Structures,2009,88:380-387.
[68] Lee S L, Kim J H. Thermal post-buckling and limit-cycle oscillation offunctionally graded panel with structural damping in supersonic airflow[J].Composite Strucures,2009,91:205-211.
[69] Ibrahim H H, Tawfik M, Ajmi M A. Non-linear panel flutter fortemperature-dependent functionally graded material panels[J]. ComputationalMechanics,2008,41:325-334.
[70] Prakash T, Ganapathi M. Supersonic flutter characteristics of functionallygraded flat panels including thermal effects[J]. Composite Structures,2006,72:10-18.
[71]阮苗,王忠民,王砚.陶瓷/金属非保守FGM斜板的颤振分析[J].中国机械工程,2011,22(13):1580-1584.
[72] Gray C E, Mei C, Shore C P. Finite element method for large-amplitudetwo-dimensional panel flutter at hypersonic speeds[J]. AIAA Journal,1991,29(2):290-298.
[73] Kouchakzadeh M A, Rasekh M, Haddadpour H. Panel flutter analysis ofgeneral laminated composite plates[J]. Composite Structures,2010,92:2906-2915.
[74]万志强,邵珂,杨超,王科.非均匀铺层壁板复合材料机翼气动弹性分析[J].复合材料学报,2008,25(1):196-199.
[75]杨智春,谭光辉,夏巍.铺层方式对复合材料壁板热颤振特性的影响[J].宇航学报,2008,29(3):1047-1052.
[76]王战玺，秦现生，白晶，李靖.复合材料层合板的颤振预测和模态交叉分析[J].振动与冲击,2012,30(12):7-11.
[77] Beloiua D M, Ibrahima R A, Pettit C L. Influence of boundary conditionsrelaxation on panel flutter with compressive in-plane loads[J]. Journal ofFluids and Structures,2005:743-767.
[78] Higuchi K, Dowell E H. Effect of structural damping on flutter of plates with afollower force[J]. AIAA Journal,1992,30(3):820-825.
[79]陈大林,杨翊仁,肖世富,胡绍全.超音速流中二维壁板的Hopf分叉[J].工程力学,2008,25(4):214-217.
[80]陈大林,杨翊仁,胡绍全.三维薄板在超音速气流作用下的非线性颤振研究[J].强度与环境,2008,35(2):12-17.
[81] Dowell E H. Nonlinear flutter of curved plates[J]. AIAA Journal,1969,7:424-431.
[82] Dowell E H. Nonlinear flutter of curved plates II[J]. AIAA Journal,1970,8:259-261.
[83] Dowell E H. Nonlinear oscillations of a fluttering plate II[J]. AIAA Journal,1967,5:1856-1862.
[84]高扬,杨智春.复合材料曲壁板与平壁板热颤振热性的对比[J].振动与冲击,2011,30(4):55-59.
[85]杨智春,周建,谷迎松.超音速气流中受热曲壁板的非线性颤振特性[J].力学学报,2012,44(1):30-38.
[86]周建,杨智春,贺顺.活塞理论气动力的静压修正方法及在曲壁板颤振分析中的应用[J].航空学报,2013,34(X): XXX-XXX.
[87]叶献辉,杨翊仁,肖艳平.热环境下三维壁板大气紊流动力响应分析[J].工程力学,2009,26(6):233-237.
[88]肖艳平,杨翊仁,叶献辉.边界松弛对壁板颤振响应的影响分析[J].工程力学,2012,29(11):40-45.
[89]苑凯华,邱志平.含不确定参数的复合材料壁板热颤振分析[J].航空学报,2010,31(1):119-124.
[90] Koo, K N, Hwang W S. Effects of hysteretic and aerodynamic damping onsupersonic panel flutter of composite plates [J]. Journal of Sound and Vibration,2004,273(3):569-583.
[91]张云峰,刘占生.粘弹壁板颤振的非线性动力特性[J].推进技术,2007,28(1):103-107.
[92]肖艳平,杨翊仁,叶献辉.三维粘弹壁板颤振分析[J].振动与冲击,2011,30(1):82-86.
[93] Gordnier R E, Visbal M R. Development of a three-dimensional viscousaeroelastic solver for nonlinear panel flutter. Journal of Fluids and Structures,2002,16:497-527.
[94]尹传家.飞行器的颤振.北京：原子能出版社,2007：241-252.
[95]中国人民解放军总装备部军事训练教材编辑工作委员会.高超声速气动热和热防护.北京：国防工业出版社，2003：37-45.
[96] Bisplinghoff R. Some structural and aeroelastic consideration of high-speedflight[J]. Journal of the Aerospace Science,1956,23(4):289-329.
[97]郭虎伦.非线性机翼的分岔特性分析及其参数控制[D].哈尔滨，哈尔滨工业大学博士学位论文：4-11.
[98] Budiansky B, Mayers J. Influence of aerodynamic heating on the effectivetorsional stiffness of thin wings[J]. Journal of the Aeronautical Sciences,1956,23(12):1081-1093.
