Vehicle-passenger-structure interaction of uniform bridges traversed by moving vehicles

An investigation into the dynamics of vehicle-occupant-structure-induced vibration of bridges traversed by moving vehicles is presented. The vehicle including the driver and passengers is modelled as a half-car planar model with six degrees-of-freedom, and the bridge is assumed to obey the Euler-Bernoulli beam theory with arbitrary conventional boundary conditions. Due to the continuously moving location of the variable loads on the bridge, the governing differential equations become rather complicated. The numerical simulations presented here are for the case of vehicle travelling at a constant speed on a uniform bridge with simply supported end conditions. The relationship between the bridge vibration characteristics and the vehicle speed is rendered, which yields into a search for a particular speed that determines the maximum values of the dynamic deflection and the bending moment of the bridge. Results at different vehicle speeds demonstrate that the maximum dynamic deflection occurs at the vicinity of the bridge mid-span, while the maximum bending moment occurs at ±20% of the mid-span point. It is shown that one can find a critical speed at which the maximum values of the bridge dynamic deflection and the bending moment attain their global maxima.     

Critical speed for the dynamics of truck events on bridges with a smooth road surface

Simple numerical models of point loads are used to represent single and multiple vehicle events on two-lane bridges with a good road profile. While such models are insufficiently complex to calculate dynamic amplification accurately, they are presented here to provide an understanding of the influence of speed and distance between vehicles on the bridge dynamic response. Critical combinations of speed as a function of main bridge natural frequency and meeting point of two vehicles travelling in opposite directions are identified. It is proposed that such simple models can be used to estimate the pattern of critical speeds versus dynamic amplification of the bridge response for trucks on a relatively smooth surface. The crossing of a three-dimensional spring-dashpot truck is simulated over a bridge plate model to test this hypothesis for a range of road roughness. Further validation is carried out using the site-specific mean pattern associated to field measurements of bridge strains when traversed by a truck population. The latter is found to be closely resembled by the theoretical pattern derived from simple point load models.     

A finite element method prediction of the vibration of a bridge subjected to a moving vehicle load

This paper is concerned with the analysis of dynamic deflection and acceleration of a concrete bridge which is subjected to a moving vehicle load. The bridge, to be constructed across the River Brahmaputra in India, consists of 20 main spans, and each main span is assumed to be double cantilever type with a small suspended span. The moving vehicle is modeled as one degree of freedom. The deflections and accelerations at specific locations on the bridge when the vehicle moves at constant speed are analyzed by using the finite element method.     

Structural damage identification for railway bridges based on train-induced bridge responses and sensitivity analysis

A damage identification approach using train-induced responses and sensitivity analysis is proposed for the nondestructive evaluation of railway bridges. The dynamic responses of railway bridges under moving trains composed of multiple vehicles are calculated by a train-bridge dynamic interaction analysis. Using the stiffness variation of the bridge element as an index for damage identification, the sensitivities of train-induced bridge responses to structural damage are analyzed and the sensitivity matrices are formed. By comparing the theoretical measurement responses of one measurement point in two different states, the damage indices of all elements are updated iteratively, and finally the absolute or relative damage is located and quantified. A three-span continuous bridge numerical example proves that the proposed dynamic response sensitivity-based FE model updating damage identification method is not only effective to detect local damage of railway bridges, but also insensitive to the track irregularity and the measurement noise.     

Dynamic response of a monorail steel bridge under a moving train

This study proposes a dynamic response analysis procedure for traffic-induced vibration of a monorail bridge and train. Each car in the monorail train is idealized as a dynamic system of 15-degrees-of-freedom. The governing equations of motion for a three-dimensional monorail bridge-train interaction system are derived using Lagrange's formulation for monorail trains, and a finite-element method for modal analysis of monorail bridges. Analytical results on dynamic response of the monorail train and bridge are compared with field-test data in order to verify the validity of the proposed analysis procedure, and a positive correlation is found. An interesting feature of the monorail bridge response is that sway motion is caused by torsional behavior resulting from eccentricity between the shear center of the bridge section and the train load.     

