应用碳纤维缆索的大跨度悬索桥抗风稳定性研究

为了探讨碳纤维复合材料缆索在大跨度悬索桥中应用的可能性,以主缆等轴向刚度为原则,拟定了一座主跨为1490m的碳纤维复合材料主缆悬索桥,并运用三维非线性计算理论进行了空气静力和动力稳定性分析。通过与同跨度钢主缆悬索桥的比较,讨论了不同主缆材料对大跨度悬索桥抗风稳定性的影响。分析结果表明:大跨度悬索桥采用碳纤维复合材料主缆后,静风作用下结构的变形增大,但其静风稳定性却与钢主缆悬索桥基本接近;由于结构自振频率特别是扭转频率有显著的提高,使得其空气动力稳定性要比钢主缆悬索桥好。因此从抗风稳定性角度而言,大跨度悬索桥采用碳纤维复合材料主缆是可行的,但是主缆截面尺寸的确定应采用等轴向刚度的准则。     

长跨柔性悬索桥风致抖振响应分析

以某主跨500 m的大跨度悬索桥为工程背景,对长跨柔性悬索桥在脉动风荷载作用下的抖振响应进行了分析和计算,得到了一些有借鉴性的结论。模态分析表明,大跨度悬索桥的自振频率较低,为典型的风敏感柔性结构。当同时考虑抖振力和自激力时,根据极值理论可以得到悬索桥主梁的抖振位移响应极值,结果表明,竖向、水平和扭转方向的最大抖振位移响应极值均发生在主跨跨中处,且数值较大,在结构设计中不容忽略。     

Estimating aeroelastic effects from full bridge responses by operational modal analysis

This paper deals with the estimation of structural modal parameters of long-span bridges from their recorded wind-excited response, by separating structural properties from aeroelastic effects using information on the incoming wind velocity. Specific attention is devoted to structural damping ratios, as their accurate estimations are of crucial importance in bridge engineering. However, uncertainties affecting damping ratios estimates often complicate any attempt towards their accurate assessment. More importantly, in the case of long-span bridges, aerodynamic damping often hides the actual structural one, even at low wind velocities. In this paper, the use of a data-driven stochastic subspace approach, specifically conceived to eliminate, as much as possible, analyst's arbitrariness and to deal with the non-whiteness of the wind excitation, is proposed for system identification. Structural properties are then separated from aeroelastic effects via nonlinear regressions of the modal parameter estimates at different mean wind velocities. Application of this technique to field measurements and numerically simulated buffeting response data referred to a real suspension bridge is finally presented, showing its effectiveness for separating structural from aerodynamic damping in practical case studies.     

State-of-the-art of long-span bridge engineering in China

This paper introduces the state-of-the-art of longspan bridge engineering in China with emphases on recent long-span bridge projects, bridge deck configuration and material, design codes of long-span bridges and improvement of aerodynamic performance. The recent long-span bridge projects include thirty-eight completed suspension bridges, cable-stayed and arch bridges with a main span over 400 m, and eighteen major bridges are under construction. The bridge deck configuration and material, with prestressed concrete decks, steel-concrete composite decks and steel box decks together with several popular cross-sections, are presented. The third part briefly outlines four design codes, including static and dynamic design for highway long-span bridges, and the recent engineering experiences gained from several aerodynamic vibration control projects of long-span bridges are shared in the last part.     

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.     

Parametric study on the aerodynamic stability of a long-span suspension bridge

The aerodynamic stability becomes a governing factor in designing long-span suspension bridges. In this paper, using the method of three-dimensional nonlinear aerodynamic stability analysis, parametric analyses on the aerodynamic stability of the Runyang bridge over the Yangtze River are performed including the structural system, the cable sag, the side span length, the depth, dead load and supporting system of the deck, etc. Some important design parameters that affect the aerodynamic stability of the bridge are pointed out, and the favorable structural system of the bridge is also discussed based on the wind stability.     

