液体火箭的多体动力学建模与仿真研究
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摘要
液体火箭是典型的时变系统，也是复杂的动力学耦合系统，其动力学问题对于火箭的设计与研制极为重要。本文采用多体动力学方法研究液体火箭的动力学建模与仿真问题，主要开展三方面工作：
首先，提出了变质量液体火箭的多体动力学建模方法。先基于有限段方法建立未加注火箭的柔性多体系统模型，再提出变质量质点系的达朗贝尔-拉格朗日原理，并结合拉氏乘子法建立柔性变质量充液贮箱的多体建模单元，然后提出变质量贮箱时变晃动的等效力学模型和变质量质点的建模方法。最后，采用状态空间方程方法实现了时变控制在多体系统中的建模；采用约束力方程方法实现了火箭分离过程的多体建模；采用谐波叠加法生成随机样本，实现了火箭跨音速抖振的多体动力学建模；考虑地球外形及其自转，给出了各项时变外载荷的多体建模方法。液体火箭的动力学方程为微分代数方程组，可采用BDF方法和Newton-Raphson迭代法进行数值求解。针对所提出的建模方法给出若干验证算例。通过多体动力学仿真结果与文献结果和解析解的对比，验证了多体建模方法的正确性。
其次，根据本文提出的建模方法建立大型捆绑式液体运载火箭的多体系统模型，开展火箭“大气飞行-助推分离”连续过程的精确动力学仿真，实现了姿控、弹道、推进剂消耗与晃动以及箭体振动的耦合分析。根据多体动力学仿真结果分析了飞行箭体的动力学行为，预示了飞行箭体的姿态运动、各贮箱的推进剂晃动、箭体飞行轨迹以及助推器的分离过程；根据多体仿真结果还分析了箭体结构振动和动载荷，给出了姿控喷管摇摆幅度、箭体关键部位动间隙以及飞行全程全箭的动载荷包络。跨音速脉动压力使得箭体姿态、喷管摆角和箭体动载荷在跨音速时段之内剧烈振荡，但对飞行轨迹无显著影响，而其对晃动的扰动影响将持续到跨音速时段之后。
最后，采用多体动力学建模方法实现了大型捆绑式液体运载火箭“结构-姿控-Pogo”耦合大回路的稳定性分析，研究了火箭姿控回路和Pogo回路之间的相互耦合影响。基于火箭的多体系统模型分别开展姿控回路、Pogo回路以及耦合大回路三种情况下的稳定性分析，通过结果对比阐明了大型捆绑火箭的姿控回路可影响Pogo稳定性，空间耦合模态对姿控回路和Pogo回路间的耦合程度有关键影响，从而明确了耦合大回路稳定性分析的必要性。
Liquid-propellant launch vehicle is a typical time-varying system and also acomplicated dynamic coupling system, whose dynamic problems are extremelysignificant for the design and developing process. This paper has researched on themodeling and simulation of liquid-propellant launch vehicles based on the method ofmultibody dynamics. Three are mainly three parts within this paper:
Firstly, multibody dynamic modeling methods were presented for all aspects of thedynamics of liquid-propellant launch vehicles. Based on the finite segment approach, aflexible multibody system was established for the empty launch vehicle withoutpropellant. D’Alembert-Lagrange principle for variable mass particles was presentedand a multibody dynamic modeling element for the flexible propellant tank withvariable mass was described with the method of Lagrange multiplier. A equivalentmechanical model was presented for the small-amplitude sloshing of variable-massliquid tanks and the dynamic model for a mass-varying particle was generated withinthe multibody dynamics framework. Time-varying control loop was realized in themultibody system by way of state space equations with non-constant coefficientmatrices. With the constraint force equation approach, dynamic separation process wasmodeled for the multibody launch vehicles. By applying the harmonic wavesuperposition method, stochastic pressure on the launch vehicle within transonic flightwas generated based on the power spectrum density. And other time-varying forces suchas gravity and aerodynamic force were modeled considering the geometry and rotationof the earth. The governing equation for the launch vehicle system is a group ofdifferential algebraic equations, which can be solved numerically by BDF methodstogether with Newton-Raphson iteration. Several validation examples were given forthe modeling methods given in the paper. Comparison between multibody simulationresults and reference or theoretical results showed that the multibody modelingapproach presented in the paper works well.
Secondly, a large strap-on liquid-propellant launch vehicle was modeled as amultibody system with the modeling methods given in the previous part and accuratemultibody dynamic simulation was conducted for the atmospherical flight and booster separation of the launch vehicle. Multibody dynamic simulations realized the couplinganalysis of attitude, trajectory, sloshing, mass variation and structural vibration. Basedon multibody simulation, the dynamic behaviors such as attitude motion, propellantsloshing, flight trajectory and separation process were predicted and also structuralvibration and dynamic inner forces were analyzed. Rotational angles of nozzles,structural dynamic gaps for some critical positions and envelops for the whole vehicleand the whole flight were examined in detail. Numerical results showed that randompressure within transonic flight causes attitude, nozzle angles and dynamic inner forcesto vibrate strongly only during the transonic process, but has no significant influence ontrajectory, while its effect on propellant sloshing will continue for a period of time afterthe transonic stage.
Finally, the stability analysis for the “structure-control-Pogo” coupling loop of theliquid-propellant launch vehicle was realized by the approach of multibody dynamics.Effects of the coupling between the control loop and Pogo loop were investigated.Respective stabilities for control loop, Pogo loop and “structure-control-Pogo” couplingloop were analyzed and compared, illustrating that control loop could affect the Pogostability, and the spatial coupling modes of large strap-on launch vehicles couldstrengthen the coupling between control loop and Pogo loop. Thus stability analysis forthe “structure-control-Pogo” coupling loop is necessary especially for large launchvehicles.
