桥梁断面颤振导数识别的加权整体最小二乘法

在已有研究的基础上 ,基于桥梁节段模型自由衰减振动记录 ,提出了一种识别桥梁断面颤振导数的新方法———加权整体最小二乘法 (WELS)。该方法将同一风速下多次自由振动记录作为一个整体 ,在整体残差平方和最小的意义上同时对该风速下多次竖向和扭转运动时程曲线进行非线性最小二乘拟合 ,获取多条自由振动曲线共同的阻尼和刚度信息 ,从而提高了颤振导数识别的精度。为了避免弱信号被强信号“淹没” ,并使各时程信号的识别误差相当 ,识别过程中对各试验记录引入了加权因子 ,使各试验记录在整体残差分析中具有相同权重。此外 ,该方法对多次试验记录同时进行拟合 ,在一定程度上减弱了个别信号中有色噪声对迭代收敛性的影响 ,增加了非线性最小二乘迭代过程的稳定性。为考查加权整体最小二乘识别方法的有效性 ,分别进行了两种断面形式的节段模型风洞试验     

Identification of flutter derivatives of bridge decks with free vibration technique

The flutter derivatives of bridge decks can be determined in a unique manner on condition that the complex modal parameters of the system at one reduced frequency are obtained. Based on the idea, a new method of identifying the flutter derivatives of bridge decks is proposed and it can overcome some shortcoming of the existing method and extend the applicability of the free vibration technique at high wind velocity. The identified results have agreements with the target ones of an ideal thin-plate section and those of a thin-plate section measured by the forced vibration technique. The proposed method is reliable and effective to extract the flutter derivatives from coupled free vibration.     

Identification of aerodynamic parameters for eccentric bridge section model

The equations of motion for bridge deck section model elastically suspended in wind tunnel are formulated about mass center of the system using the Lagrangian approach, accommodating both the elasticity and damping eccentricities in the formulation. The Subsection Extended-Order Iterative Least Square (SEO-ILS) algorithm is developed in the state space for direct identification of system matrices from free vibration data of section model obtained from wind tunnel testing. The flutter derivatives can be extracted straightforwardly from the difference in the system matrices identified at zero wind velocity and at a specific wind velocity, respectively. By making use of complex modal decomposition technique, a procedure is employed to correct the system matrix at zero wind velocity considering both eccentricities. The proposed method is applied to identify the flutter derivatives of a thin plate section model and the section model of a suspension bridge. The results show a favorable agreement between the flutter derivatives of a thin plate obtained with the proposed method and those derived from the analytic formulae. The identified direct flutter derivatives of the suspension bridge section model also are in good agreements with those obtained using Scanlan's method. It is shown that the use of the corrected system matrix at zero wind velocity leads to better accuracy in identifying the flutter derivatives especially at high reduced wind velocity than using the original system matrix, and the eccentricity is found to have more influence on the cross flutter derivatives than on the direct flutter derivatives.     

风雨联合作用下大跨桥梁颤振稳定性试验研究

针对风雨联合作用下的大跨桥梁颤振稳定性,以一开槽双箱梁桥梁为研究对象,通过在大气边界层风洞中搭建的风雨联合作用试验系统,完成基于自由振动法的节段模型颤振试验。通过分析不同雨强下该桥梁主梁的颤振导数以及颤振临界风速,进而获取降雨对大跨桥梁颤振稳定性的影响规律。试验结果显示:颤振导数随雨强变化而变化,其中体现扭转气动阻尼特性的颤振导数变化较为显著,随雨强增大,颤振临界风速先增大后减小。试验结果表明:降雨对大跨桥梁的颤振导数以及颤振临界风速均有一定影响。     

形断面的压力分布特性对其颤振性能的影响

文中推导了采用模型表面压力来描述的颤振导数表达式,结合计算流体动力学方法,获取模型表面压力,分析颤振导数表达式中压力幅值和相位差的提取方法,研究模型表面压力分布特性对颤振导数以及颤振稳定性的影响。通过对模型进行合理分区,探讨模型表面不同区域对颤振导数的贡献,以此为基础分析了中央稳定板的抑振原理。研究结果表明,H形主梁上下表面旋涡的非对称分布造成了模型表面平均压力分布的非对称性,并使得模型产生顺时针转动力矩。当风速低于颤振临界风速时,对颤振导数A*2影响较大的分布压力会使模型产生逆时针转动力矩,从而维持了振动系统的平衡|而当风速达到颤振临界风速时,影响A*2的分布压力将会使模型产生顺时针转动力矩,因此破坏了振动系统的稳定性。     

