刚性路面在运动车辆作用下的动力响应

针对运动车辆引起的路面结构动力问题,采用移动荷载作用下Kelvin地基上无限大Kirchhoff薄板为力学分析模型,分析了运动车辆作用下刚性路面的动力响应。首先采用积分变换法推导了板挠度的Green函数,并通过Duhamel积分求得各种移动荷载模式作用下板稳态挠度的二维积分解析解,包括恒常和简谐移动点源、线源和面源荷载。然后采用自适应数值积分算法计算解析解中的二维无穷积分,得到了板稳态挠度的数值结果。最后对速度和阻尼等对板稳态挠度的最大值和空间分布的影响进行分析,得到了荷载临界速度,发现了板动力响应的特性和规律。     

移动荷载作用下大跨度铁路斜拉桥纵向共振机理

列车荷载作用下铁路斜拉桥将在不同方向上发生振动,列车竖向荷载作用下导致的主梁纵向振动将影响道床稳定性和伸缩装置的使用,甚至影响行车安全性和舒适性。采用等效纵向荷载研究移动荷载作用下斜拉桥纵向振动机理,推导纵向共振速度估算公式。以一大跨度铁路斜拉桥为实例,分析了不同速度的移动荷载作用下结构动力响应。结果表明,当移动荷载速度与估算纵向共振速度接近时,移动荷载通过桥梁时的纵向加载频率与桥梁一阶纵向振动频率接近,斜拉桥发生纵向共振现象,主梁和桥塔动力响应显著增大。     

Determination of the critical loading conditions for bridges under crossing trains

A procedure based on experimental and theoretical analyses to identify critical loading conditions on existing metallic railway bridges is presented. This method requires knowledge of the principal modal frequencies, and for this reason, a consolidated and simple procedure to study the bridge dynamics is herein explained. This consists of: preliminary studies; material and dynamic tests; and identification techniques to identify modal parameters and eventual non-linear behaviours. Generally the information collected can be used both to calibrate the bridge model and to obtain the refined frequency response function. In order to avoid high computational effort due to long time-history dynamic analyses by using the bridge model subjected to a series of train crossings, a new frequency domain approach for the identification of critical loading conditions is proposed. Evidence of the influence of the axle spacing and velocity of the vehicle on the dynamic magnification due to the train crossing is shown. The method is based on the construction of an excitation spectrum related to the train axle spacing and the velocity, given the weight of the vehicle. Comparison of the excitation spectrum with the frequency response function allows identification of the load patterns that bring the bridge to resonance conditions and might threaten bridge stability, bearing in mind continual changes in train technology.     

Noncontact cable force estimation with unmanned aerial vehicle and computer vision

Cables and hangers are critical components of long‐span bridges, tension forces of them are needed to be accurately measured for ensuring the safety of bridges. Traditionally, cable tension forces are measured by attached accelerometers or elastomagnetic (EM) sensors, however, applying these sensors into engineering practice are time‐consuming, labor‐intensive, and highly dangerous. To address these problems, an unmanned aerial vehicle (UAV)‐based noncontact cable force estimation method with computer vision technologies was proposed in this article. Basic concept of the proposed method is to use the UAV‐installed camera for capturing vibration images of cables from a certain distance and cable dynamic properties are extracted by analyzing captured images. It includes two aspects: (a) a line segments detector (LSD) was employed for detecting cable edges from captured video and a line matching algorithm was further proposed for extracting dynamic displacements; (b) the frequency difference of adjacent higher modal frequencies identified from relative displacements of the cable was employed for cable force calculation to avoid the difficulty of extracting fundamental frequency from UAV‐captured video. It should be noted that relative displacement herein refers to the difference between displacements of two points on the same cable. Advantages of the proposed method lie in that the proposed LSD and matching algorithm are more robust than traditional correlation‐based algorithm for calculating dynamic displacements of bridge cables and it does not need to adjust predefined parameters (i.e., subset size in correlation‐based algorithms). In addition, the combination of relative displacement and frequency difference‐based cable force estimation has the capability of enhancing the Fourier spectrum magnitude of bridge cables and reducing the effect of UAV motion on extraction of cable vibration frequencies. The effectiveness and robustness of the proposed method was verified by using an experimental inclined cable and field‐testing data of a long‐span suspension bridge. Results show that calculated cable forces with UAV technology have a good agreement with reference values measured by attached accelerometers and fixed camera, demonstrating correctness and robustness of the proposed method for cable force estimation.     

