Effects of vertical central stabilizers on nonlinear wind-induced stabilization of a closed-box girder suspension bridge with various aspect ratios

The aerodynamic shape of a closed-box girder plays an important role in the wind-induced stabilization of long-span suspension bridges. The purpose of this study is to investigate the effects of the combination of five aspect ratios and a downward vertical central stabilizer (DVCS) on nonlinear flutter and aerostatic behaviors of a super long-span suspension bridge with closed-box girders. Through conducting a series of wind-tunnel tests and nonlinear finite element analysis, the results show that the nonlinear self-excited forces and the critical wind speed (U_cr) gradually increase as the increase of the aspect ratio (i.e. the width to depth ratios). Furthermore, the application of 20% deck depth DVCS could significantly increase the nonlinear self-excited forces and U_cr for small aspect ratios of 7.9 and 7.1. Particularly, the installation of the DVCS could change the flutter divergence patterns of the bridge from soft flutter to hard flutter, especially for a relatively small aspect ratio. In addition, the aerostatic force coefficients and torsional divergence critical wind speeds of the larger aspect ratio with DVCS are significantly larger than that without DVCS. A relatively small aspect ratio of the bridge has better aerostatic performance than that with a larger aspect ratio.

     

A FORM OF AERODYNAMIC ADMITTANCE FOR USE IN BRIDGE AEROELASTIC ANALYSIS

This paper returns to, and addresses, the question of identifying the nature of aerodynamic admittance in relation to extended-span bridges in wind. Theoretical formulations for the sectional aerodynamic forces acting upon the deck girder of a long-span bridge have conventionally been composed of the sum of two kinds of terms: aeroelastic terms and buffeting terms. The former employ frequency-dependent coefficients (“flutter derivatives”) associated with sinusoidal displacements of the structure, while the latter have typically been expressed in quasi-static terms with fixed lift, drag and moment coefficients. This inconsistency of formulation has required that at some point the buffeting terms, functions of gust velocity, be adjusted to a more compatible form through the introduction of the so-called aerodynamic admittance factors that are frequency-dependent. The present paper identifies a form of these several section-force factors as functions of the flutter derivatives themselves.     

我国大跨度缆索承重桥梁的空气动力性能研究

本文介绍了我国大跨度桥梁空气动力性能方面的研究情况。以同济大学土木工程防灾国家重点实验室所从事的桥梁空气动力性能的理论和试验研究工作中的几个主要方面为重点,介绍最新进展,其中包括非线性颤振的频域分析,颤振分析的全模态技术,基于计算流体动力学的数值风洞等研究课题。     

主动控制翼板抑制悬索桥颤振的研究

主动控制翼板是一种新型桥梁气动措施。本文基于非定常气动力理论，推演了安装主动控制翼板后作用在整个桥梁主梁单位长度上气动力表达式，从增加系统扭转阻尼的角度，研究了翼板主动扭转振动参数的选取。在此基础上，对某大跨悬索桥方案进行了二自由度颤振分析，结果表明：合理选取翼板的主动扭转振动参数，主动控制翼板能够有效地提高该桥的颤振稳定性。     

EXPERIMENTAL DETERMINATION OF THE AERODYNAMIC ADMITTANCE OF A BRIDGE DECK SEGMENT

The gust loading on bridge decks is described by the dynamic forces on a chord-wise strip and by the spatial distribution of these forces across the span. An experimental method to evaluate the aerodynamic admittance of a segment of a bridge deck that includes a combination of the cross-sectional admittance and the spatial distribution of the forces is presented in this paper. The method is based on wind tunnel tests in turbulent flow on a motionless section model of the deck. The approach has been validated experimentally on a closed-box girder bridge deck but can be applied to bridge decks of any cross-section.     

Aeroelastic Wind Forces on Flexible Bridge Girders

Non-stationary aeroelastic wind force processes on a streamlined bridge deck are modelled for use within computations in the range of statistically stationary girder oscillation and for the mathematical investigation of the limit of aeroelastic stability. Time Domain (TD) methods, as the direct integration on a finite-element (FE) model, are applied in structural analyses for taking into consideration both geometric and physical nonlinearities. The FE method requires a continuous form of the force model, which permits an arbitrary discretization in time. The present model is based on continuous step response functions of Wagner-type, taking advantage of modern advances of that theory. Special emphasis is put on the continuity and the existence of equivalent representations in time and frequency domains. A realistic wind load model must include measured force functions and effects from the wind turbulence. For that reason, the force functions are calibrated in wind tunnel tests on section models in grid turbulence and boundary layer flow. The aeroelastic in-phase and out-of-phase forces are identified from highly accurate calibrations experiments on section models up to high frequencies which permits to decrease the time step increment. Turbulence effects on the aeroelastic coefficients are included in mean terms.     