首先，提出了变质量液体火箭的多体动力学建模方法。先基于有限段方法建立未加注火箭的柔性多体系统模型，再提出变质量质点系的达朗贝尔-拉格朗日原理，并结合拉氏乘子法建立柔性变质量充液贮箱的多体建模单元，然后提出变质量贮箱时变晃动的等效力学模型和变质量质点的建模方法。最后，采用状态空间方程方法实现了时变控制在多体系统中的建模；采用约束力方程方法实现了火箭分离过程的多体建模；采用谐波叠加法生成随机样本，实现了火箭跨音速抖振的多体动力学建模；考虑地球外形及其自转，给出了各项时变外载荷的多体建模方法。液体火箭的动力学方程为微分代数方程组，可采用BDF方法和Newton-Raphson迭代法进行数值求解。针对所提出的建模方法给出若干验证算例。通过多体动力学仿真结果与文献结果和解析解的对比，验证了多体建模方法的正确性。
其次，根据本文提出的建模方法建立大型捆绑式液体运载火箭的多体系统模型，开展火箭“大气飞行-助推分离”连续过程的精确动力学仿真，实现了姿控、弹道、推进剂消耗与晃动以及箭体振动的耦合分析。根据多体动力学仿真结果分析了飞行箭体的动力学行为，预示了飞行箭体的姿态运动、各贮箱的推进剂晃动、箭体飞行轨迹以及助推器的分离过程；根据多体仿真结果还分析了箭体结构振动和动载荷，给出了姿控喷管摇摆幅度、箭体关键部位动间隙以及飞行全程全箭的动载荷包络。跨音速脉动压力使得箭体姿态、喷管摆角和箭体动载荷在跨音速时段之内剧烈振荡，但对飞行轨迹无显著影响，而其对晃动的扰动影响将持续到跨音速时段之后。
最后，采用多体动力学建模方法实现了大型捆绑式液体运载火箭“结构-姿控-Pogo”耦合大回路的稳定性分析，研究了火箭姿控回路和Pogo回路之间的相互耦合影响。基于火箭的多体系统模型分别开展姿控回路、Pogo回路以及耦合大回路三种情况下的稳定性分析，通过结果对比阐明了大型捆绑火箭的姿控回路可影响Pogo稳定性，空间耦合模态对姿控回路和Pogo回路间的耦合程度有关键影响，从而明确了耦合大回路稳定性分析的必要性。
Liquid-propellant launch vehicle is a typical time-varying system and also acomplicated dynamic coupling system, whose dynamic problems are extremelysignificant for the design and developing process. This paper has researched on themodeling and simulation of liquid-propellant launch vehicles based on the method ofmultibody dynamics. Three are mainly three parts within this paper:
Firstly, multibody dynamic modeling methods were presented for all aspects of thedynamics of liquid-propellant launch vehicles. Based on the finite segment approach, aflexible multibody system was established for the empty launch vehicle withoutpropellant. D’Alembert-Lagrange principle for variable mass particles was presentedand a multibody dynamic modeling element for the flexible propellant tank withvariable mass was described with the method of Lagrange multiplier. A equivalentmechanical model was presented for the small-amplitude sloshing of variable-massliquid tanks and the dynamic model for a mass-varying particle was generated withinthe multibody dynamics framework. Time-varying control loop was realized in themultibody system by way of state space equations with non-constant coefficientmatrices. With the constraint force equation approach, dynamic separation process wasmodeled for the multibody launch vehicles. By applying the harmonic wavesuperposition method, stochastic pressure on the launch vehicle within transonic flightwas generated based on the power spectrum density. And other time-varying forces suchas gravity and aerodynamic force were modeled considering the geometry and rotationof the earth. The governing equation for the launch vehicle system is a group ofdifferential algebraic equations, which can be solved numerically by BDF methodstogether with Newton-Raphson iteration. Several validation examples were given forthe modeling methods given in the paper. Comparison between multibody simulationresults and reference or theoretical results showed that the multibody modelingapproach presented in the paper works well.
Secondly, a large strap-on liquid-propellant launch vehicle was modeled as amultibody system with the modeling methods given in the previous part and accuratemultibody dynamic simulation was conducted for the atmospherical flight and booster separation of the launch vehicle. Multibody dynamic simulations realized the couplinganalysis of attitude, trajectory, sloshing, mass variation and structural vibration. Basedon multibody simulation, the dynamic behaviors such as attitude motion, propellantsloshing, flight trajectory and separation process were predicted and also structuralvibration and dynamic inner forces were analyzed. Rotational angles of nozzles,structural dynamic gaps for some critical positions and envelops for the whole vehicleand the whole flight were examined in detail. Numerical results showed that randompressure within transonic flight causes attitude, nozzle angles and dynamic inner forcesto vibrate strongly only during the transonic process, but has no significant influence ontrajectory, while its effect on propellant sloshing will continue for a period of time afterthe transonic stage.
Finally, the stability analysis for the “structure-control-Pogo” coupling loop of theliquid-propellant launch vehicle was realized by the approach of multibody dynamics.Effects of the coupling between the control loop and Pogo loop were investigated.Respective stabilities for control loop, Pogo loop and “structure-control-Pogo” couplingloop were analyzed and compared, illustrating that control loop could affect the Pogostability, and the spatial coupling modes of large strap-on launch vehicles couldstrengthen the coupling between control loop and Pogo loop. Thus stability analysis forthe “structure-control-Pogo” coupling loop is necessary especially for large launchvehicles.