[99]范绪箕.高速飞行器热结构分析与应用.国防工业出版社.北京,2009:21-23.
[100] Yang T Y, Han A D. Flutter of thermally buckled finite element panels. AIAAJournal,1976,14:975-977.
[101]夏巍,杨智春.超音速气流中受热壁板的稳定性分析[J].力学学报.2007,39(5):602-609.
[102]夏巍,杨智春,谷迎松.超声速气流中受热壁板的二次失稳型颤振[J].航空学报.2009.30(10):1851-1856.
[103]李丽丽,赵永辉.超音速下热壁板的颤振分析[J].动力学与控制学报.2012,10(1):67-70.
[104]叶献辉,杨翊仁.三维壁板热颤振分析[J].振动与冲击.2008,27(6):55-59.
[105]叶献辉,杨翊仁,范晨光.热环境下壁板非线性颤振分析[J].计算力学学报.2009,26(5):684-689.
[106]王晓庆,韩景龙,张军红.不同气流偏角下的壁板热颤振分析及多目标优化设计[J].航空学报.2010,31(11):2195-2201.
[107]苑凯华,邱志平.高超声速气流中复合材料壁板热颤振分析[J].南京航空航天大学学报.2010,43(3):313-317.
[108]周良强,陈予恕,陈芳启.超音速气流中受热壁板的非线性动力学分析[J].科学技术与工程.2010,10(19):4744-4747.
[109]杨智春,张蕊丽.基于最大李雅普诺夫指数的壁板热颤振特性分析[J].西北工业大学学报.2009,27(6):770-776.
[110]杨智春,夏巍,张蕊丽.温度分布对复合材料壁板颤振特性的影响[J].宇航学报.2010,31(3):850-854.
[111] Motagaly K A, Duan B, Mei C. Nonlinear panel response at high acousticexcitations and supersonic speeds[C].40th Structures, Structural Dynamics,and Materials Conference and Exhibit, St. Louis,1999.
[112] Ibrahim H H, Yoo H H, Tawfik M, Lee K S. Thermo-acoustic random responseof temperature-dependent functionally graded material panels[J]. ComputMech,2010,46:377-386.
[113] Ibrahim H H, Yoo H H, Lee K S. Supersonic flutter of functionally gradedpanels subjected to acoustic and thermal loads[J]. Journal of Aircraft,2009,46(2):593-600.
[114] Surace G, Udrescu R. Finite-element analysis of the fluttering panels excitedby external forces. Journal of Sound and Vibration,1999,224(5):917-935.
[115] Abdel M K, Duan B, Mei C. Active control of nonlinear panel flutter underyawed supersonic flow[J]. AIAA Paper,2003,2003-1514.
[116] Chandiramani N K, Plaut R H, Librescu L I. Nonperiodic flutter of a buckledcomposite panel[J]. Sadhana,1995,20:671-689.
[117]杨智春,夏巍.壁板颤振的分析模型、数值求解方法和研究进展[J].力学进展,2010,40(1):81-98.
[118]赵永辉.气动弹性力学与控制[M].北京：科学出版社，2007:11-16.
[119]尹坚平,刘鸿信,倪乃琛.动力吸振器用于抑制加肋薄板振动和声辐射的研究[J].同济大学学报,1989,17(2):195-203.
[120]孙朝晖,戴扬,王冲,孙进才.飞机壁板附加动力吸振器后的振动与声辐射[J].西北工业大学学报,1993,11(4):470-475.
[121]孙朝晖,孙进才,王冲,戴扬.动力吸振器用于提高壁板隔声量的研究[J].噪声与振动控制,1995,1:10-13.
[122]孙朝晖,戴扬,王冲,孙进才.飞机壁板减振降噪中动力吸振器的设计及实验研究[J].噪声与振动控制.1995,4:10-13.
[123]宛敏红.薄板结构的吸振控制研究[D].西北工业大学硕士学位论文.
[124]杨智春,杨飞,张玲凌.动力吸振器用于夹层壁板颤振抑制的研究[J].振动与冲击,2009,28(2):24-28.
[125]杨飞,杨智春,王巍.吸振夹层壁板颤振抑制的吸振器频率设计[J].振动与冲击，2009,28(7)：65-68
[126] Liao C L, Sun Y W. Flutter analysis of stiffened laminated composite platesand shells in supersonic flow[J]. AIAA Journal,1993,31(10):1897-1905.
[127] Lee D M, Lee I. Supersonic flutter analysis of stiffened isotropic andanisotropic panels[J]. AIAA Journal,1996,34(3):637-639.
[128] Oh I K, Lee I, Lee D M. Non-linear transient response of fluttering stiffenedcomposite plates subject to thermal load[J]. Journal of Sound and vibration,2001,245(4):715-736.
[129] Lee D M, Lee I. Vibration Analysis of Anisotropic Plates with EccentricStiffener[J]. Computers&Structures,1995,57(1):99-105.