Optimization method based on Generalized Pattern Search Algorithm to identify bridge parameters indirectly by a passing vehicle

Generalized Pattern Search Algorithm (GPSA) has rarely been investigated for structural health monitoring, but may have potential application in civil engineering, because it does not require any gradient information of the objective function. Meanwhile, indirect identification is an attractive concept that recognizes the bridge parameters by the vehicle responses. This paper proposes a theoretical indirect identification method based on optimization method, and the implementation is performed by the GPSA. Firstly, the GPSA theory is investigated, and a simple example is employed to describe the process of the algorithm. Secondly, a theoretical indirect identification method is proposed, based on the optimization method rather than the conventional transforms from time domain to frequency domain. The proposed method can identify the parameters of the vehicle–bridge system, including the bridge stiffness and the 1st frequency. Based on the optimization method, the feasibility and accuracy of GPSA are demonstrated with 0.06% of errors. The GPSA shows good robustness in the identifications with various noise levels, and the maximum error is about 3.30% and can be accepted for the engineering application even with a SNR 5 noise level. The computation time relies only on the function evaluation times, and is not positively related to the noise level. Thirdly, the performance of GPSA is compared with that of Genetic Algorithm (GA). The accuracy of GPSA and GA are approximately equivalent with various noise levels. Compared with GA, GPSA needs fewer iterations and much fewer evaluations, therefore is more efficient in the identification with an almost consistent accuracy with various noise levels.     

Reducing slab track vibration into bridge using elastic materials in high speed railway

In this paper, the problem of vibration transmission from slab track structures into bridge is studied by theoretical analysis. A vehicle-track-bridge coupling system dynamics model is established based on a multibody dynamics theory and a finite element method. The system model consists of vehicle model, track-bridge model and wheel/rail interaction model. The vehicle model is established based on the multibody dynamics theory, and the tack-bridge model is established by the finite element method. The vehicle model and track-bridge model are coupled through wheel/rail interaction model, and the track irregularities are included. The system dynamic responses are calculated, and the effectiveness of elastic materials in vibration reducing is discussed. The results demonstrate that elastic materials like slab mat layer inserted between slab track and bridge can reduce vibration transmitted from track into the bridge. Some suggestions for the design and application of slab mat are provided in the end of the paper.     

Finite element modelling for fatigue stress analysis of large suspension bridges

Fatigue is an important failure mode for large suspension bridges under traffic loadings. However, large suspension bridges have so many attributes that it is difficult to analyze their fatigue damage using experimental measurement methods. Numerical simulation is a feasible method of studying such fatigue damage. In British standards, the finite element method is recommended as a rigorous method for steel bridge fatigue analysis. This paper aims at developing a finite element (FE) model of a large suspension steel bridge for fatigue stress analysis. As a case study, a FE model of the Tsing Ma Bridge is presented. The verification of the model is carried out with the help of the measured bridge modal characteristics and the online data measured by the structural health monitoring system installed on the bridge. The results show that the constructed FE model is efficient for bridge dynamic analysis. Global structural analyses using the developed FE model are presented to determine the components of the nominal stress generated by railway loadings and some typical highway loadings. The critical locations in the bridge main span are also identified with the numerical results of the global FE stress analysis. Local stress analysis of a typical weld connection is carried out to obtain the hot-spot stresses in the region. These results provide a basis for evaluating fatigue damage and predicting the remaining life of the bridge.     

Brownian flights over a fractal nest and first-passage statistics on irregular surfaces

The diffusive motion of Brownian particles near irregular interfaces plays a crucial role in various transport phenomena in nature and industry. Most diffusion-reaction processes in confining interfacial systems involve a sequence of Brownian flights in the bulk, connecting successive hits with the interface (Brownian bridges). The statistics of times and displacements separating two interface encounters are then determinant in the overall transport. We present a theoretical and numerical analysis of this complex first-passage problem. We show that the bridge statistics is directly related to the Minkowski content of the surface within the usual diffusion length. In the case of self-similar or self-affine interfaces, we show and check numerically that the bridge statistics follows power laws with exponents depending directly on the surface fractal dimension.     