引文
[1]龙乐豪.总体设计（上）[M].北京:中国宇航出版社,1989.
[2] Jeb S O, Johnson M D, Wetherbee J D, et al.,"State Space Implementation ofLinear Perturbation Dynamics Equations for Flexible Launch Vehicles " presentedat AIAA Guidance, Navigation, and Control Conference, Chicago, Illinois,2009.
[3] Jeb S O,"A Flight Dynamics Model for a Multi-Actuated Flexible Rocket Vehicle "presented at AIAA Atmospheric Flight Mechanics Conference, Portland, Oregon,2011.
[4] Baldesi G, Monaco S, Berard C, et al.,"Modelling, Simulation and Validation ofDifferent Control Strategies for a Launch Vehicle with a Non Neglegible Roll Rate" presented at AIAA Atmospheric Flight Mechanics Conference and Exhibit,Honolulu, Hawaii,2008.
[5]赵治华.液体火箭POGO振动的多体动力学建模及稳定性分析[博士学位论文].北京:清华大学航天航空学院,2011.
[6] Rosser J B, Newton R R, Cross G L. Mathematical Theory of Rocket Flight[M].New York: McGraw-Hill,1947.
[7] Thomson W T. Introduction to Space Dynamics[M]. New York: Wiley,1963.
[8] Grubin C. Mechanics of Variable Mass Systems[J]. Journal of Franklin Institute,1963,276:305-312.
[9] Dryer M. Advances in the Astronautical Sciences[M]. Los Angeles: WesternPulication Press,1963.
[10] Seamus T T,"An integrated vehicle simulation for the development and validationof a commercial reusable launch vehicle " presented at AIAA Modeling andSimulation Technologies Conference and Exhibit, Boston, MA,1998.
[11] Seide P, Effect of Constant Longitudinal Acceleration on the Transverse Vibrationof Uniform Beams, Aerospace Corp.21OCT1963.
[12] Beal T R. Dynamic Stability of a Flexible Missile Under Constant and PulsatingThrust [J]. AIAA Journal,1965,3:486-494.
[13] Birnbaum J,"Bending Vibration of a Perforated Grain Solid Propellant DuringPowered Flight," presented at IAS meeting, Paper61-30,1961.
[14] Edelen D G, On the Dynamic Effect of Fuel Flow on the Motion of Boost Vehicles,RM-3268-NASA, Rand Corp.1962.
[15] Meirovitch L, Wesley D A. On the dynamic characteristics of a variable-massslender elastic body under high acceleration[J]. AIAA Journal,1967,5:1439-1447.
[16] Meirovitch L. general motion of a variable-mass flexible rocket with internalflow[J]. Journal of Spacecraft and Rockets,1970,7:186-195.
[17] Arun K B,"Kane's equations for a variable mass flexible body system," presentedat AIAA/AAS Astrodynamics Specialist Conference and Exhibit, Boston, MA,1998.
[18] Arun K B. dynamics of a variable-mass, flexible-body system[J]. Journal ofGuidance, Control and Dynamics,2000,23:501-508.
[19] Huang X,"dynamics of flexible launch vehicles with variable mass," presented at44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada,2006.
[20] Patrick A T,"modeling and simulation of variable mass, flexible structures,"presented at AIAA Modeling and Simulation Technologies Conference, Chicago,Illinois,2009.
[21] Leslie J Q,"mode selection techniques in variable mass flexible body modeling,"presented at AIAA Modeling and Simulation Technologies Conference, Toronto,Ontario,2010.
[22]曾江红,王照林.航天器液体晃动动力学的研究方法概述[J].强度与环境,1997,4:37-43.
[23] Norman H A, The dynamic behavior of liquids in moving containers,SP-106,Southwest Research Institute, NASA1966.
[24] Franklin T D, The new "Dynamic behavior of liquids in moving containers",Southwest Research Institute, San Antonio, Texas2000.
[25] Playter R, Elgersma M, Morton B,"Modeling of the coupled nonlinear dynamics ofbooster vehicles, including flex modes, engines, and slosh " presented at SAE,ASME, and ASEE, Joint Propulsion Conference,26th, Orlando, FL,1990.
[26] Bayle O,"Influence of the ATV Propellant Sloshing on the GNC Performance "presented at AIAA Guidance, Navigation, and Control Conference and Exhibit,Monterey, California,2002.
[27] Kailash K, Dan B,"Inversion Based Multibody Control: Launch Vehicle with FuelSlosh," presented at AIAA Guidance, Navigation, and Control Conference andExhibit, San Francisco, California,2005.
[28] Ashivni S, Chetan N, Ananthkrishnan N,"Modeling and Stability Analysis ofCoupled Slosh-Vehicle Dynamics in Planar Atmospheric Flight " presented at44thAIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada,2006.
[29] Brandon M, David G,"Integrated CFD and Controls Analysis Interface for HighAccuracy Liquid Propellant Slosh Predictions " presented at50th AIAA AerospaceSciences Meeting including the New Horizons Forum and Aerospace Exposition,Nashville, Tennessee,2012.
[30] Rajeev L, Adimurthy V. Separation Dynamics of Ullage Rockets[J]. JOURNAL OFGUIDANCE, CONTROL, AND DYNAMICS,1994,17:426-434.
[31] Rajeev L. Separation Dynamics of Strap-On Boosters in the Atmosphere[J].JOURNAL OF GUIDANCE, CONTROL, AND DYNAMICS,1997,20:633-639.
