用户名: 密码: 验证码:
旋翼柔性多体系统气动弹性研究
详细信息    本馆镜像全文|  推荐本文 |  |   获取CNKI官网全文
摘要
柔性多体系统动力学方法在旋翼气弹动力学分析中的应用是当前国内外的一个研究热点,为能建立旋翼多体系统气弹动力学模型,不论是柔性多体系统动力学方法还是旋翼动力学和气动建模都需要作相应的改进。本文开展了旋翼多体系统动力学建模方法研究,发展了可用于气弹分析的旋翼多体系统气弹动力学分析方法与程序,对分析方法各部分的准确性进行了验证,并将旋翼多体系统动力学模型应用于旋翼气弹分析中。
     本文首先建立了一种能够在多体系统动力学模型中应用,且适合于气弹分析的高精度桨叶动力学模型,并对模型的准确性和计算精度进行了验证。模型修正了桨叶预扭引起的剖面坐标基矢量非正交对应变能的影响,采用了准确的变形运动非线性几何关系,应变、动能以隐式表达并可采用位移有限元离散。为便于在多体系统动力学模型中与其它构件组合,通过代入数值后逐级展开提取了质量矩阵。由于桨叶与其它构件对接时对接面处约束力做功的计算过程和气动载荷做功一致,将约束力直接作为Lagrange乘子,最终得到含有对接面约束力的桨叶构件动力学方程。此外在高精度桨叶动力学模型的基础上对各环节的表达式进行精度的截断,得到了一种计算量较小,在小变形等情况下也足够准确的二阶精度桨叶动力学模型,用于模拟变距摇臂等弹性变形较小的构件。通过对模型桨叶加载后非线性变形的计算,变形状态下模型桨叶的频率计算,复合材料异形桨叶固有模态的计算与试验测试,验证了本文建立的高精度桨叶动力学模型的准确性。
     通过合并构件动力学方程并以约束方程体现构件之间的连接关系,建立旋翼多体系统动力学控制方程,并将旋翼气动载荷处理为非约束力元,以非完整约束的形式并入控制方程。通过建立铰链动力学方程和含铰链构件动力学方程,使识别非独立自由度的过程简化,约束方程的列写形式统一。旋翼连续旋转造成角位移约束方程求解中出现奇点,选择在旋转坐标系中建立以Rodriguez参数表示的角位移约束方程,相对旋转坐标系的转动始终为小量,从而避免了奇点的出现。旋翼气动力的计算采用非定常与动态失速模型和自由尾迹模型,通过对分布载荷做功表达式的分析,将旋翼气动力转换为一种非约束力元,在多体系统动力学模型中体现为一组非完整约束,从而使气动力的计算过程独立于桨叶构件的动力学建模,便于气动力计算中根据自身模型的需求设定计算步长和求解格式。
     旋翼多体系统动力学控制方程以广义坐标分离法进行缩并,得到只含有独立自由度的非线性刚性微分方程,发展了一套适合于此类方程直接积分求解的局部间断有限元积分方法。方程缩并中加入了约束协调模块,解决了约束违约问题。研究了局部间断有限元积分方法用于刚性方程积分计算的稳定性、阻尼和周期延迟等问题,并在积分方法中嵌入了Newton-Broyden组合法,解决了隐式求解格式中反复求取切线矩阵及其逆矩阵造成计算量过大的问题,显著提高了计算效率的同时,尤其适合用于旋翼多体系统动力学控制方程这种难以得到关于状态量Jacobi矩阵的方程求解瞬态响应。
     针对旋翼气弹动力学分析的需求,建立旋翼动力学方程与气动力方程耦合求解的瞬态响应以及周期稳态响应计算流程,研究了气弹动力学瞬态响应分析法中,桨距激振方式、衰减信号处理与阻尼识别等问题。采用本文的旋翼多体系统动力学建模方法构建无铰式旋翼和无轴承旋翼模型,以瞬态响应分析法计算悬停和前飞状态气弹稳定性,通过与试验数据对比验证了本文的建模方法、求解流程等各环节的正确性。此外还对比和分析了桨叶动力学模型、旋翼入流模型、响应求解方法等因素对气弹稳定性分析精度的影响,以及旋翼结构设计参数对旋翼摆振阻尼变化趋势的影响。
The rotor flexible multibody system dynamic model is a research focus in rotor aeroelasticdynamics field. To introduce the flexible multibody system dynamics method into the rotor dynamicsmodeling, corresponding improvement should be implemented for multibody system dynamics androtor dynamics modeling. The rotor flexible multibody system dynamical model and its solutionmetheod of dynamic response have been investigated. To verify the developed model and method, thetransient analysis of a model blade and the aeroelastic analysis of rotors are also presented in thisdissertation.