Biomechanically inspired modelling of pedestrian-induced forces on laterally oscillating structures

Despite considerable interest among engineers and scientists, bi-directional interaction between walking pedestrians and lively bridges has still not been well understood. In an attempt to bridge this gap a biomechanically inspired model of the human response to lateral bridge motion is presented and explored. The simple inverted pendulum model captures the key features of pedestrian lateral balance and the resulting forces on the structure. The forces include self-excited components that can be effectively modelled as frequency-dependent added damping and mass to the structure. The results of numerical simulations are in reasonable agreement with recent experimental measurements of humans walking on a laterally oscillating treadmill, and in very good agreement with measurements on full-scale bridges. In contrast to many other models of lateral pedestrian loading, synchronisation with the bridge motion is not involved. A parametric study of the model is conducted, revealing that as pedestrians slow down as a crowd becomes more dense, their resulting lower pacing rates generate larger self-excited forces. For typical pedestrian parameters, the potential to generate negative damping arises for any lateral bridge vibration frequency above 0.43 Hz, depending on the walking frequency. Stability boundaries of the combined pedestrian–structure system are presented in terms of the structural damping ratio and pedestrian-to-bridge mass ratio, revealing complex relations between damping demand and bridge and pedestrian frequencies, due to the added mass effect. Finally it is demonstrated that the model can produce simultaneous self-excited forces on multiple structural modes, and a realistic full simulation of a large number of pedestrians, walking randomly and interacting with a bridge, produces structural behaviour in very good agreement with site observations.     

Free Vibration Analysis of RC Box-Girder Bridges Using FEM

The free vibration analysis of simply supported box-girder bridges is carried out using the finite element method. The fundamental frequency is determined in straight, skew, curved and skew-curved box-girder bridges. It is important to analyse the combined effect of skewness and curvature because skew-curved box-girder bridge behaviour cannot be predicted by simply adding the individual effects of skewness and curvature. At first, an existing model is considered to validate the present approach. A convergence study is carried out to decide the mesh size in the finite element method. An exhaustive parametric study is conducted to determine the fundamental frequency of box-girder bridges with varying skew angle, curve angle, span, span-depth ratio and cell number. The skew angle is varied from 0° to 60°, curve angle is varied from 0° to 60°, span is changed from 25 to 50 m, span-depth ratio is varied from 10 to 16, and single cell & double cell are used in the present study. A total of 420 bridge models are used for parametric study in the investigation. Mode shapes of the skew-curved bridge are also presented. The fundamental frequency of the skew-curved box-girder bridge is found to be more than the straight bridge, so, the skew-curved box-girder bridge is preferable. The present study may be useful in the design of box-girder bridges.     

桥梁拉索损伤声发射监测研究进展

大量索承体系桥梁即将达到20–30年的拉索寿命期,开展有效的拉索损伤监测方法研究有利于保障大桥结构安全。本文简要论述了现有桥梁拉索损伤检测及监测方法的适用性,重点综述了近40年来声发射技术应用于桥梁拉索监测的研究进展,以及在腐蚀、疲劳、断丝等损伤监测方面所取得的研究成果。结合实测数据在采集、数据处理过程中的难点及参数分析盲点,探讨了现有研究成果应用于特大桥梁拉索损伤监测仍需解决的问题,并针对性地提出了研究思路。     

Vehicle–bridge interaction analysis under high-speed trains

The dynamic interaction between high-speed train and simply supported girders is studied by theoretical analysis and field experiment in this paper. The dynamic interaction model of the train–bridge system is established, in which the rigid-body dynamics theory, finite element method and wheel–rail displacement corresponding assumption are adopted for the vehicle model, bridge model and wheel–rail interaction model, respectively. The measured track irregularities are taken as the system excitation. The responses of a 24 m-span PC box girder bridge are calculated. The proposed analysis model and the solution method are verified through the comparison between the calculated results and the measured results.     

Rupture energy of a pendular liquid bridge

We propose a simple expression for the rupture energy of a pendular liquid bridge between two spheres, taking into account capillary and viscous (lubrication) forces. In the case of capillary forces only, the results are in accordance with curve fitting expressions proposed by Simons et al. [2] and Willett et al. [5]. We performed accurate measurements of the force exerted by liquid bridges between two spheres. Experimental results are found to be close to theoretical values. A reasonable agreement is also found in the presence of viscous forces. Finally, for small bridge volumes, the rupture criterion given by Lian et al. [10] is modified, taking into account additional viscous effects. Received 18 September 2000 and Received in final form 10 June 2001     

Moving force identification based on the frequency-time domain method

This paper addresses the problem on the identification of moving vehicle axle loads based on measured bridge responses using a frequency-time domain method. The focus is on the evaluation of two solutions to the overdetermined set of equations established as part of the identification method. The two solutions are (i) direct calculation of the pseudo-inverse and (ii) calculation of the pseudo-inverse via the singular value decomposition (SVD) technique. For this purpose, a bridge-vehicle system model was fabricated in the laboratory and the bending moment responses of bridge model were measured as a two-axle vehicle model moved across the bridge deck. The moving axle loads are then calculated from the measured responses via the two solutions to the over-determined set of equations. The effects of changes in the bridge-vehicle system, measurement and algorithm parameters on the two solutions are evaluated. Case studies show that the moving force identification is more feasible and its accuracy acceptable with the use of the SVD technique. This technique can effectively enhance the identification method and improve the identification accuracy over that of the direct pseudo-inverse solution.     