猫道对大尺寸主缆气动干扰效应风洞试验研究

悬索桥施工期猫道对主缆存在气动干扰效应,从而可能对主缆的驰振性能产生一定影响。文章选取某大跨悬索桥施工期主缆尖顶型和平顶型两种施工方案中共五种工况进行研究。首先,采用3D打印技术制作主缆模型,利用风洞试验方法分别得到不考虑猫道气动干扰影响及考虑猫道气动干扰影响下五种工况的气动力系数,并进行对比分析|然后根据登哈托判据对主缆在-3°～3°风攻角范围内的驰振性能进行分析和对比。结果表明：猫道的气动干扰效应使主缆的阻力系数有所减小,升力系数也发生了明显改变|猫道对0°风攻角时主缆1#和4#驰振性能影响较大,在分析施工期主缆的驰振现象时,猫道的气动干扰效应不能忽略。     

空间缆索体系悬索桥的抗风稳定性研究

为了探索理想的大跨度悬索桥的缆索体系以提高其横向及扭转刚度,以大跨度地锚式悬索桥——润扬长江公路大桥南汊桥为工程背景,采用不同缆索空间布置形式试设计三座具有空间缆索体系的方案桥,采用三维非线性空气静力和动力稳定性分析方法,分别对其动力特性、空气静力和动力稳定性进行分析和比较,并探讨具有良好抗风稳定性的大跨度悬索桥的合理缆索体系。结果表明:悬索桥采用内倾式空间缆索体系后,结构的侧弯及扭转频率增大,结构的空气动力稳定性增强;而采用外倾式空间缆索体系时,结构的侧弯及扭转频率减小,但结构的静风稳定性增强;考虑到悬索桥的空气动力稳定性一般比静风稳定性差,因此从总体抗风稳定性考虑,大跨度悬索桥采用内倾式空间缆索体系则比较有利。     

大跨度非对称悬索桥振动基频的参数敏感性分析

为了研究大跨度非对称悬索桥的动力特性,基于ANSYS软件建立了某大跨度主缆不等高支承悬索桥的三维有限元模型。在计算自振频率时考虑了表征结构非对称的参数,进行了前20阶模态分析,并分析了矢跨比、结构非对称参数、加劲梁抗弯刚度及主塔抗弯刚度等关键结构参数对其振动频率的影响。研究结果表明：不同的参数对非对称悬索桥振动基频的敏感性不同,一阶竖弯和扭转频率随矢跨比的增大减小,相对于正对称的振动频率,反对称的频率对矢跨比参数更敏感;非对称悬索桥的一阶反对称竖弯和扭转基频不受非对称结构参数的影响,而正对称竖弯和扭转基频随非对称结构参数的增大而减小;一阶横弯的自振频率对加劲梁刚度的变化非常敏感,当加劲梁的抗弯刚度增加到原来的3倍时,结构原有的振型次序发生了改变,但主塔抗弯刚度参数的变化对结构各向频率的影响很小,研究结果可为非对称悬索桥的结构设计和动力分析提供参考。     

Investigation on influence factors of buffeting response of bridges and its aeroelastic model verification for Xiaoguan Bridge

A time-domain procedure for analyzing buffeting responses of bridges is presented and implemented in ANSYS, formulated taking into account the self-excited forces, aerodynamic admittance functions (AAFs) and the coherence of buffeting forces. The buffeting forces simulated based on the span-wise coherence of buffeting forces and also considering the aerodynamic admittance functions, together with the steady aerodynamic forces are applied as external loads to the structural model to analyze the buffeting responses in time domain. In order to account for self-excited forces, elemental aeroelastic stiffness and aeroelastic damping matrices for spatial beam elements are derived following the quasi-steady theory and are incorporated in buffeting analysis through the user-defined Matrix27 element in ANSYS. The procedure is applied to the Xiaoguan Bridge, China, during the longest double cantilever stage of construction. The wind tunnel tests of four typical bridge section models are performed to measure the aerodynamic parameters of the bridge including the steady aerodynamic coefficients and aerodynamic admittance functions. The bridge aeroelastic model testing is also carried out, and coherence functions of buffeting forces are derived from the measured buffeting forces. The measurement results of the displacements and internal forces are compared with those obtained from the analytical predictions. The influence factors, including aeroelastic effect, aerodynamic admittance functions and coherence of buffeting forces, are studied in some detail. It is shown the present method inclusive of above factors gives much closer predictions of buffeting responses to the experimental results.     