[32] Seongjin C. Numerical Analysis on Separation Dynamics of Strap-On Boosters inthe Atmosphere[J]. JOURNAL OF SPACECRAFT AND ROCKETS,2002,39:439-446.
[33] Paul V T. Modeling Multibody Stage Separation Dynamics Using Constraint ForceEquation Methodology[J]. Journal of Spacecraft and Rockets,2011,48:573-583.
[34] Harold C L. Determination of Launch-Vehicle Response to Detailed WindProfiles[J]. Journal of Spacecraft and Rockets,1964,2:62-67.
[35] James R S. Problems of Atmospheric Wind Inputs for Missile and Space VehicleDesign[J]. Journal of Spacecraft and Rockets,1964,1:181-184.
[36] Kim M C, Kabe A M, Lee S S,"Atmospheric flight gust loads analysis " presentedat AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and MaterialsConference and Exhibit,40th, St. Louis, MO,1999.
[37] Sako B H, Kim M C, Kabe A M, et al. Derivation of atmospheric gust-forcingfunctions for launch-vehicle loads analysis[J]. Journal of Spacecraft and Rockets,2000,37:434-442.
[38] Rainey A G. Progress on the Launch-Vehicle Buffeting Problem[J]. Journal ofSpacecraft and Rockets,1965,2:289-299.
[39] Mohamed M R. Buffet loads prediction for a launch vehicle and comparison toflight data[J]. Journal of Spacecraft and Rockets,1992,29:849-855.
[40] Dotson K W. Vortex-inducedvibration of aheavy-liftlaunchvehicle during transonicflight[J]. Journal of Fluids and Structures,2004,19:669-680.
[41] Stanley R C. Buffet Response of a Hammerhead Launch Vehicle Wind-TunnelModel[J]. Journal of Spacecraft and Rockets,1992,29:379-385.
[42] William A E,"Numerical Simulation of Titan IVB Transonic Buffet Environment "presented at20th AIAA Applied Aerodynamics Conference, St. Louis, Missouri,2002.
[43] Dotson K W, Baker R L, Sako B H. Launch vehicle buffeting with aeroelasticcoupling effects[J]. Journal of Fluids and Structures,2000,14:1145-1171.
[44] Dotson K W, Baker R L, Sako B H. Launch vehicle self-sustained oscillation fromaeroelastic coupling part1: theory[J]. Journal of Spacecraft and Rockets,1998,35:365-373.
[45] Rubin S. Longitudinal Instability of Liquid Rockets Due to Propulsion Feedback(Pogo)[J]. Journal of Spacecraft and Rockets,1966,3:1188-1195.
[46] Walker J H, Winje R A, McKenna K J, An Investigation of Low FrequencyLongitudinal Vibration of the Titan II Missile during Stage I Flight, TRW SpaceTechnology Labs, Rept.6438-6001-RU-000March1964.
[47] Goldman R L, Miessner W W, Longitudinal Oscillation Instability Study POGO, inSimulation: SAGE1966.
[48] Wagner R G, Rubin S,"Detection of Titan Pogo Characteristics by Analysis ofRandom Data," presented at Proc. ASME Symposium on Stochastic Processes inDynamical Problems, Los Angeles,1969.
[49] Larsen C E. NASA Experience with Pogo in Human Spaceflight Vehicles[J].2008.
[50] Dordain J J, Lourme D, Estoueig C. Study on Pogo Effect on Launchers Europa-IIand Diamond-B[J]. Acta Astronautica,1974,1:1357-1384.
[51]马道远,王其政,荣克林.液体捆绑火箭POGO稳定性分析的闭环传递函数法[J].强度与环境,2010,1:1-7.
[52] Rubin S. Prevention of Coupled Structure-Propulsion Instability (Pogo)[J]. AIAASP-8055, October1970.
[53] Oppenheim B W, Rubin S. Advanced Pogo stability analysis for liquid rockets [J].Journal of Spacecraft and Rockets,1993,30:360-373.
[54] Wittenburg J E. Dynamics of systems of rigid bodies [M]. Stuttgart Teubner,1977.
[55] Haug E J. Computer aided kinematics and dynamics of mechanical systems[M].Berlin: Springer-Verlag,1989.
[56] Schiehlen W. Multibody system dynamics-Roots and perspectives[J]. MultibodySystem Dynamics,1997,1:149-188.
[57] Shabana A A. Dynamics of multibody systems[M]. New York: Wiley,1989.
[58] Huston R L. Multibody Dynamics[M]. Boston: Butterworths,1990.
[59] Shabana A A. Flexible multibody dynamics:Review of Past and RecentDevelopments[J]. Multibody System Dynamics,1997,1:189-222.
[60] Shabana A A. Definition of the slopes and the finite element absolute nodalcoordinate formulation[J]. Multibody System Dynamics,1997,1:339-348.
[61] Yakoub R Y, Shabana A A. Three Dimensional Absolute Nodal CoordinateFormulation for Beam Elements-Implementation and Applications[J]. ASME,Journal of mechanical design,2001,123:614-621.
[62] Shabana A A, Yakoub R Y. Three Dimensional Absolute Nodal CoordinateFormulation for Beam Elements-Theory[J]. ASME, Journal of mechanical design,2001,123:606-613.
[63] Von D S. Analysis of large flexible body deformation in multibody systems usingabsolute coordinates[J]. Multibody System Dynamics,2002,8:409-432.
[64] Dmitrochenko O N, Pogorelov D Y. Generalization of plate finite elements forabsolute nodal coordinate formulation[J]. Multibody System Dynamics,2003,10:17-43.
