Multidisciplinary approach to aeroelastic studies of long-span bridges

This paper focuses on the design of long-span suspension bridges under aeroelastic constraints. Such challenging structures need to be protected against wind-induced instabilities as flutter. The authors envision that a set of scientific disciplines not currently used in bridge engineering may help along the design process and constitute a useful tool. First, the formulation of sensitivity analysis of flutter speed is described, indicating how this technique can be a guide for engineers making changes in the prototype; two examples of important bridges, as the Great Belt and Messina Strait, are used to demonstrate the capability of this approach. Then, the idea of producing computer animations to represent the aeroelastic deformation of bridges simulating virtual boundary layer wind tunnel testing is presented showing pictures of the Tacoma Narrows and Messina Bridges. Finally, the advantages of introducing distributed computing to make easier to implement the previously mentioned techniques are demonstrated. The authors have previously published papers related with sensitivity analysis in bridges or computer animations of the aeroelastic behaviour of suspension bridges. However, this is the first time that their comprehensive multidisciplinary approach is presented.     

Sensitivity analysis of bridge flutter with respect to mechanical parameters of the deck

A methodology for carrying out an analytical sensitivity analysis of the flutter phenomenon in long-span bridges is developed. Decks of bridges are generally bluff bodies and therefore the aeroelastic forces under wind action have to be experimentally evaluated in wind tunnels. Such forces depend on the response frequency of the bridge, which is not known until the problem is solved. Consequently, the calculus of the critical wind speed that initiates the flutter instability comprises a complex nonlinear eigenvalue problem. During the design phase, the sensitivity analysis gives very interesting information about the gradient of the flutter speed with respect to the key chosen design variables, moments of inertia of the bridge deck. The presented method is applied to the Great Belt and Vasco da Gama Bridges, as well as to the old Tacoma Bridge.     

Ultimate load carrying capacity of the Lu Pu steel arch bridge under static wind loads

This paper investigates the ultimate load carrying capacity of the Lu Pu Bridge under static wind loads through the spatial finite element model. Both geometric and material nonlinearities are involved in the analysis. The Lu Pu Bridge is a long-span half-through-type steel arch bridge with a 550 m-long central span under construction in Shanghai, China. This will be the longest central span of any arch bridge in the world. Three load combinations are used in the ultimate load capacity analysis of the bridge. Combination I: combined dead and live loads over the entire bridge. Combination II: combined dead and wind loads. Combination III: combined dead load, wind load and live load over the entire bridge. Ultimate load capacity of the bridge is first investigated under load combinations I and II. Attention is paid mainly to investigate the load capacity of the bridge under load combination III. In the case of load combination III, the influences of several parameters (i.e., loading sequence, three components of wind loads and wind loads of individual bridge element) on the ultimate load capacity of the bridge are discussed. It is concluded that wind loads result in significant reduction in the ultimate load capacity when applied wind loads become large.     

Optimum design of long-span suspension bridges considering aeroelastic and kinematic constraints

Cable supported bridges are wind prone structures. Therefore, their aerodynamic behaviour must be studied in depth in order to guarantee their safe performance. In the last decades important achievements have been reached in the study of bridges under wind-induced actions. On the other hand, non-conventional design techniques such as sensitivity analysis or optimum design have not been applied although they have proved their feasibility in the automobile or aeronautic industries. The aim of this research work is to demonstrate how non-conventional design techniques can help designers when dealing with long span bridges considering their aeroelastic behaviour. In that respect, the comprehensive analytical optimum design problem formulation is presented. In the application example the optimum design of the challenging Messina Strait Bridge is carried out. The chosen initial design has been the year 2002 design proposal. Up to a 33% deck material saving has been obtained after finishing the optimization process.     