Direct identification of flutter derivatives and aerodynamic admittances of bridge decks

Flutter derivatives and aerodynamic admittances provide basis of predicting the critical wind speed in flutter and buffeting analysis of long-span cable-supported bridges. In this paper, one popular stochastic system identification technique, covariance-driven stochastic subspace identification (SSI in short), is first presented for estimation of the flutter derivatives and aerodynamic admittances of bridge decks from their random responses in turbulent flow. Numerical simulations of an ideal thin plate are adopted to extract these aerodynamic parameters to evaluate the applicability of the present method. Then wind tunnel tests of a streamlined thin plate model and a Π type blunt bridge section model were conducted in turbulent flow and the flutter derivatives and aerodynamic admittances are determined by the SSI technique. The identified aerodynamic parameters are compared with the theoretical ones and the results indicate the applicability of the current method.     

Time-domain and frequency-domain approaches to identification of bridge flutter derivatives

Flutter derivatives are essential for flutter analysis of long-span bridges, and they are generally identified from the vibration testing data of a sectional model suspended in a wind tunnel. Making use of the forced vibration testing data of three sectional models, namely, a thin-plate model, a nearly streamlined model, and a bluff-body model, a comparative study was made to identify the flutter derivatives of each model by using a time-domain method and a frequency-domain method. It was shown that all the flutter derivatives of the thin-plate model identified with the frequency-domain method and time-domain method, respectively, agree very well. Moreover, some of the flutter derivatives of each of the other two models identified with the two methods deviate to some extent. More precisely, the frequency-domain method usually results in smooth curves of the flutter derivatives. The formulation of time-domain method makes the identification results of flutter derivatives relatively sensitive to the signal phase lag between vibration state vector and aerodynamic forces and also prone to be disturbed by noise and nonlinearity.     

风雨共同作用下平板模型的气动导数试验研究

气动导数是大跨桥梁结构颤振和抖振分析中确定颤振临界风速和抖振响应的重要依据。在实际中 ,强风(特别是台风 )一般总伴随着暴雨。但遗憾的是 ,目前所有的研究均是在均匀风场或紊流风场中识别气动导数 ,而没有考虑暴雨的作用。本文采用随机系统识别方法 ,在模拟的风雨共同作用条件下识别了薄平板模型的气动导数。初步研究结果表明 ,风雨共同作用下平板结构的气动导数明显不同于仅有风作用的结果。这一新发现值得研究人员和工程技术人员的重视     

风驱雨作用下桥梁主梁颤振节段模型试验研究

针对风驱雨作用下桥梁主梁的颤振问题,依据风驱雨作用和主梁振动特点,给出了分别考虑雨滴冲击和表面积水后的降雨相似关系,并探讨了其选取原则。选取大跨度桥梁较常采用的典型断面,通过节段模型试验模拟了风驱雨对主梁断面的颤振导数和颤振发生过程的影响。试验结果表明:主梁断面的颤振气动导数随雨强的变化无明显规律,各导数的变化量值相当,随风速增加,降雨引起的导数变化有所加大,但基本没有改变其随风速变化的整体趋势,试验雨强120mm/h时,模型颤振临界风速会有20%～30%左右的提高,但考虑雨强相似比后可以认为降雨对桥梁主梁的风致颤振失稳特征的影响基本可以忽略。     

桥板颤振导数的比较和敏感性分析 第一部分：试验数据分析

为评估风载下桥板的性能,通常采用多年来发展的两个独特的方法（自由和强迫振动）,从风洞模型试验中得到桥板气动弹性系数。尽管已有众多的研究者对每个技术优缺点进行分析,但文献中缺少对试验结果的系统比较。本研究的意义在于进行与长期颤振导数试验数据相关的评估,包括分析和解释自由和强迫振动两种方法的异同点。从2002年开始,美国的爱荷华州大学和日本的公立研究所着手进行桥颤振导数的研究。试验包括的截面类型很广,从矩形棱柱到改进型,尤其考虑了当前在大跨桥中采用空气动力学设计梁的趋势。同时系统地分析和比较了两种方法颤振导数的试验结果。在相关的论文中,对敏感性进行分析以研究大跨桥在气动弹性不稳定时颤振导数数据中所隐含的不同点。     