[65] Gerstmayr J, Schoberl J. A3D finite element method for flexible multibodysystems[J]. Multibody System Dynamics,2006,15:309-324.
[66] Moller H, Lund E, Jorge A C. Simulation of Fluid Loaded Flexible MultibodySystems[J]. Multibody System Dynamics,2005,13:113-128.
[67] Samin J C, Bruls O, Collard J F. Multiphysics modeling and optimization ofmechatronic multibody systems [J]. Multibody System Dynamics,2007,18:345-373.
[68] Liu J Y, Lu H,"Nonlinear formulation for flexible multibody system applied withthermal load," presented at Proceedings of the ASME International DesignEngineering Technical Conferences and Computers and Information in EngineeringConference, New York,2007.
[69]刘延柱.多刚体系统动力学[M].北京:高等教育出版社,1989.
[70]袁士杰,吕哲勤.多刚体系统动力学[M].北京:北京理工大学出版社,1992.
[71]洪嘉振.多体系统动力学——理论、计算方法和应用[M].上海:上海交通大学出版社,1992.
[72]黄文虎,邵成勋.多柔体系统动力学[M].北京:科学出版社,1996.
[73]陆佑方.柔性多体系统动力学[M].北京:高等教育出版社,1996.
[74]洪嘉振.计算多体系统动力学[M].北京:高等教育出版社,1999.
[75]刘铸永,洪嘉振.柔性多体系统动力学研究现状与展望[J].计算力学学报,2008,25:411-416.
[76]虞磊.基于绝对节点坐标的柔性多体系统建模与计算方法研究[博士学位论文].北京:清华大学航天航空学院,2010.
[77] Arun K B. Contributions of Multibody Dynamics to Space Flight: A BriefReview[J]. Journal of Guidance, Control and Dynamics,2003,26:385-394.
[78] Martin S, Wolf K, Arnold J,"Multibody Simulation of the Free-Flying ElasticAircraft," presented at46th AIAA/ASME/ASCE/AHS/ASC Structures, StructuralDynamics and Materials Conference AIAA-2005-2280, Austin, Texas,2005.
[79] Zhao Z, Ren G. Multibody Dynamic Approach of Flight Dynamics and NonlinearAeroelasticity of Flexible Aircraft[J]. AIAA Journal,2011,49:41-54.
[80] Eric M Q, Jill L P, Prasun N D. Multibody Modeling and Simulation for MarsPhoenix Entry, Descent, and Landing[J]. Journal of Spacecraft and Rockets,2011,48:765-771.
[81] Bauer H F, Fluid Oscillations in the Containers of a Space Vehicle and theInfluence upon Stability, NASA TR R-187,Marshall Space Flight Center,Huntsville,Alabama1964.
[82] Connelly J D, Huston R L. The dynamics of flexible multibody systems-a finitesegment approach.1. Theoretical aspects[J]. Computers and Structures,1994,50:255-258.
[83] Cheng Y, Dai S L, Ren G X. A hybrid finite segment/finite element modelling andexperiment on a flexible deployment system[J]. Journal of Sound and Vibration,2002,258:931-949.
[84]赵振军.非线性气动弹性与飞行力学耦合分析的多体动力学方法[博士学位论文].北京:清华大学航天航空学院,2009.
[85]张雄,王天舒.计算动力学[M].北京:清华大学出版社,2007.
[86] Fowles G R. Analytical mechanics[M]. New York: Holt, Rienhart and Winston,1977.
[87] Fowles G R, Cassiday G L. Analytical mechanics[M]. London: Brooks/Cole,2005.
[88]李俊峰,张雄,任革学.理论力学[M].北京:清华大学出版社,2001.
[89]王勖成.有限单元法[M].北京:清华大学出版社,2003.
[90]刘延柱.高等动力学[M].北京:高等教育出版社,2001.
[91]龙乐豪.总体设计（中）[M].北京:中国宇航出版社,1993.
[92] Brogan W L. Modern control theory3rd ed[M]. Englewood Cliffs, N.J: PrenticeHall,1991.
[93]陈方泉,马思文,金国斌.基于ISTA功率谱密度的MATLAB随机过程时域样本再现[J].包装工程,2006,27:64-66.
[94]李方泽,刘馥清,王正.工程振动测试与分析[M].北京:高等教育出版社,1992.
[95]李德葆,陆秋海.工程振动试验分析[M].北京:清华大学出版社,2004.
[96]徐明友,丁松滨.飞行动力学[M].北京:科学出版社,2003.
[97] Hairer E, Norsett S P, Wanner G. Solving Ordinary Differential Equations I:Non-stiff Problems,2nd ed.[M]. Berlin: Springer-Verlag,1996.
[98] Hairer E, Wanner G. Solving Ordinary Differential Equations II:Stiff andDifferential-Algebraic Problems,2nd ed.[M]. Berlin: Springer-Verlag,1996.
[99]汤家力.含时变索梁柔性多体系统的建模与数值方法研究[博士学位论文].北京:清华大学航天航空学院,2009.
[100] Hong D, Tang J, Ren G. Dynamic modeling of mass-flowing linear medium withlarge amplitude displacement and rotation[J]. Journal of Fluids and Structures,2011,27:1137-1148.
[101]同济大学数学教研室.高等数学下册第四版[M].北京:高等教育出版社,1996.
[102]刘延柱,陈书群.非线性振动[M].北京:高等教育出版社,2001.
[103]李庆扬,关治,白峰杉.数值计算原理[M].北京:清华大学出版社,2000.
[104] About G B, Bonnal C, David N, et al.,"A new approach of pogo phenomenonthree-dimensional studies of the Ariane4launcher," presented at InternationalAstronautical Congress,37th, Innsbruck, Austria,1986.
