超大超柔周期性阻尼结构中波传播特性的保结构分析方法

The study on the propagation characteristics of the elastic wave in the ultra-large ultra-flexible periodic damping structure is not only the demand of the dynamic analysis for the future mega aerospace structures, but also the precondition of the active control on the dynamic responses for the mega structures based on the wave absorption theory. Thus, the structure-preserving method will be proposed to investigate the propagation characteristics of the elastic wave in the ultra-large ultra-flexible periodic damping structure systematically in this project..Considering the damping of the structure material and the discontinuous (non-smooth) unilateral displacement constraint conditions on the boundaries between the basic components of the aerospace structure, the governing equation for the wave propagating in the ultra-large ultra-flexible periodic damping structure under the Lagrange framework will be established firstly. Then, based on the Hamilton variation principle, the infinite-dimensional Hamilton canonical system with damping will be deduced from the governing equation. Subsequently, according to the symplectic dimensionality reduction method and multi-symplectic order reduction method, the generalized multi-symplectic approximate symmetric form will be derived from the canonical systems, which will preserve all of the inherent geometric properties of the original system theoretically. For the approximate symmetric form, the generalized multi-symplectic schemes will be constructed to investigate the propagation characteristics of the elastic wave in the ultra-large ultra-flexible periodic damping structure finally. The numerical results of this project will reveal the attenuation characteristic of the elastic wave propagating in the flexible damping components, the power flow redistribution law on the boundary of the basic components in the ultra-large ultra-flexible periodic damping structure, and the energy exchange mechanism in the local interaction region of the elastic waves..Studying the propagation characteristics of the elastic wave in the ultra-large ultra-flexible periodic damping structure by structure-preserving method will not only improve the structure-preserving theoretical system, but also lay the foundation of the active control design for the ultra-large ultra-flexible periodic damping structure.

波在超大超柔周期性阻尼结构中的传播特性研究是巨型航天结构动力学分析的需要，也是从波吸收角度对巨型结构动响应进行主动控制的前提条件。以空间太阳能电站这类超大超柔航天结构为研究背景，考虑材料阻尼和基本构件边界处非连续/非光滑单边位移约束，建立波在超大超柔周期性阻尼结构中传播的Lagrange控制方程；基于Hamilton变分原理，将控制方程导入耗散无限维正则系统；借助辛降维和多辛降阶理论，构造其广义多辛近似对称形式，该形式保持了原系统的全部几何性质；针对该形式，建立保结构分析方法系统研究超大超柔周期性阻尼结构中波传播特性，揭示弹性波在柔性阻尼构件中传播的衰减特性、在交汇区域局部能量交换机理及在周期性结构基本构件边界处的功率流重分布规律。.发展长时间数值稳定的保结构分析方法探索超大超柔周期性阻尼结构中波传播特性，不仅完善保结构算法理论体系，而且为超大超柔周期性阻尼结构的主动控制提供理论依据。

针对超大超柔周期性阻尼结构中波传播问题，发展计算效率高、长时间数值稳定、能真实反映波传播特性的保结构分析方法，不仅是结构动力学分析的需要，也是从波吸收角度对结构动响应进行主动控制的前提条件。. 本项目主要开展了如下四个方面研究工作：Hamilton动力学系统的保结构分析方法；保结构方法在碳纳米管非线性动力学问题中的应用；超大空间柔性构件的动力学建模与耦合动力学问题的保结构分析方法；超大空间组合结构的动力学建模与波传播特性的保结构分析方法。在Hamilton动力学系统的保结构分析方法研究方面，基于广义多辛理论，建立了动力学系统对称破缺与保结构理论之间的内在联系。在保结构方法在碳纳米管非线性动力学问题中的应用方面，将保结构分析方法应用于碳纳米管非线性动力学问题的分析，揭示了阻尼耗散对碳纳米管非线性特性的影响机理。在超大空间柔性构件的动力学建模与耦合动力学问题的保结构分析方法研究方面，发现了超大空间柔性构件新的稳定姿态。在超大空间组合结构的动力学建模与波传播特性的保结构分析方法研究方面，发现了薄板内弹性波传播的阻尼特性和碰撞特性等新颖的波传播特性。. 本项目采用保结构方法系统分析超大超柔周期性阻尼结构中弹性波的传播特性，研究弹性波的衰减特性以及在构件边界处的能量转换、功率流重分布和在交汇区域的能量交换等局部几何性质，为超大超柔空间可展开结构的波动控制提供理论依据。