     A high accuracy component dynamic model of rotor blade is developed, which is suitable foraeroelasticity analysis of rotor and integrated into flexible multibody system dynamic model easily.The nonorthogonal of base vectors in a helix coordinates, caused by the pretwist of the blade, and itsinfluence on the finite deflection strain tensor of the blade dynamic model is correlated. The exactnonlinear deflection geometry is also adopted. The implicit expressions of strain energy and kineticenergy could be discreted by displacement finite element. For the convenience of integrating intoflexible multibody system dynamic model, mass matrix is extracted using recurrence method. As theexpression form of the work of airload and constraint loads are the same, the Lagrange multipliers inthe component dynamic equations are represented by the constraint force directly. Based on the highaccuracy component dynamic equations, a second order accuracy blade component model is alsoobtained, which is suitable for modeling the small deflection and with much lower computationalcomplexity than the accuracy component model. To verify the correctness of the analysis result, aspecial-shaped blade mode test is conducted. Correlations between the analysis results and theexperimental data from Princeton beam test and Minguet’s composite beam experiments are alsoimpelementd.
     The rotor multibody system dynamic control equations are composed of the component dynamicequations, holonomic constraint equations and nonholonomic constraint equations. Connectionsbetween the structural components of rotor system produce the holonomic constraint equations, andnonholonomic constraint equations are produced in force elements used for airloads modeling. Tosimplify the form of holonomic constraint equations, the joint dynamic equations are introduced, andthe dynamic equations of component containing a joint are deduced. To avoid singularities for largerotations of the rotor, the angular constraint equations, expressed by Rodriguez parameters, are modified by introduced a nominal motion. The rotor airloads are calculated from the unsteady airfoilaerodynamics with dynamic stall and free wake model. Force elements of rotor airloads are alsodeduced, and integrated into the rotor multibody system as the nonholonomic constraints, in order toseparate the solution procedure of the aerodynamic model from the solution of multibody systemdynamic control equations.
     Using the generalized coordinate partitioning algorithm, dynamic control equations of rotormultibody system, with differential algebraic form, are reduced to ordinary differencal equations, anda locoal discontinuous Galerkin (LDG) integration method is developed to solve the equations. Thespectral radius, algorithmic damping and period elongation of LDG method are investigated.According to the nonlinear implicit expression and high stiffness ratio of the system equations, theLDG method, which is an implicit integration algorithm, are modified by combining with theNewton-Broyden method. The LDG integration method exhibits excellent numerical stability, andwithout calculating the Jacobi matrices and their inverse matrices, the method also exhibits goodcomputational efficiency.
     To verify the correctness of the developed rotor flexible multibody system dynamic model andtransient intergration method, the transient analysis of model blade and the aeroelastic analysis ofmodel rotor are implemented. The influence study of stability analysis method, blade structure modeland inflow model is also implemented. It demonstrates that the developed method is useful forimproving computation precision of aeroelastic stability.
引文
[1] Philippe G. How technology has served and will serve the cost reduction target. Proceeding of55th Annual Forum of the American Helicopter Society. AHS Inc, Montreal, Canada,1999:2353-2362.
    [2] Ni Xianping, Cai Ruhong, Cao Xijin, et al. Present situation and prospects of helicoptertechnology. Proceeding of60th Annual Forum of the American Helicopter Society. AHS Inc,Baltimore MD,2004:1-11.
    [3] Donald L K. Comprehensive rotorcraft analysis: past, present and future. Proceeding of46thAIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference,Austin, TX, United states,2005:5502-5512.
    [4] Johnson W. Comprehensive analytical model of rotorcraft aerodynamics and dynamics,volume I: theory. Johnson Aeronautics, Palo Alto, California,2006.
    [5] Johnson W. Comprehensive helicopter analysis: a state-of-art review. Washington D C:NASA-TM-78539,1978.
    [6] Ajay S. Design and development of a four-bladed bearingless main rotor system for theUSMC H-1upgrade program. Proceeding of55th Annual Forum of the American HelicopterSociety. AHS Inc, Quebec, Canada,1999:2157-2169.
    [7] Yoshiyuki Niwa. The development of the new observation helicopter (XOH-1). Proceeding of54th Annual Forum of the American Helicopter Society. AHS Inc, Washington, DC,1998:1285-1297.
    [8] Legender P. Spheriflex rotor hub:15years of continuous improvement. Proceeding of57thAnnual Forum of the American Helicopter Society. AHS Inc, Washington DC,2001.