Passive aeroelastic control of a suspension bridge during erection

This study presents a system based on passively controlled leading- and trailing-edge flaps that is designed to suppress wind-induced instabilities such as flutter and torsional divergence. The utility of the approach is demonstrated on a three-dimensional bridge model. Particular emphasis is placed on the early stages of the deck erection process when the bridge is particularly vulnerable to flutter. The flaps are activated by the deck's movements though passive phase-compensating mechanisms comprising of springs, dampers and inerters. It is demonstrated that optimised compensator parameters, and optimum hinge locations, result in a substantially improved deck aerodynamic performance. Particular importance is given to ensuring that the controlled system has good closed-loop ‘robustness’ properties, or in other words, that the controlled system has a high tolerance to parameter variations and uncertainties in the system dynamics. The practical use of a nonlinear optimisation algorithm with a FE bridge aeroelastic model, which includes the flap dynamics, necessitates the use of reduced-order models. A novel model reduction procedure that is based on the retention of dominant poles is introduced into the aeroelastic modelling framework. Multimodal interactions are observed at the various erection stages and conclusions are drawn with regard to the contributions of various modes of vibration to aeroelastic instabilities. The main advantage of this approach lies on the passive system's simplicity and its ability to simultaneously increase the flutter and torsional divergence boundaries. The Humber Bridge in the U.K. is chosen as a study example for numerical simulations.     

Nonlinear parametric modeling of suspension bridges under aeroelastic forces: torsional divergence and flutter

A fully nonlinear model of suspension bridges parameterized by one single space coordinate is proposed to describe overall three-dimensional motions. The nonlinear equations of motion are obtained via a direct total Lagrangian formulation and the kinematics, for the deck-girder and the suspension cables, feature the finite displacements of the associated base lines and the flexural and torsional rotations of the deck cross-sections assumed rigid in their own planes. The strain-displacement relationships for the generalized strain parameters, the elongations in the cables, the deck elongation, and the three curvatures, retain the full geometric nonlinearities. The proposed nonlinear model with its full extensional-flexural-torsional coupling is employed to study the torsional divergence caused by the static part of the wind-induced forces. Two suspension bridges are considered as case studies: the Runyang bridge (main span 1,490?m) and the Hu Men bridge (main span 888?m) in China. The evaluation of the onset of the static instability and the post-critical behavior takes into account the prestressed condition of the bridge subject to dead loads. The dynamic bifurcation that occurs at the onset of flutter is also studied accounting for the prestressed equilibrium state about which the equations of motion are obtained via an updated Lagrangian formulation. Such a bifurcation is investigated in the context of the parametric nonlinear model considering the model parameters of the Runyang Suspension Bridge together with its aeroelastic derivatives. The calculated critical wind speeds for the onset of the static and dynamic bifurcations are compared with the results obtained via linear analysis and the main differences are highlighted. Parametric sensitivity studies are carried out to assess the influence of the design parameters on the instabilities associated with the bridge aeroelastic response.     

Analysis of self-excited forces for a box-girder bridge deck through unsteady RANS simulations

This paper presents the results of two-dimensional numerical simulations of the flow field around a trapezoidal box-girder bridge section with later cantilevers, experiencing small-amplitude heaving or pitching harmonic oscillations. Unsteady Reynolds-averaged Navier–Stokes equations are solved in conjunction with an eddy-viscosity and an explicit algebraic Reynolds stress model. Flutter derivatives are determined and compared with wind tunnel results, showing fairly good agreement. The degree of sharpness of the deck lower edges is found to play a key role in the aeroelastic behavior of the profile. In particular, the bridge section fully behaves as a bluff body and is prone to low-reduced-wind-speed torsional galloping in the case of perfectly sharp edges. By contrast, the presence of a small radius of curvature in the section lower corners changes the nature of the instability to coupled flutter and significantly postpones the stability threshold, in line with a quasi-streamlined body behavior. Moreover, a wide sensitivity study is carried out, investigating the influence on the self-excited forces of the amplitude of oscillation, mean angle of attack and Reynolds number. In particular, the numerical simulations for the geometry with smooth lower edges highlight the regime transition occurring when the Reynolds number is varied, with significant effects on the flutter derivatives. Finally, the numerical flow visualizations provide a physical explanation of some phenomena observed in the wind tunnel experiments.     