[130]张晓梅,任勇生,李磊.埋入SMA纤维的复合材料壁板的气弹稳定性研究[J].太原科技大学学报,2010,31(6):497-501.
[131] Lee J J, Choi S. Thermal buckling and postbuckling analysis of a laminatedcomposite beam with embedded SMA Actuators[J]. Composite Structures,1999,47:695-703.
[132] Park J S, Kim J H, Moon S H. Thermal post-buckling and fluttercharacteristics of composite plates embedded with shape memory alloyfibers[J]. Composites: Part B,2005,36:627-636.
[133] Ibrahim H H, Tawfik M, Hani M N, Yoo H H. Aerothermoacoustic response ofshape memory alloy hybrid composite panels[J]. Journal of Aircraft,2009,46(5):1544-1555.
[134]李敏,陈伟民,贾丽杰.压电驱动器的气动弹性应用[J].航空学报.2009,30(12):2301-2310.
[135] Moon S H, Kim S J. Active and Passive Suppressions of Nonlinear PanelFlutter Using Finite Element Method. AIAA Journal,2001,39(11):2042-2050.
[136] Scott R C, Weisshaar T A. Controlling panel flutter using adaptive materials[J].Journal of Aircraft,1991,31:213-222.
[137] Zhou R C, Xue D Y, Mei Huang J K, Mei C. Suppression of nonlinear panelflutter with piezoelectric actuators using finite element methods[J]. AIAAJournal,1995,33:1098-1105.
[138] Zhou R C, Xue D Y, Mei Huang J K. Suppression of nonlinear panel flutter atsupersonic speeds and elevated temperatures[J]. AIAA Journal,1996,34:347-354
[139] Moon S H, Hwang J S. Panel flutter suppression with an optimal controllerbased on the nonlinear model using piezoelectric materials[J]. CompositeStructures,2005,68:371-379.
[140]苑凯华邱志平.压电复合材料壁板颤振的控制[J].北京航空航天大学学报.2009,35(12):1429-1433.
[141]宋智广,李凤明.主动约束层阻尼对超声速梁结构颤振特性的影响[J].固体力学学报.2010,31(SI):115-119.
[142] Li F M. Actice aeroelastic flutter suppression of a supersonic plate withpiezoelectric material[J]. International Journal of Engineering Science,2012,51:190-203.
[143] Sadri A M, Wright J R, Wynne R J. LQG control design for panel fluttersuppression using piezoelectric actuators. Smart Materials and Structures,2002,11:834-839.
[144] Onawola O O, Sinha S C. A feedback linearization approach for panel fluttersuppression with piezoelectric actuation. Journal of Computational andNonlinear Dynamics,2011,6(031006):1-8.
[145] Korbahti B. Specially orthotropic panel flutter control using PID controller.Acta Mech,2010,212:191-197.
[146]赵秀芳，曹树谦.用Normal Form直接法研究壁板的热颤振与控制[J].振动与冲击,2012,13(11)：54-56
[147] Chen G, Li Y, Yan G R. Active Control Law Design for Flutter/LCOSuppression Based on Reduced Order Model Method[J]. Chinese Journal ofAeronautics,2010,23:639-646
[148] Lee Y Y, Guo X. Non-linear vibration suppression of a composite panel subjectto random acoustic excitation using piezoelectric actuators. MechanicalSystems and Signal Processing,2007,21:1153-1173.
[149] Wang Z X, Qin X S, Yang H T Y. Active suppression of panel flutter withpiezoelectric actuators using eigenvector orientation method. Journal of Soundand Vibration,2012,331:1469-1482.
[150]曹志远.板壳振动理论[M].北京:中国铁道出版社,1989,231-233.
[151]刘新东,刘伟.复合材料力学基础[M].西安:西北工业大学出版社,2010:101-104.
[152]李东旭.高等结构动力学[M].长沙:国防科技大学出版社,1997:232-237.
[153]叶献辉.壁板非线性气动弹性颤振及稳定性研究[D].成都:西南交通大学博士学位论文,53-54.
[154] Kirillov O N. A theory of the destabilization paradox in non-conservativesystems[J]. Acta Mechanica,2005,174:145-166.
[155] Kirillov O N, Verhulst F. Paradoxes of dissipation-induced destabilization orwho opend Whitney’s umbrella?[J]. Journal of Applied Mathematics andMechanics,2010,90(6):462-488.
[156]刘延柱,陈文良,陈立群.振动力学[M].北京：高等教育出版社:130-131.
[157]伍良生,顾仲权,张阿舟.阻尼动力吸振器减振问题的进一步研究[J].振动与冲击,1994,13(1):1-7.
[158]舒仲周,张继业,曹登庆.运动稳定性[M].北京：中国铁道出版社,2001：220-227.
[159]谢祚水.结构优化设计概念[M].北京：国防工业出版社，1997:52-57.
[2]曹秀云.近空间飞行器成为各国近期研究的热点（下）[J].中国航天,2006,7:30-32.
[3]蒋持平,柴慧,严鹏.近空间高超声速飞行器防热隔热与热力耦合研究进展[J].力学与实践,2011,33(1):1-9.