    [9] Sivaneri N T, Chopra I. Finite element analysis for bearingless rotor blade aeroelasticity.Journal of the American Helicopter Society,1984,29(2):42-51.
    [10] Dixon P G C, Bishop H E. The bearingless main rotor. Journal of the American HelicopterSociety,1980,25(3):15-21.
    [11] Pitt D M, Peters D A. Theoretical prediction of dynamic inflow derivatives. Proceeding of6thEuropean Rotorcraft and Powered Lift Aircraft Forum, England,1980: No.47.
    [12] He Chengjian. Development and application of a generalized dynamic wake theory for liftingrotor [Ph.D. thesis]. Georgia Institute of Technology, Atlanta, Georgia,1989.
    [13] Greenberg J M. Airfoil in sinusoidal motion in pulsating streem. NACA Report, TN1326,1947.
    [14] Wayne J. Helicopter theory. Washington D C: Dover Publications,1994.
    [15] Bramwell A R S, Done G, Balmford D. Bramwell’s helicopter dynamics. Washington D C:American Institute of Aeronautics and Astronautics,2001.
    [16] Stewart, W. Higher harmonics of flapping on the helicopter rotor. Aeronautical ResearchCouncil, CP121,1952.
    [17] Zbrozek, J K. The simple harmonic motion of a helicopter rotor with hinged blades.Aeronautical Research Council R&M2813,1949.
    [18] Bagai A. Contributions to the mathematical modeling of rotor flow-fields using apseudo-implicit free-wake analysis [Ph.D. thesis]. College Park, Maryland: University ofMaryland,1995.
    [19] Ballin M G. Validation of a real-time engineering simulation of the UH-60A helicopter.NASA-TM-88360,1987.
    [20] Houbolt J C, Brooks G W. Differential equations of motion for combined flapwise bending,chordwise bending and torsion of twisted nonuniform rotor blades. NACA Report,1346,1958.
    [21] Bennett R L. Rotor system design and evaluation using a general purpose helicopter flightsimulation program. Specialists Meeting on Helicopter Rotor Loads Prediction Methods,Milan, Italy, March1973: AGARD-CP-122.
    [22] Bielawa R L. Aeroelastic analysis for helicopter rotor blades with time-variable, nonlinearstructural twist and multiple structural redundancy. NASA-CR-2638,1976.
    [23] Johnson W. A comprehensive analytical model of rotorcraft aerodynamics and dynamics, part I:analysis development. NASA-TM-81182,1980.
    [24] Johnson W. Assessment of aerodynamic and dynamic models in a comprehensive analysis forrotorcraft. Computers and Mathematics with Applications,1986,12(1).11-28.
    [25] Friedmann P P, Tong P. Dynamic nonlin earelastic stability of helicopter rotor blades in hoverand in forward flight. NASA-CR-114485,1972.
    [26] Friedmann P P, Tong P. Non-linear flap-lag dynamics of hingeless helicopter blades in hoverand in forward flight. Journal of Sound and Vibration,1973,30(1):9–31.
    [27] Ormiston R A, Hodges D H. Linear flap-lag dynamics of hingeless helicopter rotor blades inhover. Journal of the American Helicopter Society,1972,17(2):2-14.
    [28] Hodges D H, Ormiston R A, Peters D A. On the nonlinear deformation geometry ofeuler-bernoulli beam. NASA-TP-1566,1980.
    [29] Hodges D H, Dowell E H. Nonlinear equation of motion for the elastic bending and torsion oftwisted nonuniform rotor blades. NASA-TN-D-7818,1974.
    [30] Hodges D H, Ormiston R A, Robert A. Stability of elastic bending and torsion of uniformcantilever rotor blades in hover with variable structural coupling. NASA-TN-D8192,1976.
    [31] Rosen A, Friedmann P P. Nonlinear equations of equilibrium for elastic helicopter or windblades undergoing moderate deformation. NASA-CR-159478,1978.
    [32] Rosen A, Friedmann P P. The nonlinear behavior of elastic slender straight beams undergoingsmall strains ans moderate rotations. Journal of Applied Mechanics,1978,46(1):161-168.
    [33] Bir G, Chopra I. University of Marrland Advanced Rotorcraft Code (UMARC) TheoryManual[R]. UM Aero Report,1992.
    [34] Hodges D H. Discussion of the nonlinear behavior of elastic slender straight beamsungergoing small strain and moderate rotations. Journal of Applied Mechanics,1980,47(3):688-689.
    [35] Hodges D H. Torsion of pretwisted beams due to axial loading. Journal of Applied Mechanics,1980,47(2):393-397.
