太阳帆骨架简化模型自旋展开过程中保结构特性研究
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摘要
针对相控阵空间太阳能电站系统(solar power satellite via arbitrarily large phased array,简称SPS-ALPHA)中太阳帆骨架自旋展开过程中的简化动力学模型,采用辛算法研究了太阳帆骨架的动力响应,并模拟分析了结构振动特性、约束违约及能量保持的情况。首先,建立太阳帆骨架展开过程中的简化模型,基于变分原理将描述简化模型的拉格朗日(Lagrange)方程导入哈密尔顿体系,进而建立模型的正则控制方程;随后,分别采用辛Runge-Kutta方法和经典Runge-Kutta方法模拟骨架结构自旋展开过程,并对比分析了展开过程中的位移约束及能量误差问题。数值模拟结果显示:与经典RungeKutta方法相比,辛Runge-Kutta方法能更好地处理骨架结构自旋展开过程中的约束违约问题及保持系统的总能量不变,并且具有良好的数值稳定性。
For the simplified dynamic model of the skeleton structure of solar sail in the solar power satellite via arbitrarily large phased array system( SPS-ALPHA) in the deploying process,the symplectic method is employed to simulate the dynamic behaviors of the skeleton structure of solar sail and the characteristic of vibration,the constraints default as well as the energy-preserving of the system are all discussed in this paper.Firstly,the simplified dynamic model of the skeleton structure is established based on the variational principle,which is rewritten in the form of the associated canonical equation in Hamilton framework from the Lagrange equation that describes the deploying process of the skeleton structure of solar sail. And then,the equation is numerically simulated by the symplectic Runge-Kutta method and the classical Runge-Kutta method respectively. Comparing with the classical Runge-Kutta method,the symplectic Runge-Kutta method employed in this paper can preserve the displacement constraint and the system energy well with excellent numerical stability.
For the simplified dynamic model of the skeleton structure of solar sail in the solar power satellite via arbitrarily large phased array system( SPS-ALPHA) in the deploying process,the symplectic method is employed to simulate the dynamic behaviors of the skeleton structure of solar sail and the characteristic of vibration,the constraints default as well as the energy-preserving of the system are all discussed in this paper.Firstly,the simplified dynamic model of the skeleton structure is established based on the variational principle,which is rewritten in the form of the associated canonical equation in Hamilton framework from the Lagrange equation that describes the deploying process of the skeleton structure of solar sail. And then,the equation is numerically simulated by the symplectic Runge-Kutta method and the classical Runge-Kutta method respectively. Comparing with the classical Runge-Kutta method,the symplectic Runge-Kutta method employed in this paper can preserve the displacement constraint and the system energy well with excellent numerical stability.
引文
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[2]王新栋,胡伟鹏,邓子辰.空间太阳能电站太阳能接收器二维展开过程的保结构分析[J].动力学与控制学报,2015,13(6):406-409Wang Xindong,Hu Weipeng,Deng Zichen.Structure-Preserving Analysis of 2D Deploying Process for Solar Power Receiver of Solar Power Satellite[J].Journal of Dynamics and Control,2015,13(6):406-409(in Chinese)
[3]赵将,刘铖,田强,等.黏弹性薄膜太阳帆自旋展开动力学分析[J].力学学报,2013,45(5):746-753Zhao Jiang,Liu Cheng,Tian Qiang,et al.Dynamic Analysis of Spinning Deployment of a Solar Sail Composed of Viscoelastic Membranes[J].Chinese Journal of Theoretical and Applied Mechanics,2013,45(5):746-753(in Chinese)
[4]周晓俊,周春燕,张新兴,等.太阳帆自旋展开动力学地面模拟试验研究[J].振动工程学报,2015,28(2):175-182Zhou Xiaojun,Zhou Chunyan,Zhang Xinxing,et al.Ground Simulation Tests of Spinning Deployment Dynamics of a Solar Sail[J].Journal of Vibration Engineering,2015,28(2):175-182(in Chinese)
[5]胡海岩,田强,张伟,等.大型网架式可展开空间结构的非线性动力与控制[J].力学进展,2013,43(4):390-414Hu Haiyan,Tian Qiang,Zhang Wei,et al.Nonlinear Dynamics and Control of Large Deployable Space Structures Composed of Trusses and Meshes[J].Advances in Mechanics,2013,43(4):390-414(in Chinese)
[6]Feng Kang.On Difference Schemes and Symplectic Geometry[C]∥Proceeding of the 1984 Beijing Symposium on D D,Beijing,China,1984
[7]Zhong Wanxie.Some Developments of Computational Solid Mechanics in China[J].Computers&Structures,1988,30(4):783-788
[8]Hairer E,Lubich C,Wanner G.Geometric Numerical Integration:Structure Preserving Algorithms for Ordinary Differential Equations[M].Berlin,Springer-Verlag,2002
[9]Bridges T J.Multi-Symplectic Structures and Wave Propagation[J].Mathematical Proceedings of the Cambridge Philosophical Society,1997,121(1):147-190
[10]李庆军,叶学华,王博,等.辛Runge-Kutta方法在卫星交会对接中的非线性动力学应用研究[J].应用数学和力学,2014,35(12):1299-1307Li Qingjun,Ye Xuehua,Wang Bo,et al.Nonlinear Dynamic Behavior of the Satellite Rendezvous and Docking Based on the Symplectic Runge-Kutta Method[J].Applied Mathematics and Mechanics,2014,35(12):1299-1307(in Chinese)