考虑动力刚化的挠性航天器的动力学建模与分析
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摘要
本文以含有挠性太阳能帆板的卫星为研究对象,建立了考虑动力刚化效应的刚柔耦合动力学模型,并与传统的线性模型进行了对比。首先,通过Hamilton变分原理建立了考虑动力刚化效应的挠性卫星的姿态运动和结构振动的偏微分方程;之后,通过假设模态法对偏微分方程进行离散,得到离散化后的线性模型和动力刚化模型;最后,给出了某些特定外界激励下两种模型动力学响应的数值仿真结果。仿真结果表明,动力刚化效应将对卫星的柔性结构振动产生较大影响;在一定的外界激励下,采用线型模型的计算结果与动力刚化模型的计算结果之间存在较大偏差。
A satellite with flexible solar panels is studied in this paper. The rigid-flexible coupling dynamic model considering stiffening effect is proposed and compared with the traditional linear model.The partial differential equations of the attitude motion and structural vibration of the flexible satellite with considering stiffening effect are firstly derived from Hamilton's principle. Then the linear model and the dynamic stiffening model are obtained by discretizing the partial differential equations using assumption mode method. At last,numerical simulations of the dynamic responses of the two models under certain external excitation are presented. The results show that stiffening effect has a significant influence on the flexible structure vibration,and there will be a lot of deviation between the results computed by the linear model and dynamic model under a certain external excitation.
A satellite with flexible solar panels is studied in this paper. The rigid-flexible coupling dynamic model considering stiffening effect is proposed and compared with the traditional linear model.The partial differential equations of the attitude motion and structural vibration of the flexible satellite with considering stiffening effect are firstly derived from Hamilton's principle. Then the linear model and the dynamic stiffening model are obtained by discretizing the partial differential equations using assumption mode method. At last,numerical simulations of the dynamic responses of the two models under certain external excitation are presented. The results show that stiffening effect has a significant influence on the flexible structure vibration,and there will be a lot of deviation between the results computed by the linear model and dynamic model under a certain external excitation.
引文
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[14]方建士,章定国.旋转悬臂梁的刚柔耦合动力学建模与频率分析[J].计算力学学报,2012,29(3):333-339.
[15]章定国,朱志远.一类刚柔耦合系统的动力刚化分析[J].南京理工大学学报,2006,30(1):21-26.
[16]方建士,黎亮,章定国等.基于刚柔耦合动力学的旋转悬臂梁的频率转向与振型转换特性[J].机械工程学报,2015,51(17):59-65.
[17]杨辉,洪嘉振,余征跃.动力刚化问题的实验研究[J].力学学报,2004,36(1):118-124.
[18]杨辉,洪嘉振,余征跃.刚-柔耦合多体系统动力学建模与数值仿真[J].计算力学学报,2003,20(4):402-408.
[19]张雷.航天器分步展开式太阳翼设计与研究[D].上海:上海交通大学,2012.
[20]张亚辉,林家浩.结构动力学基础[M].大连理工大学出版社,2007.
[21]LIU Y,WU S,ZHANG K,et al.Parametrical Excitation Model for Rigid-Flexible Coupling System of Solar Power Satellite[J].Journal of Guidance,Control,and Dynamics,2017.
[2]GRAHNE M S,SIMBURGER E J.Inflatable solar arrays[J].Progress in Astronautics and Aeronautics.,2001,191:463-479.
[3]李洋.柔性航天器在轨振动主动控制研究[D].西安:西安电子科技大学,2013.
[4]MEIROVITCH L.Dynamics and control of structures[M].John Wiley&Sons,1990.
[5]MEIROVITCH L,SILVERBERG L M.Active vibration suppression of a cantilever wing[J].Journal of Sound and Vibration,1984,97(3):489-498.
[6]MEIROVITCH L.A modal analysis for the response of linear gyroscopic systems[J].Journal of Applied Mechanics,1975,42(2):446-450.
[7]CHANDRA R,STEMPLE A D,CHOPRA I.Thin-walled composite beams under bending,torsional,and extensional loads[J].Journal of Aircraft,1990,27(7):619-626.
[8]STEMPLE A D,LEE S W.Finite-element model for composite beams with arbitrary cross-sectional warping[J].AIAA journal,1988,26(12):1512-1520.
[9]KANE T R,RYAN R,BANERJEE A K.Dynamics of a cantilever beam attached to a moving base[J].Journal of Guidance,Control,and Dynamics,1987,10(2):139-151.
[10]WU S C,HAUG E J.Geometric non-linear substructuring for dynamics of flexible mechanical systems[J].International Journal for Numerical Methods in Engineering,1988,26(10):2211-2226.
[11]ZHANG D J,LIU C Q,HUSTON R L.On the dynamics of an arbitrary flexible body with large overall motion:an integrated approach[J].Journal of Structural Mechanics,1995,23(3):419-438.
[12]YOO H H,RYAN R R,SCOTT R A.Dynamics of flexible beams undergoing overall motions[J].Journal of Sound and vibration,1995,181(2):261-278.
[13]YOO H H,SHIN S H.Vibration analysis of rotating cantilever beams[J].Journal of Sound and Vibration,1998,212(5):807-828.
[14]方建士,章定国.旋转悬臂梁的刚柔耦合动力学建模与频率分析[J].计算力学学报,2012,29(3):333-339.
[15]章定国,朱志远.一类刚柔耦合系统的动力刚化分析[J].南京理工大学学报,2006,30(1):21-26.
[16]方建士,黎亮,章定国等.基于刚柔耦合动力学的旋转悬臂梁的频率转向与振型转换特性[J].机械工程学报,2015,51(17):59-65.
[17]杨辉,洪嘉振,余征跃.动力刚化问题的实验研究[J].力学学报,2004,36(1):118-124.
[18]杨辉,洪嘉振,余征跃.刚-柔耦合多体系统动力学建模与数值仿真[J].计算力学学报,2003,20(4):402-408.
[19]张雷.航天器分步展开式太阳翼设计与研究[D].上海:上海交通大学,2012.
[20]张亚辉,林家浩.结构动力学基础[M].大连理工大学出版社,2007.
[21]LIU Y,WU S,ZHANG K,et al.Parametrical Excitation Model for Rigid-Flexible Coupling System of Solar Power Satellite[J].Journal of Guidance,Control,and Dynamics,2017.