[4]陈予恕,郭虎伦,钟顺.高超声速飞行器若干问题研究进展[J].飞航导弹.2009,8:26-33.
[5]蔡亚梅,汪丽萍.美国的高超声速飞行器发展计划及关键技术分析[J].航天制造技术.2012,12(6):4-7.
[6]沈海军,程凯,杨莉.近空间飞行器[M].北京:航空工业出版社,2012：1-25
[7]李建林.临近空间高超声速飞行器发展研究[M].北京:中国宇航出版社,2012：1-4.
[8]孟凡颢,钟腾育.用壁板颤振理论解决某系列飞机的方向舵蒙皮裂纹故障[J].飞机设计2000,4:1-6
[9] Park J S, Kim J H, Moon S H. Thermal post-bulking and flutter characteristicsof composite plates embebded with shape memory alloy fibers[J]. CompositePart B: Engineering,2005,36:627-636.
[10]杨智春,夏巍,孙浩.高速飞行器壁板颤振的分析模型和分析方法[J].应用力学学报,2006,23(4):537-542.
[11] Garrick I E, Reed W H. Historical development of aircraft flutter[J]. Journal ofAircraft,1981,18(11):897-912.
[12]杨超,许赟,谢长川.高超声速飞行器气动弹性力学研究综述[J].航空学报,2010,31(1):1-11.
[13] Zhou R C, Xue D Y, Mei C. Finite element time domain modal formulation fornonlinear flutter of composite panels [J]. AIAA Journal,1994,32(10):2044-2052.
[14]王渤成,邵敏.有限单元法基本原理和数值方法[M].北京：清华大学出版社，1997：15-20.
[15] Cheng G F, Mei C. Finite element modal formulation for hypersonic panelflutter analysis with thermal effects[J]. AIAA,2004,42(4):687-695.
[16] Eastep F E, McIntosh S C. Analysis of nonliearn panel flutter and responseunder random excitation or nonlinear aerodynamic loading[J]. AIAA Journal,1971,9(3):411-418.
[17]黄琳,段志生,杨剑影.近空间高超声速飞行器对控制科学的挑战[J].控制理论与应用.2011,28(10):1496-1505.
[18] Dowell E H. A review of the aeroelastic stability of plates and shells[J]. AIAAJournal,1970,8(3):385-399.
[19] Bendiksen O O. Review of unsteady transonic aerodynamics: Theory andapplications. Progress in Aerospace Sciences,2011,47:135-167.
[20] Lighthill M J. Oscillating airfoils at high mach number[J]. Journal ofAeornautical Science,1953,20(6):402-406.
[21] Ashely H, Zartarian G. Piston theory-a new aerodynamic tool foraeroelastician[J]. Journal of Aeornautical Science,1956,23(10):1109-1118.
[22]陈劲松,曹军.超声速和高超声速翼型非定常气动力的一种近似计算方法[J].空气动力学报,1990,8(3):339-344.
[23]杨炳渊,宋伟力.用当地流活塞理论计算大攻角翼面超音速颤振[J].振动与冲击,1995,15(2):60-63
[24]王乐,王毅,南宫自军.活塞理论及其改进方法在超声速翼面颤振分析中的应用[J].导弹与航天运载技术.2011,4:13-17.
[25] Selvam R Qu P, Z Q, Zhen Q. Three-dimensional nonlinear panel flutter atsupersonic euler flow[C].43rd AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics, and Materials Conference, Denver, Colorado,2002.
[26] Dowell E H. Nonlinear oscillations of a fluttering plate. I[J]. AIAA Journal,1966,4(7):1267-1275.
[27] Scott R C, Weisshaar T A. Panel flutter suppression using adaptive materialactuators[J]. Journal of Aircraft,1994,31(1):213-222.
[28]张晓梅,任勇生,李磊.埋入SMA纤维的复合材料壁板的气弹稳定性研究[J].太原科技大学学报,2010,31(6):497-501.
[29] Olson M D. Finite elements applied to panel flutter[J]. AIAA Journal,1967,5(12):2267-2270.
[30] Rao K S, Rao G V. Large amplitude supersonic flutter of panels with endselastically restrained against rotation[J]. Computers and Structures,1980,11(3):197-201.
[31] Sarma B S, Varadan T K. Nonlinear panel flutter by finite element method.AIAA Journal,1988,26:566-574.
[32] Olson M D. Some flutter solutions using finite elements[J]. AIAA Journal,1970,8(4):747-752.
[33] Yuan K H, Qiu Z P. Nonlinear flutter analysis of stiffened composite panels insupersonic flow[J]. Science China Physics, Mechanics&Astronomy,53(2):336-344.
[34] Mei C, Rogers J L. Application of NASTRAN to large deflection supersonicflutter of panels. NASA TM X-3428,1976:67-97.
[35] Mei C. A finite element approach for nonlinear panel flutter. AIAA Journal,1977,15:1107-1110.
