考虑一阶气动非线性效应的桥梁断面弯扭耦合颤振稳态响应振幅分析方法

Reasonably estimating bridge flutter amplitude is one of the key scientific issues to develop more economical criterion for long span bridge flutter design and safety evaluation. Aiming at vertical-torsional coupling flutter, this project explores analytical method for estimating steady-state response amplitude of bridge deck flutter in two dimensions with two degrees of freedom. Firstly, theoretical derivation is started with simple harmonic motion hypothesis. The bridge flutter dynamic system is approximated as weak nonlinear system where the amplitude of response is changed slowly. The flutter derivatives are expressed as function with three variables including reduced wind speed, non-dimensional amplitude and mean angle of attack. First order harmonic balance method and step by step analysis method are applied to solve flutter equations of vertical-torsional motion and to estimate steady state amplitude of flutter. Then, experimental verification is performed on section model test of streamlined box girder and twin-side girder. Static aerodynamic coefficients and nonlinear flutter derivatives are identified. Nonlinear stiffness and structural damping of the dynamic model system are measured. Based on these parameters, the new analytical method is used to calculate the steady state amplitudes of these two section models. The theoretical results are in contrast to experimental results and the application range of the method is discussed. Finally, the method is used to investigate the influence of structural damping ration on flutter amplitude for these two sections, as long as the corresponding energy mechanism. Results of this project are conductive to improve present theory system of bridge flutter analysis.

桥梁颤振振幅的合理预测，是发展更经济的大跨度桥梁颤振设计和安全评价标准须重点解决的科学问题。本项目针对弯扭耦合型桥梁颤振，探索可用于预测桥梁断面颤振稳态响应振幅的二维二自由度耦合颤振理论分析方法。首先，采用理论推导，基于桥梁颤振运动的简谐极限环假设，将桥梁颤振系统近视为振幅缓变的弱非线性体系，把颤振导数表达为折算风速、无量纲颤振振幅、平均风攻角的三元函数，应用一阶谐波平衡法和颤振分步分析法，求解弯扭耦合颤振运动方程，预测颤振稳态响应振幅。随后，进行试验验证，制作流线型箱梁、边主梁断面节段模型，测试断面的静力三分力系数、非线性颤振导数，识别弹性悬挂模型系统的非线性刚度和结构阻尼，基于理论预测模型的颤振稳态响应振幅，并与颤振试验振幅对比，探讨理论的工程适用范围。最后，应用理论，系统研究结构阻尼比对两类桥梁断面颤振振幅响应的影响差异，揭示其能量机制。研究成果有益于完善现有桥梁颤振分析的理论体系。

现有的桥梁颤振设计方法单纯以颤振临界风速作为桥梁颤振安全的唯一评价指标，并不能足够准确地描述桥梁颤振发生时的安全程度，科学合理的估计桥梁颤振振幅及其随风速变化规律，是提高超大跨度桥梁颤振抗风设计经济性的关键前提。本项目针对大跨度桥梁常见的弯扭耦合型颤振，考虑气动力关于振幅的一阶非线性效应，进一步发展桥梁断面的二自由度弯扭耦合颤振分析理论。采用理论推导的方式，将在非线性颤振自激力模型中，将颤振导数表达为折算风速、颤振振幅、平均风攻角的三元函数。在数学求解过程中，将桥梁颤振系统视为振幅缓变的弱非线性体系，基于一阶谐波平衡法结合分步分析法，求解二维二自由度弯扭耦合颤振运动方程，实现了对桥梁颤振稳态响应振幅的理论分析。在风洞试验中通过弹簧悬挂节段模型的颤振测试，在准确识别弹性悬挂模型体系自身阻尼非线性的基础上，开展颤振振幅论的试验研究工作，揭示了二维桥梁断面颤振响应特征和系统阻尼比随风速的演化特征，研究了结构阻尼对颤振响应的影响规律。研究结果表明，桥梁断面的非线性颤振响应行为表现为振幅随风速逐渐增大，结构阻尼不仅影响颤振临界风速，还能显著影响颤振响应振幅，这使得增加阻尼可作为一种潜在的手段用于桥梁颤振的响应控制。本项目的研究成果，一方面对于发展未来超大跨度桥梁颤振抗风设计标准、提高颤振设计的经济性有积极作用，另一方面还可为评价现有已建成的大跨度桥梁在遭遇未来极端天气气候事件而不幸发生颤振时的安全性，提供理论分析手段和安全评价工具。