大挠性多体结构卫星刚柔耦合动力学研究
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摘要
随着航天技术的发展,现代大型航天器通常都带有大型挠性结构。如大尺度挠性天线、太阳帆板和大型空间桁架等。在航天器结构日趋复杂的同时,在轨运行航天器的运动因素也更加复杂多样。例如航天器整体经历的轨道转移、大角度姿态运动,航天器柔性部件的伸展运动、展开运动、大角度机动等。这些大范围的刚体运动将激发柔性体的弹性变形运动,而且这两种运动相互耦合,相互影响,导致其动力学行为非常复杂,出现动力刚化等特殊动力学现象。因此,研究航天器大范围刚体运动与其挠性附件弹性变形运动的刚柔耦合动力学具有重要的意义。本文就这个问题,进行了以下几个方面的研究:
1) 针对航天器结构中常见的梁式构件,建立了计及动力刚化的刚柔耦合一次近似动力学方程。分别用假设模态法和有限元方法对梁的弹性变形进行离散,并编制了相应的程序进行数值仿真。仿真结果表明,当大范围刚体运动达到一定程度时,例如转动速度达到或超过柔性梁的一阶振动角频率时,没有计及动力刚化的传统零次近似动力学模型所得结果误差较大,甚至是完全错误的;而计及了动力刚化的一次近似刚柔耦合动力学模型能够正确反映挠性体的动力学行为,并验证了所谓的动力刚化现象,即挠性体的振动频率随着大范围刚体运动速度的增加而增大。
2) 针对航天器结构中的另外两类挠性构件,板和桁架,根据各自的特点,采用不同的建模方法得到了系统的刚柔耦合一次近似动力学模型。数值仿真结果说明:传统动力学建模方法在解决这类挠性结构经历大范围刚体运动时的动力学问题时存在严重缺陷,必须建立一次近似刚柔耦合动力学模型才能正确预示其动力学行为。
3) 针对一在轨运行的挠性多体结构卫星,建立起能够完整模拟其在轨运行动力学行为的刚柔耦合一次近似动力学方程组。为便于卫星姿态控制系统的设计,人们常把卫星模化为刚体卫星。然而,数值仿真发现,将挠性卫星模化为刚体而得到的姿态控制规律一般不适用于挠性体卫星,因为这样的控制系统可能引起卫星姿态和挠性附件弹性变形的发散。其次,在某些外界激励下,传统的零次近似动力学模型不能正确预示卫星的动力学行为,包括卫星的姿态运动和挠性体弹性变形运动,而本文所建立的刚柔耦合一次近似动力学模型能够得到满意的结果。
本文研究发现,当一些带有大型挠性附件的航天器经历大范围刚体运动时,由于其刚体运动与挠性附件弹性变形运动的耦合作用,传统的零次近似动力学模型无法正确揭示系统的动力学行为;必须建立计及动力刚度项的刚柔耦合一次近似动力学模型,才能正确预示系统的动力学行为。
本文的研究为大范围运动下挠性航天器的姿态控制系统设计及其挠性附件的振动控制系统设计奠定了基础。
With the development of aerospace technology, the large-scale spacecraft having large flexible structures appeared. The flexible structures, such as the great antenna, solar panels, large truss, had made the spacecraft configuration complex. Furthermore, the large overall motion of the spacecraft had become more complicated and diversiform. Unfortunately, the elastic deformed motion of the flexible structures aroused by the large overall motion of the spacecraft was not neglected again. Because of the coupling of the two motions, the dynamic analysis of the whole spacecraft is more difficult. What's more, the especial dynamic phenomenon, dynamic stiffening, became important in the analysis of spacecraft dynamics. Thus, research on the coupling of the large overall motion and the elastic deformed motion is important. The studies included in this thesis are as follows:Firstly, in view of the flexible beams of the spacecraft undergoing large overall motion, the rigid-flexible dynamic equations were established via the mode assumption and the finite element method. The results of numerical simulation show that the traditional dynamic modeling method can't indicate truly the dynamic action of flexible beams undergoing large overall motion. However, the dynamic model in this thesis can. Moreover, the dynamic stiffening phenomenon was verified.Secondly, in view of the flexible solar panel and large truss undergoing large overall motion, the rigid-flexible dynamic equations were established via the different methods. The results of numerical simulation show that there are some limitations in the traditional modeling method.Finally, the dynamic equations that can simulate completely the dynamic action of a flexible satellite flying on the orbit were established. It was funded that the control law of the rigid satellite's attitude can't be applied into the attitude control of the flexible satellite. Actually the attitude control system will arouse the instability of flexible satellite. Furthermore, with the effects of environment power, the traditional dynamic model can't indicate truly the dynamic action of the flexible satellite. On the contrary, the rigid-flexible dynamic model in this study can indicate the dynamic action of satellite.This research show that, the traditional dynamic model can't indicate the dynamic action of flexible satellite undergoing large overall motion because of the coupling of the rigid motion and the deformed motion. In order to indicate the dynamic action truly of the flexible satellite, it is prerequisite to establish the first order approximation rigid-flexible coupling dynamic model.