弯桥在局部损伤下的位移影响线分析

弯桥较直梁桥具有更复杂的变形以及受力特性,而针对其局部损伤识别的研究相对较少。位移影响线可以反映某一点的位移变化规律,在实际工程中可以直接测得。以弯桥位移影响线公式为依据,用梁格法建立了以某曲线匝道桥为工程背景的有限元模型,用数值方法分析了不同位置、不同程度损伤与竖向位移测量值之间的关系。结果表明,弯桥在局部损伤下的竖向位移影响线二阶导数可以识别局部损伤的位置与程度,可试用于实际工程。     

重载铁路过渡段路基动力响应特性试验研究#br#

掌握列车移动荷载作用下路基的动力响应特性可为路基沉降预测,状态评估提供依据。开展重载铁路过渡段路基动力响应测试,研究动位移峰值沿线路纵向及边坡方向的变化规律,分析路肩处动位移峰值的随机分布规律。研究列车动荷载作用下路基的动力响应特征,并揭示振动能量沿路基边坡的衰减规律。结果表明：列车动荷载对路基的作用具有明显的周期性,可将相邻车厢的两个前后转向架作为一个加载单元,在该加载单元的重复作用下路肩处的动位移峰值服从正态分布。重载列车动荷载作用下路基的振动频率主要分布在0~20Hz范围内,振动能量从路肩向坡脚方向衰减剧烈,基床层受列车动荷载影响显著,而基床以下路基受列车动荷载影响非常微小。分析结果有助于评估列车荷载作用下路基的瞬时及长期动力稳定性,同时为采用模型试验及数值分析手段研究路基动力响应特性时准确模拟重复列车动荷载提供了思路。     

Multiple damage detection in complex bridges based on strain energy extracted from single point measurement

Strain Energy of the structure can be changed with the damage at the damage location. The accurate detection of the damage location using this index in a force system is dependent on the degree of accuracy in determining the structure deformation function before and after damage. The use of modal-based methods to identify damage in complex bridges is always associated with problems due to the need to consider the effects of higher modes and the adverse effect of operational conditions on the extraction of structural modal parameters. In this paper, the deformation of the structure was determined by the concept of influence line using the Betti-Maxwell theory. Then two damage detection indicators were developed based on strain energy variations. These indices were presented separately for bending and torsion changes. Finite element analysis of a five-span concrete curved bridge was done to validate the stated methods. Damage was simulated by decreasing stiffness at different sections of the deck. The response regarding displacement of a point on the deck was measured along each span by passing a moving load on the bridge at very low speeds. Indicators of the strain energy extracted from displacement influence line and the strain energy extracted from the rotational displacement influence line (SERIL) were calculated for the studied bridge. The results show that the proposed methods have well identified the location of the damage by significantly reducing the number of sensors required to record the response. Also, the location of symmetric damages is detected with high resolution using SERIL.     

Response of a train moving on multi-span railway bridges undergoing ground settlement

This paper presents an incremental-iterative procedure to investigate the influence of ground settlement on dynamic interactions of train–bridge system. The train is simulated as a sequence of identical sprung mass units with equal intervals and the bridge system as a series of simple beams with identical properties. To resolve the train-induced vibrations of a beam structure undergoing support settlement, this study decomposes the total beam response into two parts: the static response due to vertical support settlement and the dynamic component caused by inertia effect of beam vibration. An exact solution for static displacement is presented by exerting the support displacements on the beam statically. Thus the remaining dynamic response of the vehicle/bridge coupling system is solved by Galerkin’s method and computed using an iterative approach with Newmark’s finite difference formulas. Numerical studies indicate that for the dynamic interactions of train–bridge system, the inclusion of ground settlement is generally small on the bridge response, but it can amplify drastically the vertical response of the moving train, especially for the concave-up settlement profile. This conclusion is of significance in aligning a rail route that has to cross a region with local land subsidence.     

Vereinfachte Methoden zur Berechnung der dynamischen Antwort von Eisenbahnbrücken bei Zugüberfahrt

Simplified methods to calculate the dynamic response of railway‐bridges under crossing trains. In this paper, two different methods to calculate the dynamic response of single‐span bridges under moving forces are presented. The work is focused on beam bridges with constant cross‐section in underdamped condition. In the first method, referred to as “Impulse‐method”, the effective impulse resulting from the load is approximated by simple analytical functions. The bridge is modelled as a single degree of freedom system by means of modal analysis. For this simplified system describing bridge and load, closed analytical formulae to calculate the dynamic response can be set up. The “Impulse‐method” is exemplified by the HSLM‐A1 load train given in Eurocode 1 (EC1). In the second method the response spectrum analysis widely used in earthquake engineering is adopted for the present problem. The calculation of response spectra for beam bridges under the HSLM‐A load models is demonstrated. An example shows how this method is deployed.     

