大跨度桥梁非线性颤振振幅计算方法

The criterion of flutter design of bridges is based on the flutter onset velocity. However, observed in wind tunnel tests, many aerodynamic model of long span bridges and super long span bridges had the stable large amplitude vibration since the flexibility, while the wind speed exceeded the onset speed. This research will propose a method to calculate the accuracy amplitude of flutter since the present method for flutter analysis only focus on the onset velocity which cannot be used to obtain the analysis of soft flutter and large amplitude flutter. The present method also cannot satisfied the requirements of performance-based wind-resistant design of long span bridges in the furture. Based on the obtained researches, motion-induced aerodynamic force will be studied systematically under different large amplitude vibration condition, using forced vibration sets, tensional-string sectional model tests, CFD numerical simulations. The nonlinear expression will be improved to suit to the characteristics of aerodynamic forces of typical bridge girders, and nonlinear flutter computational method of long span bridges based on the amplitude effect will be proposed to achieve the accuracy amplitude acquiring. Finally, the computational method will be verified and improved by the wind tunnel tests. The research also can provide the computational method and technical supports for flutter speed determining,performance-based wind-resistant design and wind-induced vibration control of long span bridges.

当前桥梁颤振设计准则以颤振临界风速为依据。然而风洞试验发现，很多大跨度桥梁在超过临界风速后，仍能依赖自身的柔性维持较大振幅的稳定，而不发生破坏。由于当前的颤振计算方法准确计算出颤振临界点后的振幅，不能用于桥梁的软颤振、或者较大振幅颤振状态的计算，因此无法满足未来大跨度及特大跨度桥梁基于结构性能的抗风设计要求。本项目研究在前期已取得的研究成果基础上，利用强迫振动设备和拉线悬挂节段模型风洞试验，结合CFD 数值仿真技术，系统研究典型桥梁断面自激气动力在不同运动状态的大振幅运动下的演化特征和规律，建立桥梁断面非线性自激气动力表达式，提出在四维空间搜索的考虑振幅和相位角影响的非线性颤振的计算方法，最后采用风洞试验进行验证，以实现准确计算颤振振幅的目标。研究成果可为大跨度桥梁在确定实际颤振风速、进行基于性能的抗风设计和风致振动控制三方面提供计算方法和科学依据。

由于当前广泛采用的自激力模型中气动力仅为折算风速的函数，无法计入气动力随振幅的非线性变化，其对应的颤振计算方法仅能获得临界值，无法计算出颤振临界点后桥梁的运动状态和振幅，难以满足未来超大跨度桥梁的抗风设计要求。因此有必要拓展非线性气动力模型，发展非线性颤振理论，以期获得不同条件下的非线性颤振振幅，进而为超大跨度桥梁的抗风安全设计提供依据。主要研究内容和重要成果包括：(1) 详细研究了典型桥梁断面的非线性颤振特性，揭示了复模态阻尼随振幅变化存在单调变化或抛物线变化的特性，阐释了振幅滞回现象的发生机理，揭示了非耦合气动阻尼在非线性颤振过程中的重要作用。(2)建立了桥梁断面弯扭二自由度非线性颤振计算理论，进而提出了桥梁断面随振幅变化的非线性颤振导数识别方法，交叉验证了计算理论和识别方法的准确性。(3) 建立了以时变位移为变量的非线性阻尼模型，在此基础上建立了耦合非线性自激气动力模型，提出了模型中无量纲气动参数的识别方法。(4) 提出了适用于大跨度桥梁三维非线性颤振振幅计算的双模态闭合解法，开展了主跨1700m悬索桥的三维非线性颤振计算，结果表明，计入振动模态后，非线性颤振起振风速也显著大于二维条件下的计算结果。(5)基于广义坐标，提出了求解大跨度桥梁多模态耦合非线性颤振振幅的双层迭代特征值算法，量化了加劲梁的气动差异对大跨度悬索桥非线性颤振特性的影响，揭示了多模态耦合效应对非线性颤振的作用机理。研究成果弥补了大跨度桥梁非线性颤振振幅计算理论的不足，为超大跨度桥梁抗风设计提供了重要的理论参考。