Flutter- and buffeting-based selection for long-span bridges

Flutter-based selection for the Jiangyin Bridge, a suspension bridge with a main span of 1385 m, was made through a sectional model wind tunnel test. The concept of “buffeting-based selection” of long-span suspended bridges in the preliminary design stage was proposed, and the corresponding method was developed based on the Scanlan buffeting analysis method. Fifteen long-span bridges that have been researched by the authors and other co-researchers were investigated to simplify the method further. Also, the Jiangyin Bridge was taken as an example to show the application of the buffeting-based selection method.     

Investigation on aerodynamic stability of long-span suspension bridges under erection

The aerodynamic stability of long-span suspension bridge under erection, particularly at early erection stage, is more problematic than in the final state. It is influenced by the deck erection sequence and the nonlinear effects of wind-structure interactions. Considering the geometric nonlinearity of bridge structures and the nonlinear effects of wind-structure interactions, a method of nonlinear aerodynamic stability analysis is presented to predicate the aerodynamic stability limit (flutter speed) of long-span suspension bridges during erection. Taking the Yichang Bridge over the Yangtze River as example, evolutions of flutter speeds with the deck erected by different sequences are numerically generated. The sequences of pylons to midspan and the non-symmetrical deck erection are confirmed analytically to be aerodynamically favorable for the deck erection of long-span suspension bridges, particularly at early erection stages. The flutter speeds of long-span suspension bridges under erection are greatly decreased by the nonlinear effects of wind-structure interactions.     

悬索桥施工期抗风性能及控制研究进展

大跨径悬索桥施工期尚未形成最终的结构体系,暂态结构的刚度较小,强风作用下的抗风安全性和舒适性已成为影响悬索桥安全顺利架设的关键问题。针对风荷载的特点及大跨径悬索桥施工期暂态结构的组成,分别对风荷载的模拟问题以及桥塔、猫道、缆索和加劲梁等施工期暂态结构抗风性能及控制的国内外研究现状进行了总结,同时提出了亟待解决的问题。     

Effects of structural nonlinearity and along-span wind coherence on suspension bridge aerodynamics: Some numerical simulation results

The response of suspension bridges to wind excitation is studied by means of numerical simulations with a specifically developed finite element program implementing full structural nonlinearities. A pure time-domain load model, linearized around the average configuration, is considered. The self-excited effects are included through the indicial function formulation, whereas the buffeting is considered according to the quasi-steady model. The response under turbulent wind, both fully and partially correlated, is evaluated through a Monte Carlo approach. A simplified structural model is considered, where only two cross-sections are modeled. This allows a high reduction of the number of degrees of freedom (DoFs) but maintains many characteristics of the true bridge, precluded to the classical 2-DoF sectional-model (e.g. considering more than two modes, including structural nonlinearities, introducing along-span wind coherence). The case studies of a long-span suspension bridge and a light suspension footbridge are analyzed. It is observed that structural nonlinearities deemphasize the presence of a critical flutter wind velocity, as they limit the oscillation amplitudes. On the other hand, fully correlated flow may produce an important underestimation of the structural response.     