地铁运行时引起的土的波动分析

基于有限元法分析了地铁运行引起的土的波动特性。对列车荷载进行了简化，并且考虑了地基土不同性质的影响，对各个区域采用了不同的材料参数，得到了地铁运行时的位移色度图及加速度衰减曲线。     

预应力简支梁桥在移动荷载作用下的非线性动力特性分析

考虑预应力梁的剪切变形和几何非线性,建立梁的动力学基本方程式,应用增量谐波平衡法,分析计算梁在预应力作用下的横向振动问题。通过实例计算,得到梁在移动车辆荷载作用下的幅频响应曲线和力与位移的非线性响应关系,并给出了外激励频率不同且初始预加力变化时动挠度的变化规律。计算结果表明,梁非线性位移明显大于线性位移,且荷载与位移呈明显非线性关系,非线性因素的影响不可忽略;施加预应力可以提高梁的动抗弯刚度,减少梁的动挠度值。为预应力混凝土桥梁的设计和动力特性分析提供一定的理论依据。     

简支梁桥位移与内力动力系数差异研究

动力系数是桥梁结构设计和检定中一个基本而关键的参数,其可以用位移放大系数来表示,也可以用内力(弯矩、剪力)放大系数来表示,而在桥梁的设计、检定工作中,并未注意到它们量值之间的区别.文中理论探讨了移动荷载列过桥模型的位移、内力放大系数的异同,以及不同动力系数沿简支梁桥跨长的变化规律,为区分制定桥梁动力系数的合理表达形式提供理论依据.并计算分析了车桥耦合模型与移动荷载列过桥模型的桥梁动力系数计算值的差异,结果表明应用移动荷载列模型计算简支梁桥动力系数可以得到安全可靠的结果,即可应用该模型解析解分析动力系数的主要影响因素.     

Identification of parameters of vehicles moving on bridges

This paper presents a method for identifying the parameters of vehicles moving on bridges. Two vehicle models, a single-degree-of-freedom model and a full-scale vehicle model, are used. The vehicle–bridge coupling equations are established by combining the equations of motion of both the bridge and the vehicle using the displacement relationship and the interaction force relationship at the contact point. Bridge responses including displacement, acceleration, and strain are used in the identification process. The parameters of vehicles moving on the bridge are then identified by optimizing an objective function, which is built up using the residual between the measured response time history and predicted response time history using the Genetic Algorithm. A series of case studies have been carried out and the identified results demonstrate that the proposed method is able to identify vehicle parameters very accurately. Field tests have also been performed on an existing bridge in Louisiana, and the parameters of a real truck are predicted. Since it is able to identify the parameters of moving vehicles, the methodology can be applied to improve the current weigh-in-motion techniques that usually require a smooth road surface and slow vehicle movement to minimize the dynamic effects. The methodology can also be implemented in routine traffic monitoring and control.     

求超静定结构影响线方程的新方法

直接利用解常载作用下超静定结构的位移法,将转角位移的固端弯矩和未知节点位移作为移动载荷在位置的函数。由平衡条件建立各杆端弯矩的影响线方程或杆端剪力影响线方程,再利用迭加原理求得其他量值的影响线方程。该法通俗易懂,对有侧移无侧移结构均适用,且也可用来求桁架、多跨静定梁和多跨多层静定刚架各量值的影响线。     

移动荷载下正交各向异性地基无限大板的动力响应

以薄板理论和弹性动力学理论为前提,以位移分量为基本未知量,建立了直角坐标系下的移动谐振荷载作用下正交各向异性地基上覆无限大弹性板的力学模型和动力微分方程;然后用坐标变换和Fourier积分变换,且引入边界条件,推导了移动荷载作用下无限大板的挠度和薄板与地基之间的接触应力的积分形式解。基于推导的理论方法,编制了相应的计算程序,并对薄板表面作用线性谐振荷载问题进行了算例分析,验证了方法的正确性。最后,对移动谐振荷载作用下公路路面板的动力响应进行了参数分析,研究了土体参数、板参数、荷载速度、荷载频率对其影响规律。结果表明:土体的各向异性、板厚、板的弹性模量、荷载移动的速度和振动频率对板动力响应影响很大。     