Passive stabilization of capillary bridges in air with acoustic radiation pressure

Long liquid capillary bridges are normally unstable because of the growth of a mode where one end becomes slender while the other becomes rotund. This Rayleigh-Plateau instability was suppressed for weightless bridges on NASA's KC-135 aircraft by placing the bridge in an acoustic standing wave. With an appropriate acoustic wavelength and amplitude the radiation pressure automatically squeezes more on the rotund portion of the bridge so as to suppress the growth of the relevant capillary mode. Stabilization is a natural consequence of the interaction with the steady sound field.     

Dominant frequencies of train-induced vibrations

This paper investigates the dynamic characteristics of ground vibrations induced by moving vehicles including the mass rapid transit system, high-speed train railway, and general railway on bridges, embankments, and in tunnels using field experiments and theoretical solutions. The results indicate that train-induced ground vibrations at the trainload dominant frequencies are significantly large for both subsonic and supersonic train speeds, and the vibrations from carriage natural frequencies and engine frequencies are minor. For trains moving on bridges, the resonant vibrations are serious when the natural frequencies of the bridge are close to the trainload dominant frequencies, but resonance does not occur when the carriage natural frequencies and trainload dominant frequencies match. The trainload dominant frequency and its influence factor can be computed using the two simple equations deducted in this paper.     

Bridging dielectric fluids by light: A ray optics approach

Rayleigh-Plateau instability is known to impose a stability limit for the length of a liquid bridge in weightless conditions. This fundamental limit may be exceeded by using a light field to form and stabilize dielectric fluid bridges (A. Casner, J.P. Delville, Europhys. Lett. 65, 337 (2004)). Using both new experimental data as well as a new theoretical approach, we show that both the size and the stability of such light-sustained dielectric bridge can be qualitatively explained. We present a ray optics model that encompasses the competition between surface tension effects and optical radiation pressure arising from total internal reflection inside the bridge. A critical power below which a liquid bridge can no longer be sustained by light is predicted and confirmed experimentally. The observed power dependence of the bridge diameter also agrees with the proposed stabilization mechanism.     

Eigenproperties of suspension bridges with damage

The vertical vibration of suspension bridges with a damage in the main cables is studied using a continuum formulation. Starting from a model for damaged suspended cables recently proposed in the literature, an improved expression for the dynamic increment of cable tension is derived. The nonlinear equation of motion of the damaged bridge is obtained by extending this model to include the stiffening girder. The linear undamped modal eigenproperties are then extracted, in closed-form, from the linearized equation of motion, thus generalizing to the presence of an arbitrary damage the expressions known from the literature for undamaged suspension bridges. The linear dynamics of the damaged bridge reveals to be completely described by means of the same two non-dimensional parameters that govern the linear dynamics of undamaged bridges and which account for the mechanical characteristics of both the main cable and the girder, with the addition of three non-dimensional parameters characterizing damage intensity, position and extent. After presenting the mathematical formulation, a parametric analysis is conducted with the purpose of investigating the sensitivity of natural frequencies and mode shapes to damage, which, in fact, is a crucial point concerning damage detection applications using inverse methods. All through the paper, systematic comparisons with finite element simulations are presented for the purpose of model validation.     

First-principles investigation of functionalization-defects on silicon surfaces

We present a theoretical study of chemisorption of CHC-CH₂-COOH molecules on the H:Si(1 0 0) surface. We perform simulations for different chemisorbed configurations, attained by reactions through the alkyne tail. We use the periodic slab approximation for the extended surface, within ab initio density functional theory, and analyse results from several different approaches. We conclude that structures composed of single Si-C bridges are very stable, while a previously proposed structure, with a double Si-C-Si bridge, should be metastable on the flat surface, and introduce electron and hole traps in the Si band gap.