1) 针对航天器结构中常见的梁式构件,建立了计及动力刚化的刚柔耦合一次近似动力学方程。分别用假设模态法和有限元方法对梁的弹性变形进行离散,并编制了相应的程序进行数值仿真。仿真结果表明,当大范围刚体运动达到一定程度时,例如转动速度达到或超过柔性梁的一阶振动角频率时,没有计及动力刚化的传统零次近似动力学模型所得结果误差较大,甚至是完全错误的;而计及了动力刚化的一次近似刚柔耦合动力学模型能够正确反映挠性体的动力学行为,并验证了所谓的动力刚化现象,即挠性体的振动频率随着大范围刚体运动速度的增加而增大。
2) 针对航天器结构中的另外两类挠性构件,板和桁架,根据各自的特点,采用不同的建模方法得到了系统的刚柔耦合一次近似动力学模型。数值仿真结果说明:传统动力学建模方法在解决这类挠性结构经历大范围刚体运动时的动力学问题时存在严重缺陷,必须建立一次近似刚柔耦合动力学模型才能正确预示其动力学行为。
3) 针对一在轨运行的挠性多体结构卫星,建立起能够完整模拟其在轨运行动力学行为的刚柔耦合一次近似动力学方程组。为便于卫星姿态控制系统的设计,人们常把卫星模化为刚体卫星。然而,数值仿真发现,将挠性卫星模化为刚体而得到的姿态控制规律一般不适用于挠性体卫星,因为这样的控制系统可能引起卫星姿态和挠性附件弹性变形的发散。其次,在某些外界激励下,传统的零次近似动力学模型不能正确预示卫星的动力学行为,包括卫星的姿态运动和挠性体弹性变形运动,而本文所建立的刚柔耦合一次近似动力学模型能够得到满意的结果。
本文研究发现,当一些带有大型挠性附件的航天器经历大范围刚体运动时,由于其刚体运动与挠性附件弹性变形运动的耦合作用,传统的零次近似动力学模型无法正确揭示系统的动力学行为;必须建立计及动力刚度项的刚柔耦合一次近似动力学模型,才能正确预示系统的动力学行为。
本文的研究为大范围运动下挠性航天器的姿态控制系统设计及其挠性附件的振动控制系统设计奠定了基础。
With the development of aerospace technology, the large-scale spacecraft having large flexible structures appeared. The flexible structures, such as the great antenna, solar panels, large truss, had made the spacecraft configuration complex. Furthermore, the large overall motion of the spacecraft had become more complicated and diversiform. Unfortunately, the elastic deformed motion of the flexible structures aroused by the large overall motion of the spacecraft was not neglected again. Because of the coupling of the two motions, the dynamic analysis of the whole spacecraft is more difficult. What's more, the especial dynamic phenomenon, dynamic stiffening, became important in the analysis of spacecraft dynamics. Thus, research on the coupling of the large overall motion and the elastic deformed motion is important. The studies included in this thesis are as follows:Firstly, in view of the flexible beams of the spacecraft undergoing large overall motion, the rigid-flexible dynamic equations were established via the mode assumption and the finite element method. The results of numerical simulation show that the traditional dynamic modeling method can't indicate truly the dynamic action of flexible beams undergoing large overall motion. However, the dynamic model in this thesis can. Moreover, the dynamic stiffening phenomenon was verified.Secondly, in view of the flexible solar panel and large truss undergoing large overall motion, the rigid-flexible dynamic equations were established via the different methods. The results of numerical simulation show that there are some limitations in the traditional modeling method.Finally, the dynamic equations that can simulate completely the dynamic action of a flexible satellite flying on the orbit were established. It was funded that the control law of the rigid satellite's attitude can't be applied into the attitude control of the flexible satellite. Actually the attitude control system will arouse the instability of flexible satellite. Furthermore, with the effects of environment power, the traditional dynamic model can't indicate truly the dynamic action of the flexible satellite. On the contrary, the rigid-flexible dynamic model in this study can indicate the dynamic action of satellite.This research show that, the traditional dynamic model can't indicate the dynamic action of flexible satellite undergoing large overall motion because of the coupling of the rigid motion and the deformed motion. In order to indicate the dynamic action truly of the flexible satellite, it is prerequisite to establish the first order approximation rigid-flexible coupling dynamic model.