A numerical model for wind loads simulation on long-span bridges

A numerical model of the air flow problem around the girder of a long-span bridge is presented. The model is based on a finite volume formulation and it is able to simulate steady and non-steady wind loading conditions on the structure under the simplifying assumption, which is plausible for bridges with long spans, of a two-dimensional-like approaching flow. For a given bridge deck cross-section the proposed model allows the numerical evaluation of the flutter derivatives, which is useful to characterize in an analytical way the stability conditions of the overall wind-induced bridge response. In order to obtain satisfactory accuracy and stability of the numerical solution, a two-equation k–ϵ RNG turbulence model and special boundary conditions are employed. The accuracy and applicability of the model to wind engineering problems are successfully assessed by computing the aerodynamic behaviour of some simple cross-section shapes. Numerical results are also obtained for typical long-span bridge cross-sections and the comparison with the available wind tunnel measurements shows a good agreement.     

Computer simulation of buffeting actions of suspension bridges under turbulent wind

Suspension bridges are long-span flexible structures susceptible to various types of wind induced vibrations such as buffeting actions. In this paper, a three dimensional finite-element model formulated to deal with suspension bridges under turbulent wind is presented. In this model, all sources of geometric nonlinearity such as cable sag, force-bending moment interaction in the bridge deck and towers, and changes of bridge geometry due to large displacements, are fully considered. The wind loads, composed of steady-state wind loads, buffeting loads and self-excited loads, are converted into time domain by using the computer simulation technique. The Newmark-β step by step numerical integration algorithm is used to calculate the buffeting responses of bridges. Compared with the results obtained by classical buffeting theory, the validity of the simulation is proved.     

大跨劲性骨架拱桥混凝土外包过程动力特性及抗风性能研究

研究劲性骨架拱桥混凝土外包过程中的动力特性和抗风性能对其施工具有重要的指导意义.本文以天峨龙滩特大桥为例,采用有限元分析软件MIDAS/Civil,建立了实桥空间有限元模型,研究了在三种不同工作面条件下,不同施工阶段桥梁的自振频率以及抗风能力的变化规律.结果表明：在外包混凝土的过程中桥梁横向频率呈现单调上升的趋势,而竖向频率却呈现先下降再上升的趋势,并且会出现veering现象;抗风能力呈现出先提高,再降低,最后再提高的变化趋势;抗风性能也会受到工作面数量的影响,工作面越多,结构的横向抗风性能越弱.     

Multi-disciplinary constrained optimization of wind turbines

We describe procedures for the multi-disciplinary design optimization of wind turbines, where design parameters are optimized by maximizing a merit function, subjected to constraints that translate all relevant design requirements. Evaluation of merit function and constraints is performed by running simulations with a parametric high-fidelity aero-servo-elastic model; a detailed cross-sectional structural model is used for the minimum weight constrained sizing of the rotor blade. To reduce the computational cost, the multi-disciplinary optimization is performed by a multi-stage process that first alternates between an aerodynamic shape optimization step and a structural blade optimization one, and then combines the two to yield the final optimum solution. A complete design loop can be performed using the proposed algorithm using standard desktop computing hardware in one-two days. The design procedures are implemented in a computer program and demonstrated on the optimization of multi-MW horizontal axis wind turbines and on the design of an aero-elastically scaled wind tunnel model.     

Comparison between linear and nonlinear control strategies for variable speed wind turbines

The purpose of this work is to compare some linear and nonlinear control strategies, with the aim of benefiting as well as possible of wind energy conversion systems. Below rated wind speed, the main control objective is to perform an optimal wind power capture while avoiding strong loads on the drive train shafts. To explicitly take into consideration the low speed shaft flexibility, a two-mass nonlinear model of the wind turbine is used for controllers synthesis. After adapting a LQG controller based on the linearized model, nonlinear controllers based on a wind speed estimator are developed. They take into account the nonlinear dynamic aspect of the wind turbine and the turbulent nature of the wind. The controllers are validated upon an aeroelastic wind turbine simulator for a realistic wind speed profile. The study shows that nonlinear control strategies bring more performance in the exploitation of wind energy conversion systems.     