[2] Jeb S O, Johnson M D, Wetherbee J D, et al.,"State Space Implementation ofLinear Perturbation Dynamics Equations for Flexible Launch Vehicles " presentedat AIAA Guidance, Navigation, and Control Conference, Chicago, Illinois,2009.
[3] Jeb S O,"A Flight Dynamics Model for a Multi-Actuated Flexible Rocket Vehicle "presented at AIAA Atmospheric Flight Mechanics Conference, Portland, Oregon,2011.
[4] Baldesi G, Monaco S, Berard C, et al.,"Modelling, Simulation and Validation ofDifferent Control Strategies for a Launch Vehicle with a Non Neglegible Roll Rate" presented at AIAA Atmospheric Flight Mechanics Conference and Exhibit,Honolulu, Hawaii,2008.
[5]赵治华.液体火箭POGO振动的多体动力学建模及稳定性分析[博士学位论文].北京:清华大学航天航空学院,2011.
[6] Rosser J B, Newton R R, Cross G L. Mathematical Theory of Rocket Flight[M].New York: McGraw-Hill,1947.
[7] Thomson W T. Introduction to Space Dynamics[M]. New York: Wiley,1963.
[8] Grubin C. Mechanics of Variable Mass Systems[J]. Journal of Franklin Institute,1963,276:305-312.
[9] Dryer M. Advances in the Astronautical Sciences[M]. Los Angeles: WesternPulication Press,1963.
[10] Seamus T T,"An integrated vehicle simulation for the development and validationof a commercial reusable launch vehicle " presented at AIAA Modeling andSimulation Technologies Conference and Exhibit, Boston, MA,1998.
[11] Seide P, Effect of Constant Longitudinal Acceleration on the Transverse Vibrationof Uniform Beams, Aerospace Corp.21OCT1963.
[12] Beal T R. Dynamic Stability of a Flexible Missile Under Constant and PulsatingThrust [J]. AIAA Journal,1965,3:486-494.
[13] Birnbaum J,"Bending Vibration of a Perforated Grain Solid Propellant DuringPowered Flight," presented at IAS meeting, Paper61-30,1961.
[14] Edelen D G, On the Dynamic Effect of Fuel Flow on the Motion of Boost Vehicles,RM-3268-NASA, Rand Corp.1962.
[15] Meirovitch L, Wesley D A. On the dynamic characteristics of a variable-massslender elastic body under high acceleration[J]. AIAA Journal,1967,5:1439-1447.
[16] Meirovitch L. general motion of a variable-mass flexible rocket with internalflow[J]. Journal of Spacecraft and Rockets,1970,7:186-195.
[17] Arun K B,"Kane's equations for a variable mass flexible body system," presentedat AIAA/AAS Astrodynamics Specialist Conference and Exhibit, Boston, MA,1998.
[18] Arun K B. dynamics of a variable-mass, flexible-body system[J]. Journal ofGuidance, Control and Dynamics,2000,23:501-508.
[19] Huang X,"dynamics of flexible launch vehicles with variable mass," presented at44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada,2006.
[20] Patrick A T,"modeling and simulation of variable mass, flexible structures,"presented at AIAA Modeling and Simulation Technologies Conference, Chicago,Illinois,2009.
[21] Leslie J Q,"mode selection techniques in variable mass flexible body modeling,"presented at AIAA Modeling and Simulation Technologies Conference, Toronto,Ontario,2010.
[22]曾江红,王照林.航天器液体晃动动力学的研究方法概述[J].强度与环境,1997,4:37-43.
[23] Norman H A, The dynamic behavior of liquids in moving containers,SP-106,Southwest Research Institute, NASA1966.
[24] Franklin T D, The new "Dynamic behavior of liquids in moving containers",Southwest Research Institute, San Antonio, Texas2000.
[25] Playter R, Elgersma M, Morton B,"Modeling of the coupled nonlinear dynamics ofbooster vehicles, including flex modes, engines, and slosh " presented at SAE,ASME, and ASEE, Joint Propulsion Conference,26th, Orlando, FL,1990.
[26] Bayle O,"Influence of the ATV Propellant Sloshing on the GNC Performance "presented at AIAA Guidance, Navigation, and Control Conference and Exhibit,Monterey, California,2002.
[27] Kailash K, Dan B,"Inversion Based Multibody Control: Launch Vehicle with FuelSlosh," presented at AIAA Guidance, Navigation, and Control Conference andExhibit, San Francisco, California,2005.
[28] Ashivni S, Chetan N, Ananthkrishnan N,"Modeling and Stability Analysis ofCoupled Slosh-Vehicle Dynamics in Planar Atmospheric Flight " presented at44thAIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada,2006.
[29] Brandon M, David G,"Integrated CFD and Controls Analysis Interface for HighAccuracy Liquid Propellant Slosh Predictions " presented at50th AIAA AerospaceSciences Meeting including the New Horizons Forum and Aerospace Exposition,Nashville, Tennessee,2012.
[30] Rajeev L, Adimurthy V. Separation Dynamics of Ullage Rockets[J]. JOURNAL OFGUIDANCE, CONTROL, AND DYNAMICS,1994,17:426-434.
[31] Rajeev L. Separation Dynamics of Strap-On Boosters in the Atmosphere[J].JOURNAL OF GUIDANCE, CONTROL, AND DYNAMICS,1997,20:633-639.
[32] Seongjin C. Numerical Analysis on Separation Dynamics of Strap-On Boosters inthe Atmosphere[J]. JOURNAL OF SPACECRAFT AND ROCKETS,2002,39:439-446.