[36] Han A D, Yang T Y. Nonlinear panel flutter using high order triangular finiteelements[J]. AIAA Journal,1983,21:1453-1461.
[37] Jameson A, Schmidt W, Turkel E. Numerical solution of the euler equation byfinite volume methods using Runge-Kutta time stepping schemes[C].14thFluid and Plasma Dynamics Conference, California,1981.
[38] Atsushi H, Igor M, and Yoshiaki N. Panel Flutter Analysis with aFluid-Structure Coupled Scheme[C].33rd AIAA Fluid Dynamics Conferenceand Exhibit, Florida,2003.
[39] Epureanu B I, Tang L S, Paidousis M P. Coherent structures and their influenceon the dynamics of aeroelastic panels[J]. International Journal of Non-linearMechanics,2004,39:977-991.
[40] Selvam R P, Qu Z Q, Zheng Q. Efficient Method for Dynamic Condensation ofNonclassically Damped Vibration Systems[J]. AIAA Journal,2002,40(2):368-375.
[41]陈予恕.非线性振动[M].北京：高等教育出版社,2002:259-260.
[42] Morino L. A perturbation method for treating nonlinear panel flutterproblems[J]. AIAA Journal,1969,7(3):405-411.
[43] Kuo C C, Morino L, Dugundji L. Perturbation and harmonic balance fortreating nonlinear panel flutter[J]. AIAA Journal,1972,10:1479-1484.
[44] Kobayashi S. Flutter of a simply supported rectangular plates in a supersonicflow-two dimensional panel flutter, I simply supported, II clamped panels[J].Trans Japan Soc of Aeron and Space Sci1962,5,79-118.
[45] Bolotin V V, Grishke A A, Kounadis A N, Gantes C J. Nonlinear panel flutter inremote post-critical Domains[J]. International Journal of Nonlinear Mechanics,1998,33(5):753-764.
[46]胡海岩.应用非线性动力学[M].北京：航空工业出版社,2000:60-62.
[47] Bolotin V V. Nonconservative problems of the theory of elastic stability[M].New York: McMilian,1963:199-312.
[48] Eastep F E, McIntosh S C. Analysis of nonlinear panel flutter and responseunder random excitation or nonlinear aerodynamic loading. AIAA Journal,1971,9(3):411-418.
[49] Kuo C C, Morino L, Dugunji L. Perturbation and harmonic balance for tratingnonlinear panel flutter[J]. AIAA Journal,1972,10:1479-1484.
[50] Lau S L, Cheung Y K. Amplitude incremental variational principle fornonlinear vibration of elastic system[J]. Journal of Applied Mechanics,1981,48(4):959-964.
[51] Yuen S W, Lau S L. Effects of inplane load on nonlinear panel flutter byincremental harmonic balance method[J]. AIAA Journal,1991,29:1472-1479.
[52]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.
[53]陈大林,杨翊仁,胡绍全等.二维薄板在超音速气流作用下的热弹性颤振[J].西南交通大学学报,2007,42(6):691-694.
[54] Bolovin V V, Petrosky A V. Secondary bifurcation and global instability of anaeroelastic non-linear system in the divergence domain[J]. Journal of Soundand vibration,1996,191(3):431-451.
[55] Gray C E, Mei C. Finite element method for large-amplitude Two-Dimensionalpanel flutter at hypersonic speeds[J]. AIAA Journal,29(2):290-298.
[56] Xue D Y, Mei C. Finite element nonlinear panel flutter with arbitrarytemperatures in supersonic flow[J]. AIAA Journal,1993,31(1):154-162.
[57]范晨光.薄壳气动弹性非线性响应研究[D].成都，西南交通大学学位论文.2010:52-55.
[58]陈大林,杨翊仁,范晨光.用微分求积法计算二维薄板在超音速流中的非线性颤振[J].固体力学学报,2007,28(4):399-405.
[59]李鹏,杨翊仁,鲁丽.微分求积法分析二维亚音速壁板的失稳问题[J].动力学与控制学报.2012,10(1):11-14.
[60]梅冠华,张家忠.时滞惯性流形在三维壁板颤振数值分析中的应用[J].西安交通大学学报,2011,45(9):40-46.
[61] M R Brake, D J Segalman. Nonlinear model reduction of von Karman plateunder quasi-steady fluid flow[J]. AIAA Jounral,2010,48(10):2339-2347.
[62] Guo X Y, Mei C. Application of aeroelastic modes on nonlinear supersonicpanel flutter at elecated temperatures[J]. Computers and Sturctures,2006,84:1619-1628.
[63]赵秀芳，曹树谦.用Normal Form直接法研究壁板的热颤振与控制.振动与冲击[J].2012,13(11)：54-56
[64]丁千,陈予恕．机翼颤振的非线性动力学和控制研究[J]．科技导报，2009，27(2):53-61．
[65]丁千,王冬立.用规范型直接法研究立方非线性机翼的颤振[J].飞行力学,2005,23(3):85-88.