    [36] Dowell E H, Traybar J J. An experimental study of the nonlinear stiffness of a rotor bladeundergoing flap, lag and twist deformations. AMS Report1194, New Jersey: PrincetonUniversity,1975.
    [37] Dowell E H, Traybar J J. An experimental theoretical correlation study of nonlinear bendingand torsion deformation of a cantilever beam. Journal of Sound and Vibration,1977,50(4):533-544.
    [38] Minguet P, Dugundji J. Experiments and analysis for composite blades under large deflectionsPart I: static behavior. AIAA Journal,1990,28(9):1573-1579.
    [39] Minguet P, Dugundji J. Experiments and analysis for composite blades under large deflectionsPart II: dynamic behavior. AIAA Journal,1990,28(9):1580-1588.
    [40] Maier T H. Aeroelastic stability for straight and swept-tip rotor blades in hover and forwardflight. Proceeding of55th Annual Forum of the American Helicopter Society, AHS Inc.,Washington D C: AHS International,1999:1031-1047
    [41] Maier T H, Sharpe D L. Fundamental investigation of hingless rotor aeroelastic stability.Proceeding of51th Annual Forum of the American Helicopter Society, AHS Inc., WashingtonD C,1995:1176-1190
    [42] Chopra I. Dynamic stability of bearingless circulation control rotor blade in hover. Journal ofthe American Helicopter Society,1985,30(4):40-47
    [43] Peters D A, Ormiston R A. The effect of second order blade bending of the angle of attack ofhingeless rotor blades. Journal of the American Helicopter Society,1973,18(4):45-48.
    [44] Danielson D A, Hodges D H. A beam theory for large global rotation, moderate local rotation,and small strain. Journal of Applied Mechanics,1988,55(1):179-184.
    [45] Danielson D A, Hodges D H. Nonlinear Beam Kinematics by Decomposition of the RotationTensor. Journal of Applied Mechanics,1987,54(2):258-262.
    [46] Hodges D H. Nonlinear equation for dynamics of pretwisted beams undergoing small strainand large rotations. NASA-TP-2470,1985.
    [47] Hodges D H. A mixed variational formulation based on exact intrinsic equations for dynamicsof moving beams. International Journal of Solids and Structures,1990,26(11):1253-1273.
    [48] Atilgan A R, Hodges D H, Fulton M V, et al. Application of the variational-asymptoticalmethod to static and dynamic behavior of elastic beams. Proceedings of the32nd Structures,Structural Dynamics, and Materials Conference, Baltimore, Maryland,1991, AIAA Paper91-1026:1078-1093.
    [49] Bauchau O A, Hong C H. Nonlinear composite beam theory. Journal of Applied Mechanics,1988,55(1):156–163.
    [50] Bauchau O A, Hong C H. Large displacement analysis of naturally curved and twisted beams.AIAA Journal,1987,25(11):1469–1475.
    [51] Shang Xiaoyang, Hodges D H. Aeroelastic stability of composite rotors in hover. Proceedingsof the36th Structures, Structural Dynamics and Materials Conference, New Orleans,Louisiana,1995, AIAA Paper95-1453.2602-2610.
    [52] Crespo D S, Marcelo R M, Hodges D H. Nonlinear flexure and torsion of rotating beams withapplication to helicopter rotor blades-I formulation. Vertica,1986,10(2):151-169.
    [53] Crespo D S, Marcelo R M, Hodges D H. Nonlinear flexure and torsion of rotating beams withapplication to helicopter rotor blades-II response and stability results. Vertica,1986,10(2):171-186.
    [54] Wang J M, Chopra I, Samak D J, et al. Theoretical and experimental investigation ofaeroelastic stability of an advanced bearingless rotor in hover and forward flight. Proceedingsof the American Helicopter Society National Specialists’ Meeting on Rotorcraft Dynamics,Arlington, Texas,1989.
    [55] Friedmann P P. Recent trends in rotary-wing aeroelasticity. Vertica,1987,11(2):139-170.
    [56] Chopra I. Perspectives in aeromechanical stability of helicopter rotors. Proceedings of theAmerican Helicopter Society National Specialists’ Meeting on Rotorcraft Dynamics, Arlington,Texas,1989
    [57] Celi R, Friedmann P P. Rotor blade aeroelasticity in forward flight with an implicitaerodynamic formulation. Proceedings of the AIAA/ASME/ASCE/AHS28th Structures,Structural Dynamics and Materials Conference, Monterey, California,1987,AIAA-87-0921-CP:730-742.
