针对中心刚体-单翼大挠性结构的航天器,建立了一种非约束模态展开的动力学模型。探讨挠性航天器非约束模态动力学建模及动态特性,首先利用哈密顿原理建立了挠性航天器动力学方程,然后进行了模态离散化,分别在约束模态和非约束模态下讨论相关的特征值问题,非约束模态采用瑞利里兹法,求解了单翼挠性航天器的特征值问题,最后进行了数值仿真,比较约束模态与非约束模态之间的差异,并用有限元软件进行对比验证,得到了随着太阳能帆板长度的增加,即刚柔惯量比的减小,非约束模态比约束模态更加贴近实际情况的结论。
Abstract
An unconstrained modal dynamic model was established for a spacecraft with a central rigid body and a single wing large flexible structure. The unconstrained modal dynamic modeling and characteristics for a flexible spacecraft were discussed. Firstly, the dynamic equations of a flexible spacecraft were established by using Hamiltonian principle. Then the modal discretization was carried out, the related eigenvalue problems were studied respectively in constrained modes and unconstrained modes. The eigenvalue problems of a flexible spacecraft with a single wing were solved by using the Rayleigh Ritz method for unconstrained modes. Finally, the numerical simulation was carried out to compare the difference between constrained modes and unconstrained modes, and finite element software was used for verification. As the length of the solar panel increases, that is, the ratio of rigid to flexible inertia decreases, unconstrained modes are closer to the actual situation than constrained modes.
关键词
挠性航天器 /
非约束模态 /
动力学建模 /
特征值问题
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Key words
flexible spacecraft /
unconstrained modes /
dynamic modeling /
eigenvalue problems
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参考文献
[1] 曲广吉.航天器动力学工程[M].北京:中国科学技术出版社,2000.
QU Guang-ji. Spacecraft Dynamics Engineering [M]. Beijing: China Science and Technology Press, 2000.
[2] 邱继宝,张正平,向树红等.结构动力学及其在航天工程中的应用[M].合肥:中国科学技术大学出版社,2015.1.
QIU Ji-bao, ZHANG Zheng-ping, XIANG Shu-hong et al.Structural Dynamics and its Application in aerospace engineering [M]. Hefei: University of Science and Technology of China Press, 2015.1.
[3] Hughes P C.Recent advances in the attitude dynamics of spacecraft with flexible solar arrays[J].Canadian Aeronautics and Space Journal,1973,19(4):165-171.
[4] 罗 文.太阳翼卫星的刚柔耦合动力学建模[D].哈尔滨:哈尔滨工业大学,2015.
LUO Wen. Rigid and flexible coupling Dynamic Modeling of solar wing satellite [D]. Harbin: Harbin Institute of Technology, 2015.
[5] Hablani,H.B. Modal Identities for Multibody Elastic Spacecraft—An Aid to Selecting Modes for Simulation[C]// 27th Aerospace Sciences Meeting.:AIAA,1989.
[6] Hughes P C. Modal identities for elastic bodies with application to vehicle dynamic and control [J]. Journal Applied Mechanic,1980,47(1): 177-184.
[7] 徐小胜,于登云,曲广吉.用于惯性完备性降价的模态恒等式研究[J].航天器工程,2003,12(2):23-34.
XU Xiao-sheng, YU Deng-yun, QU Guang-ji. Research on modal identities for inertial integrity reduction [J]. Spacecraft engineering, 2003,12 (2) : 23-34.
[8] 吕 旺,向明江,叶文郁,等.挠性卫星在轨非约束模态计算研究[J].宇航学报,2014,35(4):404-409.
LV Wang, XIANG Ming-jiang, YE Wen-yu, et al. Research on the calculation of unconstrained modes in orbit for flexible satellites [J]. Journal of aerospace, 2014,35 (4) : 404-409.
[9] Enrique Barbieri. Unconstrained and constrained mode expansions for a flexible slewing link [J]. Transaction of ASME,1998, 110(6):416-421.
[10] 袁秋帆,王超磊,齐乃明等.单翼大挠性航天器全局模态动力学建模及试验[J].宇航学报,2019,40(4):369-377.
YUAN Qiu-fan, WANG Chao-lei, QI Naiming, et al. Global modal dynamics modeling and testing for large flexible single-wing spacecraft [J]. Journal of aerospace, 2019,40 (4) : 369-377.
[11] 李东旭.挠性航天器结构动力学[M].北京:科学出版社,2010.
LI Dong-xu. Structural Dynamics of flexible spacecraft [M]. Beijing: Science Press, 2010.
[12] Hablani H B. Constrained and unconstrained modes: some modeling aspects of flexible spacecraft [J]. Journal of Guidance, Control and Dynamics,1982, 5(2):164-173.
[13] Hablani,H.B.A More Accurate Modeling of the Effects of Actuators in Large Space Structures [J]. Acta Astronautica,Vol.8,1981,pp.361-376.
[14] 程亮亮,张盼龙,陈玉刚.基于ANSYS和实验的悬臂薄板模态分析[J].科技创新导报,2012,28:126.
CHENG Liang-liang, ZHANG Pang-long, CHEN Yu-gang. Modal Analysis of cantilever plate based on ANSYS and Experiment [J]. Journal of Science and Technology Innovation, 2012, 28:126.
[15] 杜 圆,李海超,庞福振,等.任意边界条件下矩形板薄板自由振动特性分析[J].振动与冲击,2019,38(19):70-76.
DU Yuan, LI Hai-chao, PANG Fu-zhen, et al. Free vibration characteristics of rectangular plate under arbitrary boundary conditions [J]. Vibration and impact, 2019,38 (19) : 70-76.
[16] A. W. LEISSAt.The free vibration of rectangular plates [J] .Journal of Sound and Vibration,1973,31(3):257-293.
[17] R. B. BHAT.Natural frequencies of rectangular plates using characteristic or thogonal polynomials in Rayleigh-Ritz method [J]. Journal of Sound and Vibration 1985,102(4): 493-499.
[18] R. B. BHAT.Flexural vibration of polygonal plates using characteristic or thogonal polynamials in two variables[J].Journal of Sound and Vibration 1987,114(1): 65-71.
[19] C. RAJALINGHAM and R. B. BHAT. Vibration of elliptic plates using characteristic or thogonal polynominals in the rayleigh-Ritz method [J]. International Journal of Mechanical Sciences, 1991, 33(9): 705-716.
[20] 曹志远.板壳振动理论[M]. 北京:中国铁道出版社,1989.
CAO Zhi-yuan. Theory of plate and shell vibration [M]. Beijing: China Railway Publishing House,1989.
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