[66]丁然.气动力及热载荷作用下功能梯度材料矩形板的非线性动力学[D].天津，天津大学博士学位论文:1-7.
[67] Sohn K J, Kim J H. Nonlinear thermal flutter of functionally graded panelsunder a supersonic flow[J]. Composite Structures,2009,88:380-387.
[68] Lee S L, Kim J H. Thermal post-buckling and limit-cycle oscillation offunctionally graded panel with structural damping in supersonic airflow[J].Composite Strucures,2009,91:205-211.
[69] Ibrahim H H, Tawfik M, Ajmi M A. Non-linear panel flutter fortemperature-dependent functionally graded material panels[J]. ComputationalMechanics,2008,41:325-334.
[70] Prakash T, Ganapathi M. Supersonic flutter characteristics of functionallygraded flat panels including thermal effects[J]. Composite Structures,2006,72:10-18.
[71]阮苗,王忠民,王砚.陶瓷/金属非保守FGM斜板的颤振分析[J].中国机械工程,2011,22(13):1580-1584.
[72] Gray C E, Mei C, Shore C P. Finite element method for large-amplitudetwo-dimensional panel flutter at hypersonic speeds[J]. AIAA Journal,1991,29(2):290-298.
[73] Kouchakzadeh M A, Rasekh M, Haddadpour H. Panel flutter analysis ofgeneral laminated composite plates[J]. Composite Structures,2010,92:2906-2915.
[74]万志强,邵珂,杨超,王科.非均匀铺层壁板复合材料机翼气动弹性分析[J].复合材料学报,2008,25(1):196-199.
[75]杨智春,谭光辉,夏巍.铺层方式对复合材料壁板热颤振特性的影响[J].宇航学报,2008,29(3):1047-1052.
[76]王战玺，秦现生，白晶，李靖.复合材料层合板的颤振预测和模态交叉分析[J].振动与冲击,2012,30(12):7-11.
[77] Beloiua D M, Ibrahima R A, Pettit C L. Influence of boundary conditionsrelaxation on panel flutter with compressive in-plane loads[J]. Journal ofFluids and Structures,2005:743-767.
[78] Higuchi K, Dowell E H. Effect of structural damping on flutter of plates with afollower force[J]. AIAA Journal,1992,30(3):820-825.
[79]陈大林,杨翊仁,肖世富,胡绍全.超音速流中二维壁板的Hopf分叉[J].工程力学,2008,25(4):214-217.
[80]陈大林,杨翊仁,胡绍全.三维薄板在超音速气流作用下的非线性颤振研究[J].强度与环境,2008,35(2):12-17.
[81] Dowell E H. Nonlinear flutter of curved plates[J]. AIAA Journal,1969,7:424-431.
[82] Dowell E H. Nonlinear flutter of curved plates II[J]. AIAA Journal,1970,8:259-261.
[83] Dowell E H. Nonlinear oscillations of a fluttering plate II[J]. AIAA Journal,1967,5:1856-1862.
[84]高扬,杨智春.复合材料曲壁板与平壁板热颤振热性的对比[J].振动与冲击,2011,30(4):55-59.
[85]杨智春,周建,谷迎松.超音速气流中受热曲壁板的非线性颤振特性[J].力学学报,2012,44(1):30-38.
[86]周建,杨智春,贺顺.活塞理论气动力的静压修正方法及在曲壁板颤振分析中的应用[J].航空学报,2013,34(X): XXX-XXX.
[87]叶献辉,杨翊仁,肖艳平.热环境下三维壁板大气紊流动力响应分析[J].工程力学,2009,26(6):233-237.
[88]肖艳平,杨翊仁,叶献辉.边界松弛对壁板颤振响应的影响分析[J].工程力学,2012,29(11):40-45.
[89]苑凯华,邱志平.含不确定参数的复合材料壁板热颤振分析[J].航空学报,2010,31(1):119-124.
[90] Koo, K N, Hwang W S. Effects of hysteretic and aerodynamic damping onsupersonic panel flutter of composite plates [J]. Journal of Sound and Vibration,2004,273(3):569-583.
[91]张云峰,刘占生.粘弹壁板颤振的非线性动力特性[J].推进技术,2007,28(1):103-107.
[92]肖艳平,杨翊仁,叶献辉.三维粘弹壁板颤振分析[J].振动与冲击,2011,30(1):82-86.
[93] Gordnier R E, Visbal M R. Development of a three-dimensional viscousaeroelastic solver for nonlinear panel flutter. Journal of Fluids and Structures,2002,16:497-527.
[94]尹传家.飞行器的颤振.北京：原子能出版社,2007：241-252.
[95]中国人民解放军总装备部军事训练教材编辑工作委员会.高超声速气动热和热防护.北京：国防工业出版社，2003：37-45.
[96] Bisplinghoff R. Some structural and aeroelastic consideration of high-speedflight[J]. Journal of the Aerospace Science,1956,23(4):289-329.
[97]郭虎伦.非线性机翼的分岔特性分析及其参数控制[D].哈尔滨，哈尔滨工业大学博士学位论文：4-11.