    [58] Celi R. Helicopter rotor blade aeroelasticity in forward flight with an implicit structuralformulation. Proceedings of the AIAA/ASME/ASCE/AHS32nd Structures, StructuralDynamics and Materials Conference, Baltimore, Maryland,1991, AIAA-91-1219-CP:2051-2058.
    [59]李攀.旋翼非定常自由尾迹及高置信度直升机飞行力学建模研究.[博士学位论文].南京:南京航空航天大学,2010.
    [60] Li Pan, Chen Renliang. A mathematical model for helicopter comprehensive analysis. ChineseJournal of Aeronautics,2010,23(3):320-326.
    [61] Johnson W. Comprehensive analytical model of rotorcraft aerodynamics and dynamics,volume II: components theory. Johnson Aeronautics, Palo Alto, California,2006.
    [62] Johnson W. Comprehensive analytical model of rotorcraft aerodynamics and dynamics,volume III: rotorcraft theory. Johnson Aeronautics, Palo Alto, California,2006.
    [63] Stephens W B, Rutkowski M J, Ormiston R A, et al. Development of the second generationcomprehensive helicopter analysis system (2GCHAS). Proceedings of the AmericanHelicopter Society National Specialists’ Meeting on Rotorcraft Dynamics, Arlington, Texas,1989.
    [64] Rutkowski M J, Ruzicka G C, Ormiston R A, et al. Comprehensive aeromechanics analysis ofcomplex rotorcraft using2GCHAS. Journal of the American Helicopter Society,1995,40(4):3-17.
    [65] Saberi H, Khoshlajeh M, Ormiston R A, et al. Overview of RCAS and application to advancedrotorcraft problems. Proceedings of the American Helicopter Society4th DecennialSpecialists’ Conference on Aeromechanics, San Francisco, California,2004:741-781.
    [66] Bauchau O A, Kang N K. A multibody formulation for helicopter structural dynamic analysis.Journal of the American Helicopter Society,1993,38(2):3-14.
    [67] Bauchau O A, Nikishkov Y G. An implicit transition matrix approach to stability analysis offlexible multibody systems. Multibody System Dynamics,2001,5:279–301.
    [68] Bauchau O A, Bottasso C L, Nikishkov Y G. Modeling rotorcraft dynamics with finite elementmultibody procedures. Mathematical and Computer Modeling,2001,33:1113–1137.
    [69] Bauchau O A, Wang Jielong. Efficient and robust approaches for rotorcraft stability analysis.Journal of the American Helicopter Society,2010,55(3):32006-1-12.
    [70] Vlasov V Z. Thin walled elastic beams, translated from Russian. Washington D C:1961.
    [71] Gjelsvik A. The theory of thin walled bars. New York: A Wiley-Interscience Publication,1981.
    [72] Nelson R, Bauld JR, Tzeng L-S. A Vlasov theory for fiber-reinforced beams with thin-walledopen cross sections. International Journal of Solids and Structures,1984,20(3):277-297.
    [73] Chandra R, Chopra I. Vibration characteristics of composite I-beams with elastic couplingsunder rotation. AHS Annual Forum47th, Phoenix: AHS,1991:661-674.
    [74] Chandra R, Chopra I. Experimental and theoretical analysis of composite I-beams with elasticcouplings. AIAA Journal,1991,29(12):2197-2206.
    [75] Chandra R, Chopra I. Structural behavior of two-cell composite rotor blades with elasticcouplings. AIAA Journal,1992,30(12):2914-2912.
    [76] Floros M W, Smith E C. Finite element modeling of open-section composite beams withwarping restraint effects. AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, andMaterials Conference and Exhibit37th, Salt Lake City: AIAA,1996:1420-1430.
    [77] Centolanza L R, Smith E C. Refined structural modeling of thick-walled closed sectioncomposite beams. AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, andMaterials Conference and Exhibit39th, Long Beach: AIAA,1998:552-568.
    [78] Jung S N, Nagaraj V T, Chopra I. Refined structural model for thin-and thick-walledcomposite rotor blades. AIAA Journal,2002,40(1):105-116.
    [79] Reddy J N, Liu C F. A higher-order theory for geometrically nonlinear analysis of compositelaminates. NASA CR4056,1987.
    [80] Reddy J N. A simple higher-order theory for laminated composite plates. Journal of AppliedMechanics,1984,51:745-752.
    [81] Reddy J N. Geometrically nonlinear transient analysis of laminated composite plates. AIAAJournal,1983,21(4):621-629.
    [82] Reddy J. A refined nonlinear theory of plates with transverse shear deformation. InternationalJournal of Solids and Structures,1984,20(9-10):881-896.
