复合柔性结构全局模态函数提取与状态空间模型构建

魏进; 曹登庆; 于涛

doi:10.6052/0459-1879-18-356

复合柔性结构全局模态函数提取与状态空间模型构建

魏进^*,
曹登庆^†,
于涛^*

* 烟台大学机电汽车工程学院,山东烟台 264005
?? 哈尔滨工业大学航天学院,哈尔滨 150001

基金项目: 国家自然科学基金重点项目资助(11732005)

详细信息

作者简介:
2) 曹登庆,教授,主要研究方向：结构动力学与振动控制. E-mail: dqcao@hit.edu.cn

中图分类号: TB122
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出版历程
- 收稿日期: 2018-10-27
- 刊出日期: 2019-03-17

EXTRACTION OF GLOBAL MODE FUNCTIONS AND CONSTRUCTION OF STATE SPACE MODEL FOR A COMPOSITE FLEXIBLE STRUCTURE

* School of Electromechanical and Automotive Engineering, Yantai University, Yantai 264005, Shandong, China
? School of Astronautics, Harbin Institute of Technology, Harbin 150001, China

摘要

摘要: 随着航空航天等领域中实际工程结构的大型化和柔性化,结构的非线性振动和主动振动控制问题越来越凸显.分析和处理此类结构出现的复杂振动问题的关键在于建立系统的非线性动力学模型与状态空间模型.对于由柔性部件、刚体、连接部件构成的复合柔性结构,由于各部件之间的振动耦合效应,单个柔性部件在悬臂、简支和自由等静定边界下的模态与结构的真实模态有较大差异.为此,本文提出复合柔性结构全局模态的解析提取方法,通过全局模态离散得到系统非线性动力学模型,从而构建状态空间模型.该方法采用笛卡尔坐标描述系统的运动,建立系统的运动方程;结合描述柔性部件的偏微分方程、刚体的常微分运动方程、连接界面处力、力矩、位移和转角的匹配条件以及系统的边界条件,利用分离变量法给出统一形式的频率方程,获取系统的固有频率和解析函数表征的全局模态.这里提出的全局模态提取方法不仅便于复合柔性结构固有频率和全局模态的参数化分析,而且为建立复合柔性结构低维非线性动力学模型和状态空间模型提供了有效的途径,对于推进这类结构的非线性动力学分析与主动振动控制研究具有重要意义.
- 柔性结构 /
- 全局模态 /
- 解析方法 /
- 非线性动力学 /
- 振动控制
Abstract: With the scale enlarging and flexibility of the actual engineering structures utilized in aerospace and other fields, the issues on the study of nonlinear vibration and active vibration control of the structure become more and more important. The key process of dealing with the vibration and control for such a kind of structure is to establish the nonlinear dynamic model and formulate the state space model of the system. For composite flexible structures composed of flexible components, rigid bodies and flexible joints, because of the vibration coupling between each part of the structure, the modes of an individual flexible component with the cantilever, simply supported and free stationary boundary are different from the real mode of the structure. In this paper, an analytic extraction method of global modes of composite flexible structures is presented, and the nonlinear dynamic model and the state-space model of the system can be obtained by the global mode discretization. Adopting the Cartesian coordinates to describe the motion of the system, establishing the motion equations of the system, and combining with the partial differential equation of the flexible part, the ordinary differential motion equation of the rigid body, the matching condition of force, moment, slope of the deflection curve and displacement at the interface, and the boundary condition of the system, the frequency equation of uniform form is given by using the separating variable method. Consequently, the natural frequencies and the global mode representation of the analytic function of the system are obtained. The global mode extraction method presented here not only facilitates the parametric analysis of the natural frequencies and global modes of composite flexible structures, but also provides an effective way to establish the low dimensional nonlinear dynamic model and the state space model of the composite flexible structure, which is of great significance for the study of nonlinear dynamic responses and the design of active vibration control of this kind of structures.
- flexible structures /
- global modes /
- analytic method /
- nonlinear dynamics /
- vibration control

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