[98] Budiansky B, Mayers J. Influence of aerodynamic heating on the effectivetorsional stiffness of thin wings[J]. Journal of the Aeronautical Sciences,1956,23(12):1081-1093.
[99]范绪箕.高速飞行器热结构分析与应用.国防工业出版社.北京,2009:21-23.
[100] Yang T Y, Han A D. Flutter of thermally buckled finite element panels. AIAAJournal,1976,14:975-977.
[101]夏巍,杨智春.超音速气流中受热壁板的稳定性分析[J].力学学报.2007,39(5):602-609.
[102]夏巍,杨智春,谷迎松.超声速气流中受热壁板的二次失稳型颤振[J].航空学报.2009.30(10):1851-1856.
[103]李丽丽,赵永辉.超音速下热壁板的颤振分析[J].动力学与控制学报.2012,10(1):67-70.
[104]叶献辉,杨翊仁.三维壁板热颤振分析[J].振动与冲击.2008,27(6):55-59.
[105]叶献辉,杨翊仁,范晨光.热环境下壁板非线性颤振分析[J].计算力学学报.2009,26(5):684-689.
[106]王晓庆,韩景龙,张军红.不同气流偏角下的壁板热颤振分析及多目标优化设计[J].航空学报.2010,31(11):2195-2201.
[107]苑凯华,邱志平.高超声速气流中复合材料壁板热颤振分析[J].南京航空航天大学学报.2010,43(3):313-317.
[108]周良强,陈予恕,陈芳启.超音速气流中受热壁板的非线性动力学分析[J].科学技术与工程.2010,10(19):4744-4747.
[109]杨智春,张蕊丽.基于最大李雅普诺夫指数的壁板热颤振特性分析[J].西北工业大学学报.2009,27(6):770-776.
[110]杨智春,夏巍,张蕊丽.温度分布对复合材料壁板颤振特性的影响[J].宇航学报.2010,31(3):850-854.
[111] Motagaly K A, Duan B, Mei C. Nonlinear panel response at high acousticexcitations and supersonic speeds[C].40th Structures, Structural Dynamics,and Materials Conference and Exhibit, St. Louis,1999.
[112] Ibrahim H H, Yoo H H, Tawfik M, Lee K S. Thermo-acoustic random responseof temperature-dependent functionally graded material panels[J]. ComputMech,2010,46:377-386.
[113] Ibrahim H H, Yoo H H, Lee K S. Supersonic flutter of functionally gradedpanels subjected to acoustic and thermal loads[J]. Journal of Aircraft,2009,46(2):593-600.
[114] Surace G, Udrescu R. Finite-element analysis of the fluttering panels excitedby external forces. Journal of Sound and Vibration,1999,224(5):917-935.
[115] Abdel M K, Duan B, Mei C. Active control of nonlinear panel flutter underyawed supersonic flow[J]. AIAA Paper,2003,2003-1514.
[116] Chandiramani N K, Plaut R H, Librescu L I. Nonperiodic flutter of a buckledcomposite panel[J]. Sadhana,1995,20:671-689.
[117]杨智春,夏巍.壁板颤振的分析模型、数值求解方法和研究进展[J].力学进展,2010,40(1):81-98.
[118]赵永辉.气动弹性力学与控制[M].北京：科学出版社，2007:11-16.
[119]尹坚平,刘鸿信,倪乃琛.动力吸振器用于抑制加肋薄板振动和声辐射的研究[J].同济大学学报,1989,17(2):195-203.
[120]孙朝晖,戴扬,王冲,孙进才.飞机壁板附加动力吸振器后的振动与声辐射[J].西北工业大学学报,1993,11(4):470-475.
[121]孙朝晖,孙进才,王冲,戴扬.动力吸振器用于提高壁板隔声量的研究[J].噪声与振动控制,1995,1:10-13.
[122]孙朝晖,戴扬,王冲,孙进才.飞机壁板减振降噪中动力吸振器的设计及实验研究[J].噪声与振动控制.1995,4:10-13.
[123]宛敏红.薄板结构的吸振控制研究[D].西北工业大学硕士学位论文.
[124]杨智春,杨飞,张玲凌.动力吸振器用于夹层壁板颤振抑制的研究[J].振动与冲击,2009,28(2):24-28.
[125]杨飞,杨智春,王巍.吸振夹层壁板颤振抑制的吸振器频率设计[J].振动与冲击，2009,28(7)：65-68
[126] Liao C L, Sun Y W. Flutter analysis of stiffened laminated composite platesand shells in supersonic flow[J]. AIAA Journal,1993,31(10):1897-1905.
[127] Lee D M, Lee I. Supersonic flutter analysis of stiffened isotropic andanisotropic panels[J]. AIAA Journal,1996,34(3):637-639.
[128] Oh I K, Lee I, Lee D M. Non-linear transient response of fluttering stiffenedcomposite plates subject to thermal load[J]. Journal of Sound and vibration,2001,245(4):715-736.