贵阳小关桥双肢薄壁墩抖振响应试验与影响因素分析

在原有抖振时域分析方法的基础上,提出一种考虑复气动导纳函数的修正和抖振力的空间相关性的抖振时域分析方法。为对现有抖振时域分析方法的验证,以贵阳小关桥为例,对其最大悬臂状态进行全桥气弹模型风洞试验,试验中不仅对抖振位移进行测量,还通过在墩底布设动态应变片完成墩底内力的实测。气动导纳函数分别取1、Sears函数和实测的桥梁断面复气动导纳函数,采用抖振力谱法得到考虑气动导纳修正的抖振力。另外对风洞中模型抖振力的空间相关性进行测量,分析气动导纳函数和抖振力空间相关性对结构抖振响应的影响,并与风洞气弹模型试验结果进行了对比分析。分析结果表明:计算分析结果与试验结果基本一致;采用结构实际气动导纳函数的抖振响应与试验更接近;采用抖振力空间相关性计算得到的抖振响应要比采用脉动风速空间相关性的计算结果偏高。     

Relationships among aerodynamic admittance functions, flutter derivatives and static coefficients for long-span bridges

Wind actions on long-span bridges are commonly considered as the superimposition of buffeting forces and self-excited forces, depending on the aerodynamic admittance functions and on the flutter derivatives, respectively. Since bridge deck sections are bluff bodies, the aerodynamic admittance functions and the flutter derivatives have to be determined experimentally by wind tunnel tests. This paper introduces a generalized quasi-static theory, defining new relationships among the flutter derivatives and the aerodynamic admittance functions. All the relationships are theoretically verified for the zero circular frequency; based upon experimental results, the validation of the relationships among the flutter derivatives is also provided for non-zero values of the frequency.     

Aeroelastic analysis of long span bridges via indicial functions considering geometric and material nonlinearity

A time domain approach for predicting the flutter response of long-span bridges was presented. The unsteady aerodynamic forces were presented by the indicial functions through a convolution integral, whereas the nonlinear least square method was used to calculate the aerodynamic indicial parameters. The nonlinear dynamic analysis which includes both the geometric and material nonlinearities due to the unsteady self excited aerodynamics force was considered. Numerical analyses were then performed using three dimensional finite element model of the suspension bridge. The results show that the geometric and material nonlinearities have a significant influence on the critical velocity and the response of long-span bridges.     

模态间气动耦合效应对调谐质量阻尼器最优参数的影响

基于多模态耦合抖振理论,导出带有被动调谐质量阻尼器(TMD)的桥梁多模态耦合抖振系统运动微分方程,采用随机振动理论求解系统运动微分方程,并编制了桥梁多模态耦合抖振TMD控制和参数分析程序。以一座斜拉桥为算例,着重分析了模态间气动耦合效应对TMD最优参数和控制效率的影响。     

Preliminary design of very long-span suspension bridges

The feasibility of very long-span suspension bridges is analysed. The relation between the geometrical parameters, the load and the material characteristics is first discussed in order to find out the limit value of the span length. An iteration procedure is then proposed to study the main aspects of the structural behaviour in the deflection theory. The results of a numerical investigation allow to state that the behaviour of a very long-span suspension bridge, both in terms of stresses and deflection, is similar to the behaviour of an unstiffened cable, the contribution of the girder being negligible.     

Flutter and buffeting performances of Third Nanjing Bridge over Yangtze River under yaw wind via aeroelastic model test

Third Nanjing Bridge over Yangtze River in China is a long-span steel cable-stayed bridge with a main span of 648 m and a closed streamline cross-section of single box. The flutter and buffeting performances of the bridge under yaw winds were investigated via a wind tunnel test of full bridge aeroelastic model at a geometric scale of 1:120. The service state and three key construction states including the longest single-cantilever state, the longest double-cantilever state with a temporary pier, and the longest double-cantilever state without any temporary pier, were considered in the test. The test was conducted in both smooth and simulated boundary layer wind fields with various combinations of wind yaw angle and inclination angle. The model was elaborately designed and manufactured, and the modal properties of the service-state model were checked before the test. The natural frequencies and mode shapes were identified automatically using a self-developed special software from the acceleration signals recorded in an ambient vibration test, where an “artificial” turbulent wind with lower mean speed of 1 m/s was used as a major ambient excitation addition to the “natural” one from the slight ground trembling. The modal damping ratios were checked using free-decay vibration approach. The testing results show that the bridge has enough aerodynamic stability for all structural states and wind directions concerned, and the most unfavorable buffeting responses often occur in yaw wind case with a yaw angle between 5° and 30°.