大跨径悬索桥空气静力和动力分析的影响因素研究

随着悬索桥跨径的增大,缆索直径以及作用在其上的风荷载、风与结构相互作用的非线性效应以及风速空间分布的非均匀性都将显著增强。以润扬长江大桥为背景,进行了缆索风荷载、风与结构相互作用的非线性效应以及风速空间非均匀分布等因素对大跨径悬索桥空气静力和动力特性影响的数值分析。分析结果表明:这些因素对大跨径悬索桥空气静力特性的影响比较大;但是对于空气动力稳定性而言,风与结构相互作用的非线性效应的影响比较显著,而其它两个因素则基本没有影响。     

Low speed flutter and limit cycle oscillations of a two-degree-of-freedom flat plate in a wind tunnel

This paper explores the dynamical response of a two-degree-of-freedom flat plate undergoing classical coupled-mode flutter in a wind tunnel. Tests are performed at low Reynolds number (Re~2.5×10⁴), using an aeroelastic set-up that enables high amplitude pitch–plunge motion. Starting from rest and increasing the flow velocity, an unstable behaviour is first observed at the merging of frequencies: after a transient growth period the system enters a low amplitude limit-cycle oscillation regime with slowly varying amplitude. For higher velocity the system transitions to higher-amplitude and stable limit cycle oscillations (LCO) with amplitude increasing with the flow velocity. Decreasing the velocity from this upper LCO branch the system remains in stable self-sustained oscillations down to 85% of the critical velocity. Starting from rest, the system can also move toward a stable LCO regime if a significant perturbation is imposed. Those results show that both the flutter boundary and post-critical behaviour are affected by nonlinear mechanisms. They also suggest that nonlinear aerodynamic effects play a significant role.     

大跨度桥梁多模态耦合颤振的TMD控制

推导了装有TMD的结构在气动自激力作用下的动力微分方程,基于模态空间中多模态耦合颤振分析手段,运用考虑安装TMD的多模态自动分析法对结构-TMD系统进行了颤振分析和TMD控制分析,使多模态自动分析法能适用于TMD颤振控制分析,避免了双参数搜索和迭代计算,提高了计算效率。对某在建三塔悬索桥进行了原结构颤振分析和TMD-结构颤振频域分析,探讨TMD控制参数对颤振临界风速的影响。     

Limit cycle oscillation behavior of transonic control surface buzz considering free-play nonlinearity

The limit cycle oscillation (LCO) behaviors of control surface buzz in transonic flow are studied. Euler equations are employed to obtain the unsteady aerodynamic forces for Type B and Type C buzz analyses, and an all-movable control surface model, a wing/control surface model and a three-dimensional wing with a full-span control surface are adopted in the study. Aerodynamic and structural describing functions are used to deal with aerodynamic and structural nonlinearities, respectively. Then the buzz speed and buzz frequency are obtained by V-g method. The LCO behavior of the transonic control surface buzz system with linear structure exhibits subcritical or supercritical bifurcation at different Mach numbers. For nonlinear structural model with a free-play nonlinearity in the control surface deflection stiffness, the double LCO phenomenon is observed in certain range of flutter speed. The free-play nonlinearity changes the stability of LCOs at small amplitudes and turns the unstable LCO into a stable one. The LCO behavior is dominated by the aerodynamic nonlinearity for the case with large control surface oscillation amplitude but by the structural nonlinearity for the case with small amplitude. Good agreements between LCO behaviors obtained by the present method and available experimental data show that our study may help to explain the experimental observation in wind tunnel tests and to understand the physical mechanism of transonic control surface buzz.     