引文
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[2] 马兴瑞,王本利,苟兴宇等著.航天器动力学—若干问题进展及应用.北京:科学出版社,2001年9月第一版.
[3] T. R. Kane, R. R. Ryant, A. K. Banerjee. Dynamics of a Cantilever Beam Attached to a Moving Base. Journal of Guidance, Control and Dynamics, 1987, 10(2): 139～151
[4] A. K. Banerjee, T. R. Kane, Dynamics of a Plate in Large Overall Motion, Journal of Applied Mechanics, 1989. 11, Vol. 56: 887-892
[5] 陆佑方,柔性多体系统动力学.北京:高等教育出版社,1996年7月第一版
[6] Wallrapp O. Linearized Flexible Multibody Dynamics Including Geometric Stiffening Effects. Mech. Strut & Mach, 1991, 19: 385～409
[7] 张策,黄永强,王子良,陈树勋.弹性连杆机构的分析与设计.北京:机械工业出版社,1996
[8] Linkins P W. Finite element appendage equations for hybrid coordinate dynamic anslysis. Journal of Solids & Structures, 1972, 8: 709～731
[9] W J Haering, R R. Ryan. New Formulation foe Flexible Beams Undergoing Large Overall Plane Motion. Journal of Guidance, Control and Dynamics. 1994,17(1): 76～83
[10] Cailos E. Padilla and Andreas H. Von Flotow. Nonlinear Strain-Displacement Relations and Flexible Multibody Dynamics. Journal of Guidance, Control and Dynamics, 1992, 15: 128～136
[11] 洪嘉振,蒋丽忠.柔性多体系统刚柔耦合动力学.力学进展,2000,30(1):15～20
[12] 于清,洪嘉振.柔性多体系统动力学的若干热点问题.力学进展,1999,29(2):145～154
[13] 洪嘉振,蒋丽忠.动力刚化与多体系统刚柔耦合动力学.计算力学学报,1999,16(3):295～300
[14] William Haering. Simple Flexible-Body Dynamic Beam Formulations: Deformation Choices, Boundary Conditions and Strain Approximations. AIAA, A01-25086, 2001-1297
[15] Yoo. H. H. and J. Chung Dynamics of Rectangular Plates Undergoing Prescribed Overall Motion. Journal of Sound and Vibration. 2001, 239(1): 123～137
[16] Yoo. H. H. Ryan. R. R. and Scott. R. A. Dynamics of Flexible Beams Undergoing Overall Motions. Journal of Sound and Vibration. 1995, 181 (2): 261～278
[17] 蒋丽忠,洪嘉振.作大运动弹性薄板中的几何非线性与耦合变形.力学学报,1999,31(2),243～249
[18] 刘才山,王玉玲等.一般柔性体连续系统的动力学建模方法.山东建筑工程学院学报,1999,14(1),59～63
[19] 杨辉,洪嘉振等.刚柔耦合多体系统动力学建模与仿真.计算力学学报,2003,20(4), 403～408
[20] 刘锦阳,洪嘉振.作大范围运动矩形薄板的建模理论和有限元离散方法.振动工程学报,2003,16(2),175～178
[21] J. C. Simo, L. Vu-Quoc. On the Dynamics of Flexible Beans Under Large Overall Motions-The Plane Case: Part Ⅰ. Journal of Applied Mechanics. December, 1986, Vol. 53, 849～854
[22] J. C. Simo, L. Vu-Quoc. On the Dynamics of Flexible Beans Under Large Overall Motions-The Plane Case: Part Ⅱ. Journal of Applied Mechanics. December, 1986, Vol. 53, 855～863
[23] Ider S. K, Amirouche F M L. Nonlinear Modeling of Flexible Multibody System Dynamics Subjected to Variable Constraints. Journal of Applied Mechanics, 1989, 56: 444～450
[24] Ider S. K, Amirouche F. M. L. The Influence of Geometric Nonlinear in the Dynamics. Journal of Applied Mechanics. 1989, 55: 830～837
[25] Bakr E. M, Shabana A. A. Geometrically Nonlinear Analysis of Multibody Systems. Computers and Structures. 1986, 23: 739～751
[26] Boutaghou Z. E, Erdman A. G Stolarski H. K. Dynamics of Flexible Beams and Plates in Large Motions. Journal of Applied Mechanic, 1992, 59: 991～999
[27] Oskar Wallrapp. Linearized Flexible Multibody Dynamics Including Geometric Stiffening Effects. Mech. Struct. & Mach. 1991, 19(3): 385～409
[28] Oskar Wallrapp and Richard Schwertassek. Representation of Geometric Stiffening in Multibody System Simulation. International Journal for Numerical Methods in Engineering. 1991, Vol. 32: 1833～1850
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