苏通大桥气弹模型气动失稳分析

大跨柔性桥梁气弹模型在风荷载作用下会产生明显的竖向、侧向位移和附加攻角。推导气弹模型实测位移修正表达式,对苏通大桥气弹模型高风速时实测位移进行修正,对比分析修正前后差异。绘制了苏通大桥主跨跨中断面、1/4断面和边跨跨中3个典型断面扭转中心的运动轨迹,分析其特点,对苏通大桥气弹模型气动失稳现象进行解释。基于随机搜索方法和随机子空间方法识别得到的模态参数,对苏通大桥气弹模型进行复模态颤振分析。分析结果表明:苏通大桥气弹模型可视为一种非常规索网复合系统,其气动失稳振动表现为保持平衡状态的竖向、侧向和扭转耦合滚动,扭转频率成分在竖弯和侧弯振动中参与很多,而竖弯和侧弯频率成分在其他两种振动中参与很少。     

移动荷载作用下加筋路堤和轨道系统的三维动力响应

用解析法研究了加筋路堤上轨道系统在移动荷载作用下的三维动力响应问题。基于Biot多孔弹性介质的波动理论,建立了加筋路堤轨道系统分析模型。将钢轨简化为无限长弹性Euler梁,将枕木简化为连续质量块,将加筋路堤作为一横观各向同性层来考虑,将下卧土体考虑为由Biot?ǘ匠堂枋龅谋ズ桶肟占洹Ａ⒐斓老低场⒓咏盥返毯拖挛酝撂宓亩Ψ匠蹋贔ourier变换域内求解荷载作用下钢轨位移和土体位移的表达式,将求得的表达式进行Fourier逆变换得到其在时域里的表达式。研究了列车移动速度、加筋路堤层的厚度、荷载幅值大小和加筋率等对路堤及轨道系统动力响应的影响。计算结果表明,钢轨竖向变形随着速度的增大呈现先增大后减小的趋势;加筋路堤上的钢轨竖向变形显著小于同厚度下未加筋路堤上的钢轨竖向变形;钢轨竖向变形随着荷载幅值的增大而增大;随着加筋率的增大而减小。     

大跨斜拉桥环境模态频率识别的最大熵法研究

大跨斜拉桥结构的振动特性随环境与运营条件的变化表现出时变的特征。本文对润扬大桥斜拉桥结构的实测加速度响应信号采用复模态指示函数法(CMIF法)进行了模态参数识别,在此基础上采用最大熵法对实测模态频率的不确定性进行了分析。分析结果表明,环境温度的变化对斜拉桥模态频率的影响是长期性的趋势,而交通荷载和风荷载对模态频率的影响则由于荷载的非平稳性呈现瞬时的颤动变化。采用最大熵法较好地改善了润扬大桥斜拉桥的环境模态频率识别效果,有效地减少了实测模态频率因车辆和风荷载随机因素影响的变异性。     

Control mode selection for modal control of long-span arch bridge

For seismic control of arch bridge, a model reduction of long-span arch bridge was implemented based on modal analysis. As for the critical mode selection, an approach based on the maximum modal displacement was presented. This approach takes into consideration the effect of external seismic excitation and is more reasonable than only considering dynamic bridge characteristics based on a modal contribution ratio. The time domain and frequency domain analysis method were used to verify the simplified model of the Nimu arch bridge in Tibet as an example. The numerical results show that the method of maximal modal displacement better analyze long-span arch bridge when multisupport seismic excitation must be considered. The reduced-order system also is more in line with the performance of the original model.     

Wind load identification using wind tunnel test data by inverse analysis

The method for modal wind load identification from across-wind load responses using Kalman filter is presented and verified using the wind tunnel test data. The Kalman filter is utilized for the inverse identification from limited measured responses and the closed-form of Kalman filter gain in modal space is derived for different types of measured response solving the Riccati equation. The wind induced responses used for the verification are measured responses from an aeroelastic wind tunnel test of a rectangular shaped concrete chimney. The displacement responses of the top part of the model are measured and used for the wind load identification, but the acceleration responses obtained by numerical differentiation of displacement are also used in order to evaluate the effect of response type on the identification result. It is found from the identification results that the proposed method identifies the modal across-wind load from measured responses with quite accuracy and the acceleration response yields more accurate wind load identification than displacement response.