大型可展天线中锁网与桁架耦合结构的混沌动力学研究

The main development trend of the satellite antenna is large scale, high precision and easy to package. The large deployable antenna is the focus and hotspot of national research at present. Because of the alternating thermal excitation, the large deployable antenna produces the large deformation and large amplitude nonlinear vibration, such as subharmonic nonlinear vibration, in which there exist large amplitude chaotic motion. Due to the instability and randomness of chaotic motion, it affects the stable operation and the observation accuracy of the antenna. Therefore, it is of great scientific significance to study the chaotic dynamics of large deployable antennas. In this project, we will establish the dynamics modeling of large deployable antennas with a lattice-truss coupling structure. The method of modal extraction is used to reduce the dimension of the system and the six-dimensional nonlinear system is obtained. The energy phase method is improved by combining the global perturbation theory, the differential geometry and the normal form. The mechanism of chaotic motion is revealed, and the geometric structure of multi-pulse jumping in the six-dimensional phase space is described. The multi-pulse chaotic dynamics of six-dimensional nonlinear system with the lattice-truss coupling structure in large deployable antennas is studied by the improved energy phase method. The research of this project is significant for optimizing the structure design of large deployable antenna and proposing vibration control schemes during operation. Results will promote the development of nonlinear global perturbation theory.

大口径、高精度和易收纳等特点是现今卫星天线的主要发展趋势，大型可展天线是国家目前研究的重点和热点。大型可展天线服役时受交变热载荷作用产生大变形、大幅值非线性振动，如次谐非线性振动、亚谐非线性振动，其中存在大幅的混沌振动。混沌振动具有不稳定性和随机性，影响天线的稳定运行和观测精度。因此，研究大型可展天线的混沌动力学具有重要的科学意义。本项目首先建立大型可展天线中锁网与桁架耦合结构的动力学模型，利用模态提取法对系统进行降维处理，得到六维非线性系统。综合利用全局摄动理论、微分几何理论、规范型理论改进能量相位法，揭示系统产生混沌运动的机理，构造六维相空间中多脉冲跳跃的几何结构。利用改进的能量相位法研究大型可展天线中锁网与桁架耦合结构的多脉冲混沌动力学。本项目的研究对优化大型可展天线的结构设计以及天线服役时控制振动策略的提出具有重要意义，同时推进非线性全局摄动理论的发展。

可展环形桁架天线具有大口径、高精度和易收纳等特点，是大型可展天线中较为理想的结构。可展环形桁架天线服役时受到空中交变热载荷作用产生大变形、大幅值的混沌振动，直接影响空间结构的稳定运行、观测精度和使用寿命。为确保天线在运行过程中的稳定性以及抑制系统产生大幅值混沌运动，在结构设计阶段进行有效的动力学建模是十分必要的。利用高维非线性系统的理论，分析并预测服役时可能产生的非线性振动，进而可以为优化结构设计提供参考。本文在对可展环形桁架天线结构的动力学行为进行分析时取得了一些创新性成果，并从理论和数值两方面证实了系统存在多脉冲混沌运动。解决了研究可展环形桁架天线系统动力学特性时存在的两个科学问题：选取系统的模态函数；构造六维相空间中多脉冲轨道的几何结构。在发展和推广高维非线性系统能量相位法时获得了突破性研究成果，通过引入特征横截面将前两维系统限定于共振情形下四维系统上，研究系统在受到小扰动影响下其稳定流形和不稳定流形的变化，给出六维相空间中流形受扰后的几何结构图，得到系统在六维相空间中的全局动力学特性。使改进后的能量相位法更适用于研究复杂六维非线性系统的多脉冲混沌运动。这些研究成果对力学、航空航天以及数学等多学科发展都具有重要的学术价值和科学意义。