[33] Paul V T. Modeling Multibody Stage Separation Dynamics Using Constraint ForceEquation Methodology[J]. Journal of Spacecraft and Rockets,2011,48:573-583.
[34] Harold C L. Determination of Launch-Vehicle Response to Detailed WindProfiles[J]. Journal of Spacecraft and Rockets,1964,2:62-67.
[35] James R S. Problems of Atmospheric Wind Inputs for Missile and Space VehicleDesign[J]. Journal of Spacecraft and Rockets,1964,1:181-184.
[36] Kim M C, Kabe A M, Lee S S,"Atmospheric flight gust loads analysis " presentedat AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and MaterialsConference and Exhibit,40th, St. Louis, MO,1999.
[37] Sako B H, Kim M C, Kabe A M, et al. Derivation of atmospheric gust-forcingfunctions for launch-vehicle loads analysis[J]. Journal of Spacecraft and Rockets,2000,37:434-442.
[38] Rainey A G. Progress on the Launch-Vehicle Buffeting Problem[J]. Journal ofSpacecraft and Rockets,1965,2:289-299.
[39] Mohamed M R. Buffet loads prediction for a launch vehicle and comparison toflight data[J]. Journal of Spacecraft and Rockets,1992,29:849-855.
[40] Dotson K W. Vortex-inducedvibration of aheavy-liftlaunchvehicle during transonicflight[J]. Journal of Fluids and Structures,2004,19:669-680.
[41] Stanley R C. Buffet Response of a Hammerhead Launch Vehicle Wind-TunnelModel[J]. Journal of Spacecraft and Rockets,1992,29:379-385.
[42] William A E,"Numerical Simulation of Titan IVB Transonic Buffet Environment "presented at20th AIAA Applied Aerodynamics Conference, St. Louis, Missouri,2002.
[43] Dotson K W, Baker R L, Sako B H. Launch vehicle buffeting with aeroelasticcoupling effects[J]. Journal of Fluids and Structures,2000,14:1145-1171.
[44] Dotson K W, Baker R L, Sako B H. Launch vehicle self-sustained oscillation fromaeroelastic coupling part1: theory[J]. Journal of Spacecraft and Rockets,1998,35:365-373.
[45] Rubin S. Longitudinal Instability of Liquid Rockets Due to Propulsion Feedback(Pogo)[J]. Journal of Spacecraft and Rockets,1966,3:1188-1195.
[46] Walker J H, Winje R A, McKenna K J, An Investigation of Low FrequencyLongitudinal Vibration of the Titan II Missile during Stage I Flight, TRW SpaceTechnology Labs, Rept.6438-6001-RU-000March1964.
[47] Goldman R L, Miessner W W, Longitudinal Oscillation Instability Study POGO, inSimulation: SAGE1966.
[48] Wagner R G, Rubin S,"Detection of Titan Pogo Characteristics by Analysis ofRandom Data," presented at Proc. ASME Symposium on Stochastic Processes inDynamical Problems, Los Angeles,1969.
[49] Larsen C E. NASA Experience with Pogo in Human Spaceflight Vehicles[J].2008.
[50] Dordain J J, Lourme D, Estoueig C. Study on Pogo Effect on Launchers Europa-IIand Diamond-B[J]. Acta Astronautica,1974,1:1357-1384.
[51]马道远,王其政,荣克林.液体捆绑火箭POGO稳定性分析的闭环传递函数法[J].强度与环境,2010,1:1-7.
[52] Rubin S. Prevention of Coupled Structure-Propulsion Instability (Pogo)[J]. AIAASP-8055, October1970.
[53] Oppenheim B W, Rubin S. Advanced Pogo stability analysis for liquid rockets [J].Journal of Spacecraft and Rockets,1993,30:360-373.
[54] Wittenburg J E. Dynamics of systems of rigid bodies [M]. Stuttgart Teubner,1977.
[55] Haug E J. Computer aided kinematics and dynamics of mechanical systems[M].Berlin: Springer-Verlag,1989.
[56] Schiehlen W. Multibody system dynamics-Roots and perspectives[J]. MultibodySystem Dynamics,1997,1:149-188.
[57] Shabana A A. Dynamics of multibody systems[M]. New York: Wiley,1989.
[58] Huston R L. Multibody Dynamics[M]. Boston: Butterworths,1990.
[59] Shabana A A. Flexible multibody dynamics:Review of Past and RecentDevelopments[J]. Multibody System Dynamics,1997,1:189-222.
[60] Shabana A A. Definition of the slopes and the finite element absolute nodalcoordinate formulation[J]. Multibody System Dynamics,1997,1:339-348.
[61] Yakoub R Y, Shabana A A. Three Dimensional Absolute Nodal CoordinateFormulation for Beam Elements-Implementation and Applications[J]. ASME,Journal of mechanical design,2001,123:614-621.
[62] Shabana A A, Yakoub R Y. Three Dimensional Absolute Nodal CoordinateFormulation for Beam Elements-Theory[J]. ASME, Journal of mechanical design,2001,123:606-613.
[63] Von D S. Analysis of large flexible body deformation in multibody systems usingabsolute coordinates[J]. Multibody System Dynamics,2002,8:409-432.
[64] Dmitrochenko O N, Pogorelov D Y. Generalization of plate finite elements forabsolute nodal coordinate formulation[J]. Multibody System Dynamics,2003,10:17-43.
[65] Gerstmayr J, Schoberl J. A3D finite element method for flexible multibodysystems[J]. Multibody System Dynamics,2006,15:309-324.
