基于全局模态理论的柔性组合结构非线性动力学建模与模型降阶研究进展
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国家自然科学基金资助项目(10772056,11732005,12372004,12002058,11302087,12002298)


Research Progress for Nonlinear Dynamics Modeling and Model Reduction of Flexible Composite Structures Based on Global Modal Theory
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    摘要:

    在工程结构设计中,理论建模是确保结构具备安全、持续与稳定运行能力的关键步骤,尤其是在动力学特性分析中不可或缺.组合结构的动力学模型通常需要降阶处理,以便进行非线性动力学分析和控制器设计.传统基于单一部件模态函数的动力学模型在经典静定边界条件下构建,结果与整体结构模态存在显著差异.全局模态理论能够揭示刚性与柔性结构运动间的耦合效应,提供准确反映组合结构振动的整体模态.本文综述了近年来全局模态方法在索、梁、板等组合结构动力学模型降阶问题中的研究进展,主要介绍基于笛卡尔和拉格朗日坐标系的多刚柔体系统全局模态求解方法;通过多梁刚性连接、索-梁组合、刚柔耦合航天器等实例,阐述全局模态方法在复杂组合结构固有特性分析中的应用.多项研究结果表明,全局模态方法不仅克服了传统方法对模态形式与数量的依赖,还在揭示复杂动力学现象及优化结构设计和振动控制中展现了显著优势.

    Abstract:

    The theoretical modeling is the critical step to ensure the safe, sustainable and stable operation of the engineering structure in the design phase, especially in the dynamical characteristics analysis. The reduced order procedure of the composite structure’s dynamical model is required so as to nonlinear dynamic analysis and controller design. However, the traditional dynamical model that established by the modal function of a single component is based on the classical statically indeterminate boundary conditions. There exists the significantly difference compared with the modes obtained by the whole structure. The global mode theory can reveal the coupling effect between rigid motion and flexible deformation of the structure, and provides the global mode that can accurately reflect the vibration of the combined structure. In this paper, the research progress of the global modal method in the reduced order for the combined structure dynamic model such as cables, beams and plates in recent years is given. The solving method for the global mode method of the multi-rigid-flexible coupling system based on the Cartesian and Lagrange coordinate is mainly focused. The application of the global modal method in the analysis of natural characteristics of the complex combined structure is illustrated by the examples such as the multi-beam rigid connection, cable-beam combination and rigid-flexible coupling spacecraft. Multiple research results show that the global mode method not only overcomes the dependence on the mode form and quantity of the traditional method, but also shows the prominent advantage in revealing complex dynamic phenomena, optimizing structural design and vibration control.

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曹登庆,曹彧腾,宋敉淘,魏进,何贵勤,方波.基于全局模态理论的柔性组合结构非线性动力学建模与模型降阶研究进展[J].动力学与控制学报,2025,23(11):28~43; Cao Dengqing, Cao Yuteng, Song Mitao, Wei Jin, He Guiqin, Fang Bo. Research Progress for Nonlinear Dynamics Modeling and Model Reduction of Flexible Composite Structures Based on Global Modal Theory[J]. Journal of Dynamics and Control,2025,23(11):28-43.

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  • 收稿日期:2024-11-13
  • 最后修改日期:2024-12-17
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  • 在线发布日期: 2025-11-28
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