    [83] Hong C H, Chopra I. Aeroelastic stability analysis of a composite rotor blade. Journal of theAmerican Helicopter Society,1985,30(2):57-67.
    [84] Smith E C, Chopra I. Formulation and evaluation of an analytical model for compositebox-beams. Journal of the American Helicopter Society,1991,36(3):23-35.
    [85] Tracy A L, Chopra I. Aeroelstic analysis of a composite bearingless rotor in forward flightusing an improved warping model. Journal of the American Helicopter Society,1995,40(3):80-91.
    [86] Kosmatka J B. Flexure-torsion behavior of sheat-deformable beams with applications toaircraft wing sections. AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics andMaterials Conference33rd, Dallas: AIAA,1992:13-15.
    [87] Giavotto V, Borri M, Mantegazza P, et al. Anisotropic beam theory and application. Computersand Structures,198316(1-4):403-413
    [88] Hodges D H. Nonlinear composite beam theory. Virginia: AIAA,2006:262-269.
    [89] Hodges D H, Atilgan A R, Cesnik C E S, et al. On a simplified strain energy function forgeometrically nonlinear behaviour of anisotropic beams. Composites Engineering,1992,2(5-7):513-26.
    [90] Volovoi V V, Hodges D H, Berdichevsky V L, et al. End effects in thin-walled beams. AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference andExhibit37th, Salt Lake City: AIAA,1996:15-17.
    [91] Volovoi V V, Hodges D H, Berdichevsky V L, et al. Construction of dynamical theories forelastic anisotropic beams. AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics,and Materials Conference and Exhibit38th, Kissimmee: AIAA,1997:7-10.
    [92] Volovoi V V, Yu W, Hodges D H. Asymptotic treatment of the Vlasov effect for compositebeams.43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and MaterialsConference, Denver: AIAA,2002:1-6.
    [93] Yu W, Hodges D H, Volovoi V V, et al. The Vlasov Theory of the Variational AsymptoticBeam Sectional Analysis.45th AIAA/ASME/ASCE/AHS/ASC Structures, StructuralDynamics and Materials Conference, Palm Springs: AIAA,2004:19-22.
    [94] Yu, W, Hodges D H, Volovoi V V, et al. A generalized Vlasov theory for composite beams.Thin-Walled Structures,2005,43(9):1493-1511.
    [95] Hodges D H, Yu W, Patil M J. Geometrically-exact, intrinsic theory for dynamics of movingcomposite plates. International Journal of Solids and Structures,2009,46(10):2036-2042.
    [96]王浩文,大变形复合材料柔性梁理论分析与试验研究.[硕士学位论文].南京:南京航空航天大学,1994.
    [97]向锦武.大变形复合材料柔性梁静、动特性分析与试验.[博士后研究工作报告].南京:南京航空航天大学,1995.
    [98] Bir G, Chopra I. University of Marrland Advanced Rotorcraft Code (UMARC) Theory Manual.UM-Aero Report,92-02,1992
    [99] Bir G, Chopra I. Status of University of Maryland Advanced Rotorcraft Code (UMARC).Proceedings of the American Helicopter Society Aeromechanics Specialists Conference, SanFrancisco, California,1994.
    [100] Floros M W. Elastically tailored composite rotor blades for stall alleviation and vibrationreduction [Ph.D. thesis]. The Pennsylvania State University,2000.
    [101] Nixon M W. Aeroelastic response and stability of tiltrotors with elastically-coupled compositerotor blades [Ph.D. thesis]. The University of Maryland,1993
    [102]陆佑方.柔性多体系统动力学.北京:高等教育出版社,1996..
    [103]洪嘉振.计算多体系统动力学.北京:高等教育出版社,1999.
    [104] Shabana A A. Dynamics of multibody systems. Cambridge: Cambridge University Press,2005.
    [105] Amirouche F. Fundamentals of multibody dynamics. theory and applications. Boston:Birkh user Boston.2005.
    [106] Edmund W, Iwona A W, Stanislaw W. Dynamics of flexible multibody systems: rigid finiteelement method. Berlin Heidelberg: Springer,2006..
    [107] Wittenburg J. Dynamics of multibody systems(2nd edition). Berlin Heidelberg: Springer,2008.
    [108] Bremer H. Elastic multibody dynamics: a direct Ritz approach. Berlin Heidelberg: Springer,2008.
    [109] Bauchau O A. Flexible multibody dynamics. Netherlands: Springer,2011.
    [110] Hodges D H, Hopkins A S, Kunz D L, et al. General Rotorcraft Aeromechanical Stabilityprogram (GRASP), theory manual. USAAVSCOM-TM-89-A-003,1990.