Flutter mechanism for rectangular prisms in smooth and turbulent flow

The aim of the present work is to clarify the flutter mechanism for suspended long span bridges via a parametric analysis on flutter instability for a set of given deck profiles. Several wind tunnel tests in the DIC-CRIACIV boundary layer wind tunnel (BLWT) have been carried out on spring suspended section models such as rectangular cylinders of different slenderness ratios B/D=5 and 12.5, where B is the longitudinal length of the prism and D is the height of the prism. The main experimental parameters needed for examining whether a given bridge profile is flutter-prone below a certain mean wind velocity are the flutter derivatives, so a system identification procedure (combined system identification method, CSIM) has been developed to extract simultaneously all flutter derivatives from two degrees of freedom (2DoF) section model test results (coupled vertical-torsional free vibration tests). The parametric analysis includes the investigation on (1) the effects of model dynamic properties on BLWT test results, (2) the consequence of turbulence on bridge stability, (3) the possible definition of an aerodynamic stability performance index (β) for rectangular cylinders for designing purposes.     

A simplified approach to bridge deck flutter

Flutter instability of flexible bridge decks is investigated in the framework of the semi-empirical Scanlan's approach based on flutter derivatives. The equations of the eigenvalue problem of stability are manipulated and simplified thanks to the analysis of a large number of dynamic and aerodynamic data. Simple expressions for critical reduced wind speed and coupling frequency are obtained. The major interest of this approximate method is the fact that only three or even two flutter derivatives are required to calculate the flutter instability limit. In addition, these aerodynamic functions are known to be quite reliable and the easiest to be identified through wind-tunnel tests. The proposed formulas seem to give accurate results in a wide range of cases, unless the frequency ratio is very close to unity. The method is shown to apply also in case of cross sections prone to torsional flutter. Finally, the paper offers a valuable insight into the flutter behavior of several types of bridges and investigates the role in the instability onset played by various structural parameters, such as frequency ratio and structural damping.     

紊流风场中桥梁气动导数识别的随机方法

气动导数是大跨桥梁结构颤振和抖振分析的重要依据。本文提出采用随机系统识别方法来识别紊流风场中的气动导数, 与当前应用较广的瞬态激励法及强迫激励法相比, 这类方法的优势在于: (1) 将紊流看作是激励, 而不是噪声, 更能反映结构实际工作状态下的特性; (2) 识别精度不受风速的制约, 可以获得较高折减风速下的气动导数; (3) 可直接在紊流风场中结构随机响应上进行识别, 无需任何人为外在激励, 试验更为简单易行。在风洞中完成了紊流风场中桥梁节段模型测振试验, 进一步利用本文的方法识别出气动导数。与相关文献提供的类似模型在均匀场和紊流场中识别结果的对比表明: 本文识别的气动导数是可靠的, 所提出的采用随机系统识别方法来识别紊流风场中气动导数的思路是可行的。     

Data-driven stochastic subspace identification of flutter derivatives of bridge decks

Most of the previous studies on flutter derivatives have used deterministic system identification techniques, in which the buffeting forces and the associated responses are considered as noises. In this paper, one of the most advanced stochastic system identification, the data-driven stochastic subspace identification technique (SSI-DATA) was proposed to extract the flutter derivatives of bridge decks from the buffeting test results. An advantage of the stochastic method is that it considers the buffeting forces and the responses as inputs rather than as noises. Numerical simulations and wind tunnel tests of a streamlined thin plate model conducted under a smooth flow by the free decay and the buffeting tests were used to validate the applicability of the SSI-DATA method. The results were compared with those from the widely used covariance-driven SSI method. Wind tunnel tests of a two-edge girder blunt type of Industrial-Ring-Road Bridge deck (IRR) were then conducted under both smooth and turbulent flows. The identified flutter derivatives of the thin plate model based on the SSI-DATA technique agree well with those obtained theoretically. The results from the thin plate and the IRR Bridge deck helped validate the reliability and applicability of the SSI-DATA technique to various experimental methods and wind flow conditions. The results for the two-edge girder blunt type section show that applying the SSI-DATA yields better results than those of the SSI-COV. The results also indicate that turbulence tends to delay the onset of flutter compared with the smooth flow case.     

