轴向运动悬臂阶梯结构的时变非线性动力学理论、实验及控制研究

The common characteristic of the axially moving cantilever structures is that the deployment length varies with time. When subjected to external loads, these structures might produce large amplitude vibration and amplitude divergence phenomena, and lose stability easier compared to fixed-length structures. The instabilities will has a harmful effect on the working accuracy and life of the structure. Therefore, it is crucial to investigate the time-varying nonlinear dynamics of axially moving cantilever structures. In this project, the fundamental theories about time-varying nonlinear dynamics of the axially moving cantilever stepped structures are studied under different working conditions. The main contents of this project are as follows: (1) Modeling of time-varying nonlinear dynamics for the axially moving cantilever stepped plates subjected to thermal loads and aerodynamic forces. (2) Developing the analytical method of nonlinear dynamics equation with constant coefficient for use in nonlinear dynamics equation with time-varying coefficient, and using expended analytical method to study the time-varying dynamics characteristics of the axially moving cantilever stepped plate. (3) Based on the results of theoretical analysis for the axial moving cantilever plate, the experiment is designed to carry out the research about time-varying dynamic characteristics. (4) Designing the feedback control law for the axially moving cantilever stepped plate, and proposing the effective solutions for the vibration suppression of time-varying structure. The goal of the research is to fully understand the dynamic responses and general law of the moving cantilever stepped plate, meanwhile, expounds the mechanism of time-varying nonlinear dynamics phenomena. This project will provide theoretical guidance for the widely used in the engineering of time-varying structures.

轴向运动悬臂结构的显著特点是结构的长度随时间变化，相比于定长结构，时变长度结构在外载荷作用下容易产生大幅值振动、振幅发散等非线性动力学现象，对结构的工作精度和寿命产生不良影响，因此深入研究其复杂时变动力学至关重要。本项目将对不同工况下轴向运动悬臂阶梯结构的时变非线性动力学特性开展基础理论研究，内容如下：(1)建立热载荷和高超音速等条件下轴向运动悬臂阶梯板时变非线性振动模型；(2)拓展用于求解时变结构非线性动力学特性的解析分析方法，开展轴向运动悬臂阶梯结构的时变特性研究；(3)基于理论分析结果设计实验，开展时变结构的动力学特性实验研究；(4)针对轴向运动悬臂阶梯结构设计反馈控制律，提出有效抑制结构振动的解决方案。本项目力求清楚掌握轴向运动悬臂阶梯结构变长度过程中的动力学响应与一般规律，清晰阐述时变系数结构非线性动力学现象发生的机理，为推动时变结构在工程中的广泛应用提供理论指导。

变长度悬臂结构的特点是轴向的长度随时间变化，这会引起结构的质量、刚度和频率等参数发生变化，当受到复杂载荷作用时容易发生复杂的动力学行为，制约时变结构在工程上的广泛应用。本项目采用了数值、解析和实验等方法研究了轴向运动悬臂阶梯结构在伸展和回收过程中的时变动力学规律。课题在以下几个方面取得了进展：(1) 研究了不同工况条件下轴向移动石墨烯增强复合材料阶梯板的时变动力学建模，并深入分析了石墨烯纳米片分布及尺寸、压电效应和温度变化等因素对时变结构动力学稳定性的影响；(2) 通过拓展经典解析方法深入研究了轴向可变展长可伸缩悬臂阶梯复合板在复杂载荷作用下的时变非线性动力学特性，发现并阐明了结构在伸缩过程中存在振幅跳跃等非线性振动现象及发生机理。(3) 针对几何非线性和多参数耦合的振动系统、提出了鲁棒复合控制策略，实现了对石墨烯增强和功能梯度等复合材料悬臂板结构的动力学优化设计和振动有效抑制；(4) 针对控制系统中存在参数不确定和大幅值非线性振动抑制难题，基于全维状态观测器提出了一种抑制悬臂板振动的控制策略，将位移模态函数与速度反馈控制器相结合，产生主动阻尼来影响结构的动力响应，从而实现了对存在几何非线性系统振动的主动抑制。本项目通过深入研究轴向运动悬臂阶梯结构的时变动力学特性，探寻轴向运动悬臂板阶梯结构的基本固有振动特性和时变全局动力学现象，获得了时变悬臂阶梯结构稳定运动的参数范围，并提出可行的振动控制策略，研究成果可为时变结构的优化设计和工程应用提供理论指导。