A numerical investigation into the aerodynamic characteristics and aeroelastic stability of a footbridge

The results of a numerical investigation into the aerodynamic characteristics and aeroelastic stability of a proposed footbridge across a highway in the north of England are presented. The longer than usual span, along with the unusual nature of the pedestrian barriers, indicated that the deck configuration was likely to be beyond the reliable limits of the British design code BD 49/01. The calculations were performed using the discrete vortex method, DIVEX, developed at the Universities of Glasgow and Strathclyde. DIVEX has been successfully validated on a wide range of problems, including the aeroelastic response of bridge deck sections. In particular, the investigation focussed on the effects of non-standard pedestrian barriers on the structural integrity of the bridge. The proposed deck configuration incorporated a barrier comprised of angled flat plates, and the bridge was found to be unstable at low wind speeds, with the plates having a strong turning effect on the flow at the leading edge of the deck. These effects are highlighted in both a static and dynamic analysis of the bridge deck, along with modifications to the design that aim to improve the aeroelastic stability of the deck. Proper orthogonal decomposition (POD) was also used to investigate the unsteady pressure field on the upper surface of the static bridge deck. The results of the flutter investigation and the POD analysis highlight the strong influence of the pedestrian barriers on the overall aerodynamic characteristics and aeroelastic stability of the bridge.     

变刚度梁弯曲解析解在桥面板中的应用

针对新型连续窄幅钢箱梁-混凝土组合桥梁,研究了该桥型桥梁的桥面板拉应力控制方法与措施．将该桥型组合桥梁等效为可变刚度的Euler梁,给出任意横向荷载作用下变刚度梁的静力弯曲解析通解,并得到三跨连续阶梯型变刚度梁变形及其内力分布特征．在此基础上,以三跨连续窄幅钢箱梁-混凝土组合桥梁为研究对象,考虑下部钢箱梁与上部混凝土桥面板完全剪力连接,通过改变负弯矩区钢箱梁壁厚、内部充填混凝土的强度、长度与高度等参数,分析得到可有效控制桥面板拉应力的关键因素．结果显示：在负弯矩区段内的钢箱梁内部充填混凝土对控制该区域混凝土桥面板拉应力效果明显,但混凝土强度影响较弱．混凝土桥面板开裂区域随钢箱梁中充填混凝土长度的增加而减少,但桥面板顶部拉应力会随混凝土充填高度的增加呈现先减小后增大的趋势,在充填高度为箱梁内部净高的20 %~30 %左右时效果较为显著,此时经济效益最佳．     

On the aerostatic divergence of suspension bridges: A cable-length-based criterion for the stiffness degradation

Motions of a suspension bridge immersed in turbulent wind flows, including both mean and stochastic, can under certain conditions lead to the degradation of the structure׳s torsional stiffness and ensuing aerodynamic torsional divergence (ATD). It is the incompressibility of the main cables that determines their effectiveness as supporting members be limited in a tension state, and dropping out of either one cable from a tension state could result in the vanish of the torsional stiffness contributed by the whole cable system. Although the physical conception is quite explicit, evaluation of the critical threshold of ATD of a suspension bridge, when experiencing stochastic aerodynamic responses, can be complicated by the deformations of the towers, the lateral oscillations of the deck and cables, and other high-order modes participating in the vibration. In view of this, a criterion based on the tracking of the length of the main cables is presented in this study. It is shown that, with the numerical example, the advent of ATD, the degradation of the system׳s stiffness, as well as some striking post-ATD behaviors, can be well explained with the proposed model by tracking the cable lengths.     

桥面槽缝对桥梁断面静态压力分布影响的实验研究

大跨度斜拉桥或悬索桥的桥梁主梁断面的气动外形是桥梁设计者们很关心的问题之一。对主梁节段模型气动力的风洞实验研究一般都只考虑了来流攻角以及模型本身结构外形的影响，而现今不少大桥在双向来回车道的中间开有槽缝，工程上可以用来改善桥面的空气动力特性以及桥梁本身的稳定性，对于这方面的实验研究进行得不多。本文拟通过风洞实验对某大桥桥梁主梁断面在各种开槽情况下的静态压力分布进行研究，进而对断面各测点的压力分布进行矢量求和获得升力系数、阻力系数和升力矩系数，由此来研究开槽与否以及开槽大小对该桥梁主梁断面的气动力的影响，同时也研究了槽中央隔板的存在对气动力系数的影响。研究表明，隔板的有无对气动力并无明显的影响，而开槽与否以及槽宽的大小对压力分布、升阻力系数以及升力矩系数有明显的影响。