Simplified prediction of wind-induced response and stability limit of slender long-span suspension bridges, based on modified quasi-steady theory: A case study

The Hardanger Bridge is currently under construction in Norway. It will have a main span of 1310 m and a girder that is only 18.3 m wide, which implies that wind-induced vibration is a major concern in the design. Buffeting response and flutter analysis of the Hardanger Bridge are treated in this paper. The self-excited forces are modelled using aerodynamic derivatives obtained from free vibration tests, quasi-steady theory, and a suggested modified quasi-steady theory. The stability limit predicted using aerodynamic derivatives corresponded well with the wind tunnel results, while the quasi-steady theory severely underestimated the critical mean wind velocity for the section model used in the wind tunnel tests. A new set of modified quasi-steady coefficients are suggested, where the experimental results of the aerodynamic derivatives are used to obtain frequency-independent model coefficients. The critical velocities predicted by the modified quasi-steady coefficients differ only by 4-5% from estimates based on the aerodynamic derivatives. The response predicted by the suggested simplified aerodynamic model is also presented, and the results indicate that adequate estimates are achieved.     

Comparative and sensitivity study of flutter derivatives of selected bridge deck sections,Part 1: Analysis of inter-laboratory experimental data

Aeroelastic coefficients (flutter derivatives) of bridge decks are routinely extracted from wind tunnel section model experiments for the assessment of performance against wind loading. Two distinct methods, developed over the years, are usually employed for this purpose (free or forced vibration). Even though advantages and disadvantages of each technique have been highlighted by numerous researchers, few examples of a systematic comparison of the experimental results are available in the literature. The significance of this study is related to the evaluation of an extended set of experimental data on flutter derivatives, and includes the analysis and interpretation of the differences recorded through the two methods.The motivation for this work emerged from the United States–Japan Benchmark Study on Bridge Flutter Derivatives that Iowa State University (ISU) in the United States and the Public Works Research Institute (PWRI) in Japan, initiated in 2002. Tests were designed to cover a wide range of solid cross sections, from bluff (rectangular prisms) to streamlined, in particular considering the current trend of engineers to use aerodynamically-designed girders for bridges with longer spans. In this paper, a systematic analysis and a comparison of laboratory results of flutter derivatives obtained at both institutions were performed. In a companion paper, a sensitivity study was performed to examine the implications of the perceived dissimilarities among flutter-derivative data sets on the aeroelastic instability of long-span bridges (single-mode and coupled-mode).     

大跨度桥梁多模态耦合颤振二分法全自动搜索

在分析和评价国内外对大跨度桥梁风致颤振研究的成果和目前各种常用颤振分析方法优缺点的基础上,基于结构的固有模态坐标,进一步完善了大跨度桥梁多模态耦合颤振的双参数搜索状态空间法。通过将结构和气流作为一个动态系统,最后将颤振问题归结为数学上一个非对称实矩阵的广义特性值问题。在求解中,风速搜索采用了二分法加速收敛技术,频率采用搜索迭代法,该方法可以按指定的搜索精度,迅速搜索到颤振临界风速和颤振频率,无须设定步长,且能真实地给出各阶模态频率和阻尼比随风速的全过程。最后对具有理想平板截面的悬臂梁进行颤振分析验证了本文方法的正确性,同时对总跨度1177m的香港汀九大桥进行颤振分析,计算得到的颤振临界风速基本与风洞试验结果基本一致,进一步表明本文方法的可靠性和高效性。     

用调谐转动惯量阻尼器控制大跨度桥梁颤振研究

针对大跨度桥梁的颤振问题,研究了利用调谐转动惯量阻尼器(TRID)进行大跨度桥梁颤振的被动控制方法。建立了具有调谐转动惯量阻尼器的桥梁在均匀风场中的系统颤振运动方程,引入状态空间向量,求解颤振临界风速。以虎门大桥为对象,分析了TRID对提高临界风速的有效性及TRID参数对控制效果的影响。