面向动力学性能优化的多组件系统保结构布局设计方法研究

Efficient and high-precision analysis of dynamic performance is pre-condition for the optimization of aerospace structure. Taking the typical multi-component system in aerospace application as background, by considering boundary and local vibration amplitude constraint conditions, the governing equation for the dynamic performance of multi-component system under Lagrange framework will be established. Then, based on the Hamilton variation principle, the Hamilton canonical system 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 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 symmetric form, the generalized multi-symplectic schemes will be constructed to investigate the high-dimensional nonlinear dynamic performance, and give out the accurate and robust numerical solution of dynamic response for multi-component system..Further, the mapping model between dynamic response and components layout scheme will be established. Taking the dynamic performance of multi-component system as optimized object, the optimization model will be established by considering constraint conditions such as assembly, components interference. The efficient solving algorithm for optimization model will be researched. The system dynamic performance is optimized through the optimization of component layout scheme. The layout optimization method for multi-component system are formed, the theoretical framework of structure-preserving algorithm is improved, and the foundation is provided for the development of aerospace equipment.

高效、高精度动力学特性分析是进行航天结构动力学优化的前提条件。项目以航天领域常见的多组件系统为研究背景，考虑边界约束和局部振动幅值约束，建立多组件系统动力学响应的Lagrange控制方程。基于Hamilton变分原理，将控制方程导入Hamilton正则系统；借助辛降维和多辛降阶理论，构造其广义多辛对称形式，以保持原系统的全部几何性质。针对该形式，建立保结构分析方法研究多组件系统的动力学特性，揭示系统的高维非线性动力学行为，给出系统精确、稳定的动力学响应数值解。.在此基础上，构建系统动力学响应与组件布局模式之间的映射模型。以动力学性能为优化目标，考虑布局可达性、组件干涉等约束条件，建立多组件系统动力学布局优化模型，研究模型的高效求解算法。通过组件布局模式的优化实现系统动力学性能优化，形成面向多组件系统的布局优化方法，完善保结构算法理论体系，为航空航天装备研制提供基础支持。

航天器中多组件系统的布局模式对系统的动力学性能具有重要影响，为此，有必要发展其动力学优化设计方法。高效、高精度动力学特性分析是进行航天结构动力学优化的前提条件，其核心即在于系统在数值计算过程中实现“保结构”。 针对多组件系统的动力学计算及布局优化问题，项目首先构造了多组件系统动力学控制方程，借助辛降维和多辛降阶理论，构造其广义多辛对称形式，揭示系统的动力学行为；进一步，考虑边界约束和局部振动幅值约束，发展了多组件系统动力学布局优化方法。项目取得的成果主要包括：（1）在计入电子器件质量、忽略电子器件尺寸的假设条件下建立了多组件系统动力学控制方程。（2）针对非均匀中心对称布局多组件系统，构建了波在非均匀圆板中传播的控制方程，基于多辛降阶思想，得到了控制方程的一阶近似对称形式。利用普雷斯曼方法，构造了一种保结构的方案来模拟波在平板中的传播。（3）针对非均匀非中心对称布局系统，提出了波在非均匀圆板中传播的控制方程，在长时间间隔内对板中的波形进行积分，再现非均匀非对称板中共振区域的叠加结果。（4）基于保结构分析方法对多组件系统的振动问题进行模拟，基于模拟结果，以电子器件加速度最大值的加权平均值最小为优化目标对电子器件的布局位置进行优化，得到了满足约束条件的布局优化结果，为航天器中的电子器件的布局优化设计提供了新的途径。

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