    [111] Kunz D L, Hodges D H. Analytical modeling of helicopter static and dynamic inducedvelocity in GRASP. USAAVSCOM-TR-87-A-11,1987.
    [112] Nguyen K, Johnson W. Evaluation of dynamic stall models with UH-60A airloads flight testdata. Proceedings of the American Helicopter Society54th Annual Forum, Washington, D.C.,1998.
    [113] Johnson W. Calculation of tilt rotor aeroacoustic model (TRAM DNW) performance, airloads,and structural loads. Proceedings of the American Helicopter Society AeromechanicsSpecialists' Meeting, Atlanta, GA,2000.
    [114] Yeo H, Shinoda P M. Investigation of rotor loads and vibration at transition speed.Proceedings of the American Helicopter Society58th Annual Forum, Montreal, Canada,2002.
    [115] Blackwell R, Millott T A. Dynamics design characteristics of the Sikorsky X2technologydemonstrator aircraft. Proceedings of64th Annual Forum of the American Helicopter Society,Montreal, Canada,2008.
    [116]王浩文,韩东,高正.考虑带有任意刚性运动的旋翼桨叶响应计算方法.振动工程学报,2006,19(3):46-50.
    [117]王益锋,王浩文,高正,等.基于多体系统动力学的旋翼桨叶响应计算方法.直升机技术,2007,151(3):20-24.
    [118]李海旭,屈香菊,王维军.倾转旋翼的多体运动建模与仿真,航空学报(英文),2010,23(4):415-422.
    [119] Leishman J G, Beddoes T S. A generalized method for unsteady airfoil behavior and dynamicstall using the indicial method. Proceedings of42nd Annual Form of the American HelicopterSociety, Washington D C,1986
    [120] Leishman J G, Beddoes T S. A semi-empirical model for dynamic stall. Journal of theAmerican Helicopter Society,1989,34(3):7-16.
    [121] Leishman J G. Principles of helicopter aerodynamics second edition. Cambridge: CambridgeUniversity Press,2007.
    [122] Landgrebe A J. The wake geometry of a hoving helicopter rotor and its influence on rotorperformance. Journal of the American Helicopter Society,1972,17(4):3-15.
    [123] Bhagwat M J. Mathematical modeling of the transient dynamics of helicopter rotor wakesusing a time-accurate free-vortex method [Ph.D. thesis]. College Park, Maryland: Universityof Maryland,2001.
    [124] Scully M P. Computation of helicopter rotor wake geometry and its influence on rotorharmonic airloads [Ph.D. thesis]. Massachusetts: Massachusetts Institute of Technology,1975.
    [125] Miller W O, Bliss D B. Direct periodic solutioin of rotor free wake calculation. Journal of theAmerican Helicopter Society,1993,38(2):53-60.
    [126] Crouse J G L, Leishman J G. A new method for improved rotor free wake convergence.Proceedings of the31st AIAA Aerospace Sciences Meeting, Reno, Nevada,1993:.AIAA-93-0872,
    [127]赵景根,高正,徐国华.直升机旋翼/机身气动干扰计算方法.南京航空航天大学学报.2000,32(4):369-374.
    [128]李春华.时间精确自由尾迹方法建模及(倾转)旋翼气动特性分析.[博士学位论文].南京:南京航空航天大学,2007.
    [129]刘伦德.带叶间减摆器直升机气动机械稳定性研究.[硕士学位论文].南京:南京航空航天大学,2006.
    [130] Shabana A A, Bauchau O A, Hulbert G M. Integration of large deformation finite element andmultibody system algorithms. Journal of Computational and Nonlinear Dynamics,.2007,2(4),351-359.
    [131] Bauchau O A, Wang J L. Stability analysis of complex multibody systems. Journal ofComputational and Nonlinear Dynamics,2006,1(1),71-80.
    [132] Borri M, Lanz M, Mantegaza P. Helicopter rotor dynamics by finite element timediscretization. L'Aerotec. Missili Spazio,1981,60(4):193-200.
    [133] Borri M. Helicopter rotor dynamics by finite element time approximation. Computers andMathematics with Applications,1986,12(1):149-160.
    [134] Bauchau O A, Theron N J. Energy decaying schemes for nonlinear beam models. ComputerMethods in Applied Mechanics and Engineering,1996,134:37–56
    [135] Bauchau O A, Theron N J. Energy decaying schemes for nonlinear elastic multibody systems.Computers and Structures,1996,59(2):317–331.
    [136]王浩文.复合材料板壳动力学特性研究及直升机旋翼/机身气弹稳定性分析.[博士学位论文].北京:清华大学,1998.