结冰风洞试验段上壁面自动顶盖装置设计与应用

为了解决模型进出试验段安装和拆卸问题,提出在结冰风洞试验段上顶面设计自动开闭顶盖,利用行车吊装模型进出的方法,研制了外形超12m2、重近5t、定位精度1mm的移动顶盖自动开闭装置。在结冰风洞试验段上壁板中心设计与移动顶盖同尺度的开孔,移动顶盖安装在提升机构的下端,通过四轴同步提升机构垂直升降,用于打开或关闭上壁板开孔;平移机构带动提升机构和移动顶盖,沿试验段上框架顶部龙门结构的两侧支撑轨梁的滑轨水平移动,使移动顶盖从风洞上壁面中心移动到过渡扩散段顶部;研制了升降、平移两轴伺服控制系统,实现了大载荷移动顶盖自动升降和平移控制,解决了移动顶盖结构设计、大载荷四轴同步提升时丝杠间相互别劲、高精度定位控制等问题。系统达到设计指标,已经应用到结冰风洞试验中,提高了试验模型更换效率。     

Support vector machine based aerodynamic analysis of cable stayed bridges

Flutter, a self-excited vibration resulting from the interaction between structural motion and aerodynamic force, is the major aspect in wind resistant design of cable stayed bridges. The critical speed for flutter of a deck section can be evaluated using the flutter derivatives obtained by sectional model testing of the bridge deck in a wind tunnel. Since it is very expensive, time consuming and laborious to conduct wind tunnel tests for all the practical dimensions of deck, the support vector machine (SVM) is applied for predicting the flutter derivatives for any deck size. The wind tunnel experimental data is collected from literature and SVM is trained. Thus predicted flutter derivatives are used for estimation of critical flutter velocity of cable stayed bridges. The effect of each aerodynamic derivative on flutter instability is investigated in this study.     

基础激励下桥梁斜拉索的非线性振动

在考虑拉索垂度的情况下建立了深圳湾公路大桥的动力学模型，利用有限元软件模拟了地震、风、车辆等荷载作用于桥梁结构时桥面及桥塔索锚固点的位移响应，以及全桥整体动力特性和索连接点的振动解，从而真实反映出基础激励对索的初始扰动，进而研究索在最不利荷载作用情况下谐波共振和参数振动的特性，并在此基础上分析了激励频率与拉索固有频率比的匹配关系，得出了激励幅值、初始索力、模态阻尼比、拉索倾角等参数对拉索非线性振动的影响．     

风力机翼型外形图的计算机辅助设计

大弯度低速翼型的外形图可采用多种设计方法进行设计,随着计算机科学的发展,采用计算机辅助设计的方法来设计大弯度低速翼型的外形图显得最为快捷,本文讨论风力机大弯度低速翼型外形图的计算机辅助设计的原理和步骤。     

Behaviour of guyed transmission line structures under tornado wind loading

Localized severe wind events, in the form of downbursts and tornadoes, are responsible of the majority of transmission line structures failures in many regions around the globe. The wind profiles associated with these events are different than the conventional boundary layer wind profile that is typically used to design the supporting towers. A comprehensive study is presented in this paper to assess and understand the performance of transmission line structures under tornado loading. The study is conducted numerically using a three-dimensional finite-element model and incorporates velocity fields for various tornado scales, which are based on a computational fluid dynamics analysis. The numerical model accounts for the nonlinear behaviour of the conductors, ground-wires, and supporting guys. An extensive parametric study is conducted by varying the location of F4 and F2 tornadoes relative to the transmission line system. The study investigates the variation of the tower members’ internal forces with the tornado locations. It also provides an insight about the structural response of the towers under tornado wind loads. The dynamic effect associated with the translation motion of the tornado is assessed. Finally, the results of the parametric study are used to assess the sensitivity of the members’ peak forces with the parameters defining the location of the tornado relative to the line.     

