大型空间环形天线服役过程中波动问题的保结构分析

With the increasing outer space activities nowadays, the study of the large-caliber and ultra-large-caliber hoop truss deployable space antenna is one of the hotspots in aerospace engineering research. Due to different kinds of disturbances, the dynamical behavior of the antenna is shown as elastic wave in the structure and the emergence of complex propagation delay and energy conversion phenomenon are taken during service of the antenna. The purpose of this project is to explore the wave characteristic of the antenna using structure-preserving method. There are three contents of this project as follows. The first is the creation of the Hamilton canonical equations for waves during service. The second is the dimensionality reduction of the high-dimensional nonlinear equations by symplectic vector subspaces method. The third is the realization of the structure-preserving method for nonlinear dynamics systems with constraints. The characteristics of the proposed method embody: the symplectic structure is natural consistent with the periodic property of the antenna and the symplectic sub-system can preserve all the geometric properties of the original system. By using the strucutre-preseving method, the constraints of the nonlinear differential-algebraic equations can be accurately satisfied. Then the original analytical and computational system based on structure-preserving method is established for the waves in the large hoop truss deployable space antenna.

口径达几十米甚至上百米的大型空间环形可展开天线是当前各航天强国实施重大航天工程时竞相研发的热点之一。天线服役过程中受到各种扰动后的动响应以弹性波方式逐渐在结构中传递，并出现复杂的传播延迟和能量转换现象。本项目旨在保结构框架下对该波动问题展开研究，建立该波动问题的保结构分析模型，针对Hamilton体系下带约束的高维非线性方程组进行降维与保结构计算，探索波在大型环形桁架和柔性反射网中的传播特性。其特点是：保结构方法的传递辛矩阵与天线本身的周期结构“天然”一致，建立的模型能完全反映原系统的特征；辛降维后的辛子系统保持原系统的所有几何性质；非线性微分-代数方程的保结构数值算法可以精确满足约束条件。最终建立一套针对服役阶段的大型空间环形可展开天线中波动问题的保结构分析方法。

大型环形可展开天线结构重量轻、柔性大、阻尼小，服役期内其结构展开锁定后具有周期性和对称性的特点，结构的大幅振动会以波动的形式传播。本项目结合保结构方法的优点，提出了研究大型环形可展天线结构波动问题的高效的动响应计算方法。主要研究成果包括：展开锁定后单/双环形桁架结构的固有特性分析，为天线结构设计和其它动力学计算提供依据；大型环形桁架结构动力分析的等效力学模型建立；大型环形可展桁架天线长期在轨运行动力学问题的保结构分析；非线性约束动力学系统的几何积分方法的建立。本项目所提出的算法在天线结构长时间在轨运行的动力学仿真中能够长时间保持系统的能量守恒，能满足系统的各级约束方程，具有高精度和长时间数值稳定的特点。在解决大型航天结构由弹性约束引起的结构、姿态与轨道强耦合动力学问题长时间数值仿真的难题方面具有广阔的应用前景。