[129] Lee D M, Lee I. Vibration Analysis of Anisotropic Plates with EccentricStiffener[J]. Computers&Structures,1995,57(1):99-105.
[130]张晓梅,任勇生,李磊.埋入SMA纤维的复合材料壁板的气弹稳定性研究[J].太原科技大学学报,2010,31(6):497-501.
[131] Lee J J, Choi S. Thermal buckling and postbuckling analysis of a laminatedcomposite beam with embedded SMA Actuators[J]. Composite Structures,1999,47:695-703.
[132] Park J S, Kim J H, Moon S H. Thermal post-buckling and fluttercharacteristics of composite plates embedded with shape memory alloyfibers[J]. Composites: Part B,2005,36:627-636.
[133] Ibrahim H H, Tawfik M, Hani M N, Yoo H H. Aerothermoacoustic response ofshape memory alloy hybrid composite panels[J]. Journal of Aircraft,2009,46(5):1544-1555.
[134]李敏,陈伟民,贾丽杰.压电驱动器的气动弹性应用[J].航空学报.2009,30(12):2301-2310.
[135] Moon S H, Kim S J. Active and Passive Suppressions of Nonlinear PanelFlutter Using Finite Element Method. AIAA Journal,2001,39(11):2042-2050.
[136] Scott R C, Weisshaar T A. Controlling panel flutter using adaptive materials[J].Journal of Aircraft,1991,31:213-222.
[137] Zhou R C, Xue D Y, Mei Huang J K, Mei C. Suppression of nonlinear panelflutter with piezoelectric actuators using finite element methods[J]. AIAAJournal,1995,33:1098-1105.
[138] Zhou R C, Xue D Y, Mei Huang J K. Suppression of nonlinear panel flutter atsupersonic speeds and elevated temperatures[J]. AIAA Journal,1996,34:347-354
[139] Moon S H, Hwang J S. Panel flutter suppression with an optimal controllerbased on the nonlinear model using piezoelectric materials[J]. CompositeStructures,2005,68:371-379.
[140]苑凯华邱志平.压电复合材料壁板颤振的控制[J].北京航空航天大学学报.2009,35(12):1429-1433.
[141]宋智广,李凤明.主动约束层阻尼对超声速梁结构颤振特性的影响[J].固体力学学报.2010,31(SI):115-119.
[142] Li F M. Actice aeroelastic flutter suppression of a supersonic plate withpiezoelectric material[J]. International Journal of Engineering Science,2012,51:190-203.
[143] Sadri A M, Wright J R, Wynne R J. LQG control design for panel fluttersuppression using piezoelectric actuators. Smart Materials and Structures,2002,11:834-839.
[144] Onawola O O, Sinha S C. A feedback linearization approach for panel fluttersuppression with piezoelectric actuation. Journal of Computational andNonlinear Dynamics,2011,6(031006):1-8.
[145] Korbahti B. Specially orthotropic panel flutter control using PID controller.Acta Mech,2010,212:191-197.
[146]赵秀芳，曹树谦.用Normal Form直接法研究壁板的热颤振与控制[J].振动与冲击,2012,13(11)：54-56
[147] Chen G, Li Y, Yan G R. Active Control Law Design for Flutter/LCOSuppression Based on Reduced Order Model Method[J]. Chinese Journal ofAeronautics,2010,23:639-646
[148] Lee Y Y, Guo X. Non-linear vibration suppression of a composite panel subjectto random acoustic excitation using piezoelectric actuators. MechanicalSystems and Signal Processing,2007,21:1153-1173.
[149] Wang Z X, Qin X S, Yang H T Y. Active suppression of panel flutter withpiezoelectric actuators using eigenvector orientation method. Journal of Soundand Vibration,2012,331:1469-1482.
[150]曹志远.板壳振动理论[M].北京:中国铁道出版社,1989,231-233.
[151]刘新东,刘伟.复合材料力学基础[M].西安:西北工业大学出版社,2010:101-104.
[152]李东旭.高等结构动力学[M].长沙:国防科技大学出版社,1997:232-237.
[153]叶献辉.壁板非线性气动弹性颤振及稳定性研究[D].成都:西南交通大学博士学位论文,53-54.
[154] Kirillov O N. A theory of the destabilization paradox in non-conservativesystems[J]. Acta Mechanica,2005,174:145-166.
[155] Kirillov O N, Verhulst F. Paradoxes of dissipation-induced destabilization orwho opend Whitney’s umbrella?[J]. Journal of Applied Mathematics andMechanics,2010,90(6):462-488.
[156]刘延柱,陈文良,陈立群.振动力学[M].北京：高等教育出版社:130-131.
[157]伍良生,顾仲权,张阿舟.阻尼动力吸振器减振问题的进一步研究[J].振动与冲击,1994,13(1):1-7.
[158]舒仲周,张继业,曹登庆.运动稳定性[M].北京：中国铁道出版社,2001：220-227.
[159]谢祚水.结构优化设计概念[M].北京：国防工业出版社，1997:52-57.