[66] Moller H, Lund E, Jorge A C. Simulation of Fluid Loaded Flexible MultibodySystems[J]. Multibody System Dynamics,2005,13:113-128.
[67] Samin J C, Bruls O, Collard J F. Multiphysics modeling and optimization ofmechatronic multibody systems [J]. Multibody System Dynamics,2007,18:345-373.
[68] Liu J Y, Lu H,"Nonlinear formulation for flexible multibody system applied withthermal load," presented at Proceedings of the ASME International DesignEngineering Technical Conferences and Computers and Information in EngineeringConference, New York,2007.
[69]刘延柱.多刚体系统动力学[M].北京:高等教育出版社,1989.
[70]袁士杰,吕哲勤.多刚体系统动力学[M].北京:北京理工大学出版社,1992.
[71]洪嘉振.多体系统动力学——理论、计算方法和应用[M].上海:上海交通大学出版社,1992.
[72]黄文虎,邵成勋.多柔体系统动力学[M].北京:科学出版社,1996.
[73]陆佑方.柔性多体系统动力学[M].北京:高等教育出版社,1996.
[74]洪嘉振.计算多体系统动力学[M].北京:高等教育出版社,1999.
[75]刘铸永,洪嘉振.柔性多体系统动力学研究现状与展望[J].计算力学学报,2008,25:411-416.
[76]虞磊.基于绝对节点坐标的柔性多体系统建模与计算方法研究[博士学位论文].北京:清华大学航天航空学院,2010.
[77] Arun K B. Contributions of Multibody Dynamics to Space Flight: A BriefReview[J]. Journal of Guidance, Control and Dynamics,2003,26:385-394.
[78] Martin S, Wolf K, Arnold J,"Multibody Simulation of the Free-Flying ElasticAircraft," presented at46th AIAA/ASME/ASCE/AHS/ASC Structures, StructuralDynamics and Materials Conference AIAA-2005-2280, Austin, Texas,2005.
[79] Zhao Z, Ren G. Multibody Dynamic Approach of Flight Dynamics and NonlinearAeroelasticity of Flexible Aircraft[J]. AIAA Journal,2011,49:41-54.
[80] Eric M Q, Jill L P, Prasun N D. Multibody Modeling and Simulation for MarsPhoenix Entry, Descent, and Landing[J]. Journal of Spacecraft and Rockets,2011,48:765-771.
[81] Bauer H F, Fluid Oscillations in the Containers of a Space Vehicle and theInfluence upon Stability, NASA TR R-187,Marshall Space Flight Center,Huntsville,Alabama1964.
[82] Connelly J D, Huston R L. The dynamics of flexible multibody systems-a finitesegment approach.1. Theoretical aspects[J]. Computers and Structures,1994,50:255-258.
[83] Cheng Y, Dai S L, Ren G X. A hybrid finite segment/finite element modelling andexperiment on a flexible deployment system[J]. Journal of Sound and Vibration,2002,258:931-949.
[84]赵振军.非线性气动弹性与飞行力学耦合分析的多体动力学方法[博士学位论文].北京:清华大学航天航空学院,2009.
[85]张雄,王天舒.计算动力学[M].北京:清华大学出版社,2007.
[86] Fowles G R. Analytical mechanics[M]. New York: Holt, Rienhart and Winston,1977.
[87] Fowles G R, Cassiday G L. Analytical mechanics[M]. London: Brooks/Cole,2005.
[88]李俊峰,张雄,任革学.理论力学[M].北京:清华大学出版社,2001.
[89]王勖成.有限单元法[M].北京:清华大学出版社,2003.
[90]刘延柱.高等动力学[M].北京:高等教育出版社,2001.
[91]龙乐豪.总体设计（中）[M].北京:中国宇航出版社,1993.
[92] Brogan W L. Modern control theory3rd ed[M]. Englewood Cliffs, N.J: PrenticeHall,1991.
[93]陈方泉,马思文,金国斌.基于ISTA功率谱密度的MATLAB随机过程时域样本再现[J].包装工程,2006,27:64-66.
[94]李方泽,刘馥清,王正.工程振动测试与分析[M].北京:高等教育出版社,1992.
[95]李德葆,陆秋海.工程振动试验分析[M].北京:清华大学出版社,2004.
[96]徐明友,丁松滨.飞行动力学[M].北京:科学出版社,2003.
[97] Hairer E, Norsett S P, Wanner G. Solving Ordinary Differential Equations I:Non-stiff Problems,2nd ed.[M]. Berlin: Springer-Verlag,1996.
[98] Hairer E, Wanner G. Solving Ordinary Differential Equations II:Stiff andDifferential-Algebraic Problems,2nd ed.[M]. Berlin: Springer-Verlag,1996.
[99]汤家力.含时变索梁柔性多体系统的建模与数值方法研究[博士学位论文].北京:清华大学航天航空学院,2009.
[100] Hong D, Tang J, Ren G. Dynamic modeling of mass-flowing linear medium withlarge amplitude displacement and rotation[J]. Journal of Fluids and Structures,2011,27:1137-1148.
[101]同济大学数学教研室.高等数学下册第四版[M].北京:高等教育出版社,1996.
[102]刘延柱,陈书群.非线性振动[M].北京:高等教育出版社,2001.
[103]李庆扬,关治,白峰杉.数值计算原理[M].北京:清华大学出版社,2000.
[104] About G B, Bonnal C, David N, et al.,"A new approach of pogo phenomenonthree-dimensional studies of the Ariane4launcher," presented at InternationalAstronautical Congress,37th, Innsbruck, Austria,1986.
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