基于数值计算的高速列车气动阻力风洞试验缩比模型选取方法

为给高速列车气动阻力风洞试验模型选取提供更多的参考依据,通过计算流体力学(Computational Fluid Dynamics,CFD)方法,研究不同比例的高速列车缩比模型对气动阻力风洞试验结果的影响.首先,计算得到开口式风洞测试段的静压系数分布曲线,为高速列车气动阻力测量试验模型的长度选择以及摆放位置提供依据;其次,通过数值计算得到全尺寸模型列车在明线运行时,以及不同比例的模型列车在风洞中运行工况下的气动阻力信息,并从阻塞效应和雷诺数的变化,以及风洞试验段内静压分布的影响这3个方面对列车模型的气动阻力结果进行分析,得到在所研究风洞中较合理的列车缩比模型比例选取范围.这种以CFD为基础进行数值仿真,选取风洞试验中列车模型比例及试验测试位置的方法,为在地面交通工具风洞中进行高速列车模型气动阻力试验的缩比模型选取提供一定依据.     

The virtual wind tunnel

The design and implementation of a virtual environment linked to a graphics workstation for the visualization of complex fluid flows are described. The system user wears a stereo head-tracked display, which effectively displays 3-D information, and an instrumented glove to intuitively position flow-visualization tools. The visualization structures and their interfaces in the virtual environment and the implementation hardware and software are described. The performance of the virtual wind tunnel is reviewed using the flow past a tapered cylinder as an example. Performance issues and future directions for the system are discussed     

Aeroelastic tailoring using fiber orientation and topology optimization

This work presents a structural optimization aided design methodology for composite laminated plates subject to fluid-structure interaction. The goal of the optimization procedure is to increase the flutter speed onset through the maximization of natural frequencies related to the vibration modes involved in the phenomenon. The aeroelastic stability analysis is performed using ZAERO software system, which includes ZONA 6 unsteady lifting surface method. The finite element method is applied to solve the structural model equilibrium equations, the eigenvalues sensitivities with respect to design variables are calculated analytically, and sequential linear programming is applied. The maximization is accomplished using two methods; the first method uses an aeroelastic analysis to determine which eigenmode causes the flutter onset, and its eigenvalue is then maximized. In the second method, a forward finite difference method is applied and the flutter speed sensitivities with respect to the eigenvalues are calculated. This sensitivity is used to guide the optimization process. Finally, a topology optimization problem is formulated to reduce the plate mass under a minimum flutter velocity constraint, using density distribution as the design variable.     

A computer program for determining wind pressures on 2-D structures

A computer program in Fortran for the numerical determination of wind loads on rigid civil-engineering structures is described. The program combines the direct boundary element method with the discrete vortex method in order to simulate the potential and viscous-flow characteristics of wind flow around structures under two-dimensional conditions. The flow chart and the subroutines of the program are given and explained in detail. The program employs linear boundary elements, and the simulation proceeds in a stepwise fashion in time. It is easy to use and can easily run on a personal computer. Numerical examples are presented to illustrate its use and demonstrate its simplicity, speed, and satisfactory accuracy. Thus this program becomes a valuable tool for the design engineer who does not have any further need to resort to expensive experiments or complicated numerical methods for the computation of wind loads on structures.     

Rain–wind induced vibrations – phenomenology,mechanical modelling and numerical analysis

The simultaneous appearance of rain and wind at cables of cable stayed bridges and hangars of arch bridges may induce varying oscillations with large amplitudes. These phenomena are identified as rain–wind induced vibrations. The paper presents a possible fluid-mechanical interpretation of rain–wind induced vibrations. Based on this interpretation a mechanical model is deduced, in order to enable numerical investigations. The complex system of nonlinear differential equations is analysed concerning the stability of solutions. Rain–wind induced vibrations exist only within a certain range of wind velocity. The lower limit of the critical velocity range is determined for various cable inclinations and angles of incidence. Furthermore, a fluid mechanical interpretation is given for the existence of the upper limit of critical velocity. The approximation of the upper limit velocities and the determination of the critical cable diameters can be derived from established fluid-mechanical correlations. The numerical investigations show that rain–wind induced oscillations occur on vertical cables, too. For the Faro–Falster Bridge, the numerical vibration analysis is carried out for the cables parallel and perpendicular to the wind direction. The analysis of the vibration frequencies is demonstrated for the Dömitz Bridge.