    [137]王浩文.直升机旋翼系统非定常载荷计算.[博士后研究工作报告].南京:南京航空航天大学,2009.
    [138]虞志浩,董凌华,邓景辉,等.旋翼异形桨叶大变形气弹动力学分析与试验研究[J].南京航空航天大学学报,2011,43(3):312-317.
    [139] Johnson W. Rotorcraft dynamics models for a comprehensive analysis. Proceedings of theAmerican Helicopter Society54th Annual Forum, AHS Inc., Washington, D.C.,1998.
    [140]蔡蒨蒨,许履瑚,梁在中,等.实用数学手册.北京:科学出版社,1992.
    [141]郭日修.弹性力学与张量分析.北京:高等教育出版社,2003.
    [142]黄克智,薛明德,陆明万.张量分析(第2版).北京:清华大学出版社,2003.
    [143]虞志浩,杨卫东,张呈林.基于多体动力学的旋翼模型与气弹稳定性.航空动力学报,2012,27(5).
    [144] Hodges D H. Review of composite rotor blade modeling. AIAA Journal,1990,28(3):561–565
    [145]施妙根,顾丽珍..科学和工程计算基础.北京:清华大学出版社,1999.
    [146] Hopkins A S, Scientist R, Ormiston R A, et al. An examination of selected problems in rotorblade structural mechanics and dynamics. Journal of the American Helicopter Society,2006,51(1):104-125.
    [147]杨卫东,邓景辉.直升机后掠桨尖旋翼气弹稳定性研究.南京航空航天大学学报,2003,35(3):248-252.
    [148] Bhagwat M J, G.Leishman J G. Generalized viscous vortex core model for application tofree-vortex wake and aeroacoustic calculations. The58th Annual Forum and TechnologyDisplay of the American Helicopter Society International. Montreal, Canada: AHS,2002:2042-2057.
    [149] Bhagwat M J, Leishman J G. Stability analysis of helicopter rotor wakes in axial flight. Journalof the American Helicopter Society,2000,45(3):165-178.
    [150] Quackenbush T R, Bliss D B, Wshspress D A, et al. Free wake analysis of hover performanceusing a new influence coefficient method. NASA CR4309,1990.
    [151] Elliot J W, Althoff S L, Sailey R H. Inflow measurement made with a laser velocimeter on ahelicopter model in forward flight, volume I: rectangular platform blades at an advance ratioof0.15. NASA TM100541,1988.
    [152] Elliot J W, Althoff S L, Sailey R H. Inflow measurement made with a laser velocimeter on ahelicopter model in forward flight, volume II: rectangular platform blades at an advance ratioof0.23. NASA TM100542,1988.
    [153] Ghee T A, Beerry J D, Zori L A, et al. Wake geometry measurements and analyticalcalculations on a small-scale rotor model. NASA-TP-3584.
    [154] Ghee T A, Elloit J W. The wake of a small-scale rotor model in forward flight using flowvisualization. Journal of the American Helicopter Society,1995,40(3):52-65.
    [155] Baumgarte E. Stabilization of constraints and integrals of motion in dynamic system.Computer Methods in Applied Mechanics and Engineering,1972,1(1):1-16
    [156] Baumgarte E. A new method of stabilization for holonomic constrains. Journal of AppliedMechanics,1982,50(4):869-870
    [157]张雄,王天舒.计算动力学.北京:清华大学出版社,2007.
    [158]邱吉宝,向树红,张正平.计算结构动力学.合肥:中国科学技术大学出版社,2009.
    [159]徐岩.非线性波动方程的间断有限元方法.[博士学位论文].合肥:中国科学技术大学,2005.
    [160] Bauchau O A. Computational schemes for flexible, nonlinear multibody systems. MultibodySystem Dynamics,1998,2:169–225.
    [161] Bauchau O A, Bottasso C L. On the design of energy preserving schemes for flexible,nonlinear multibody systems. Computer Methods in Applied Mechanics and Engineering,1999,169:61–79.
    [162] Bauchau O A, Bottasso C L, Trainelli L. Robust integration schemes for flexible multibodysystems. Computer Methods in Applied Mechanics and Engineering,2003,192:395–420.
    [163] Hulbert G M. Time finite element methods for structural dynamics. International Journal fornumerical methods in engineering,1992,33(1):307-331
    [164] Subramanian S, Ma G, Gaonkar G H, et al. Correlation of several aerodynamic models andmeasurements of hingeless-rotor trim and stability [J]. Journal of the American HelicopterSociety,2000,45(2):106-117.

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700