风-桥非线性自激系统内共振能量转移机理及应用基础研究

Research on nonlinear aerodynamic force, as well as the nonlinear vibration aroused by it, needs to be conducted especially when longer-span bridges are mainstreaming in the future. The flutter-mode-evolution phenomenon, which was observed during full aero-elastic model wind tunnel tests of a suspension bridge, is a rare case of wind-induced nonlinear vibration. Various types of nonlinear vibration are contained in the phenomenon, including vibration mode transition, soft flutter and internal resonance, and so on, which are mainly caused by nonlinear aerodynamic force and internal resonance. Besides, flutter critical velocity was substantially increased via the energy transfer of internal resonance, which provides a new potential method to control flutter. In this project, forced vibration force-testing and PIV will be utilized synchronously in wind tunnel to recognize nonlinear aerodynamic force features of the streamlined steel box deck under variable amplitude double frequency and constant amplitude single frequency vibration conditions. Expressions of the nonlinear aerodynamic force pertain to the test will be improved or established. In addition, the relationship between the emergence, development and variation of aerodynamic force and unsteady evolution pattern of flow vortex around the section will be analyzed based on the results of wind tunnel tests and CFD simulation. The conditions of internal resonance will be obtained by constructing and solving the nonlinear vibration equation of the deck-cable-tower coupled model for the suspension bridge, meanwhile, the process of flutter mode evolution will be reproduced. A flutter control method, moreover, will be established based on the vibration energy transferring to and accumulating at high-order modes, and its applicability and robustness will be investigated at the same time. This project is expected to enrich wind engineering theory of bridges and lay the foundation for the establishment and development of nonlinear flutter theory.

非线性自激力及其引起的非线性振动是为适应桥梁长大化发展而亟待研究的问题。在某悬索桥全桥气弹模型风洞试验中发现的颤振形态演化现象是难得一见的风致非线性振动案例，包含振动模态转换、软颤振和内共振等丰富的非线性效应，而非线性自激力和内共振是该现象的诱因。该现象通过内共振能量转移大幅提高了颤振临界风速，是一种潜在的全新的颤振控制措施。本项目利用强迫振动测力和PIV同步风洞试验，识别扁平钢箱梁在变幅双频和等幅单频振动状态下的非线性自激力特征，完善或建立相应的非线性自激力表达式，结合CFD方法分析非线性自激力的产生、发展和变化与断面绕流旋涡非定常演化规律的关系；通过构建并求解悬索桥梁-索-塔耦合非线性振动方程获取内共振发生的条件，再现颤振形态演化全过程；建立基于振动能量向高阶模态转移并积聚的颤振控制措施，并研究其适用性和鲁棒性。本项目研究将丰富桥梁风工程理论，为非线性颤振理论的建立和发展奠定基础。

非线性颤振是当前桥梁抗风研究的热点之一。在马鞍山长江大桥全桥气弹模型风洞试验中发现的颤振形态演化现象，包含了振动模态转化、软颤振、内共振等各类非线性效应，有必要开展机理分析。本项目从非线性自激气动力研究出发，采用风洞试验和CFD数值模拟方法分析了扁平箱梁在单频单自由度运动和弯扭不同频复合运动两种状态下的气动力非线性特征，并从流场角度探究了非线性气动力产生的机理及颤振状态下断面绕流特性、旋涡形成和运动等非定常演化规律。针对探究得到的“倍频现象”、“频率耦合现象”等非线性特征，构建了一系列非线性自激气动力模型，并论证了模型气动参数的振幅相关性。首创了三塔悬索桥弯扭耦合自由振动微分方程组，并结合三阶非线性自激力模型实现了全桥非线性颤振分析，采用“模态截断法”初步探究了扭转模态的能量传递现象。引入人工智能手段，基于改进的LSTM网络，提出了模拟桥梁断面非线性自激力的深度学习方法，结合基于卷积计算的全桥动力响应快速计算方法，实现了考虑结构全模态参与的非线性气动响应高效分析。从结构非线性角度出发，建立了马鞍山长江大桥非线性离散数学模型，模拟再现了竖弯模态至扭转模态的演化现象，并从庞加莱截面角度阐述了竖弯、扭转振动模态演化规律与机理。建立了马蒂厄方程形式的悬索桥非线性数学模型，基于马蒂厄函数理论，解释了竖弯媒介下不同阶扭转振动模态演化现象的机理，并总结了能量传递现象发生的条件。在原有的封闭系统模型基础上考虑了气动力的影响，采用连续函数重新描述了三塔悬索桥数学模型，基于分离变量法，探索了线性和非线性自激力对全桥振动模态演化的影响。揭示了结构非线性与气动力非线性对风—桥系统的能量转移的综合作用，最终，总结了颤振模态演化现象并给出了工程应用方面的建议。项目研究成果拓宽了非线性自激力建模的思路，充分挖掘了桥梁的抗风潜能，为丰富和发展非线性颤振理论做出了重要贡献。

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