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Realistic composite vehicles with 2, 3, 5 and 9 axles, consisting of a truck with one or two trailers, are addressed in this paper by computational models for vehicle–bridge interaction analysis.

The vehicle–bridge interaction (VBI) models are formed by sets of 2-D rigid blocks interconnected by mass, damping and stiffness elements to simulate their suspension system. The passage of the vehicles is performed at different speeds. Several rolling surface profiles are admitted, considering the maintenance grade of the pavement. The spectral density functions are generated from an experimental database to form the longitudinal surface irregularity profiles. A computational code written in Phyton based on the finite element method was developed considering the Euler–Bernoulli beam model.

Several models of composite heavy vehicles are presented as manufactured and currently travel on major roads. Dynamic amplification factors are presented for each type of composite vehicle.

The VBI models for compound heavy vehicles are 2-D.

This work contributes to improving the safety and lifetime of the bridges, as well as the stability and comfort of the vehicles when passing over a bridge.

The structural response of the bridge is affected by the type and size of the compound vehicles, their speed and the conservative grade of the pavement. Moreover, one axle produces vibrations that can be superposed by the vibrations of the other axles. This effect can generate not usual dynamic responses.

Over-limit transportation has the characteristics of large axle load, large number of axles and lateral distribution width. Under the action of over-limit load, the coupling vibration effect of vehicle–bridge is more obvious, and the deformation of bridge components is large. Thus, research and analysis of the vehicle–bridge coupling dynamic response of long-span bridges under over-limit transportation has practical engineering significance.

Based on the principle of invariable elastic potential energy, this paper derives dynamic model of over-limit transportation n-axis flat vehicle. The numerical simulation method is used to model and calculate a cable-stayed bridge, and the static effect of the cable-stayed bridge and the dynamic response of vehicle–bridge coupling under different parameters are compared and analyzed.

The focus is on the influence of vehicle load and vehicle velocity parameters on the stress and amplitude of different cables under over-limit transportation, and the corresponding variation law is obtained.

The research on the coupled dynamic response of cable-stayed bridges has attracted the attention of many scholars, but there are relatively few studies on the coupled vibration of out-limit vehicles and bridges. In this paper, based on finite element software, a vehicle–bridge coupling model under bulk transportation is established.

Purpose — The purpose of this paper is to present a new nonstationary, random vibration method for the analysis of coupled vehicle‐bridge systems with vertical track irregularity. Design/methodology/approach — The vehicle is modeled using a two‐layer suspension system and hence possesses ten degrees of freedom. The bridge is simulated using a Bernoulli‐Euler beam and the longitudinal track irregularity is taken as a uniformly modulated, evolutionary random process that includes phase lags between successive wheels. The pseudo‐excitation method (PEM) is extended to include time‐dependent systems for the first time, thus making it possible to compute the nonstationary random vibration of coupled vehicle‐bridge systems. Additionally, the precise integration method (PIM) is adapted to simulate continuous vehicle force variations in both time and space. Findings — The accuracy and effectiveness of the proposed PEM‐PIM method are confirmed by comparisons with Monte Carlo simulations. The influence of vehicle speed and track irregularity on system random responses are evaluated, and it is shown that the first and second derivatives of the track irregularity should not be arbitrarily ignored, as is usually the case. Originality/value — PEM and PIM are relatively new tools for the numerical solution of complicated random vibration problems and direct dynamic analyses. Until now, they have only been applied to time‐independent systems. However, it is shown herein that the proposed PEM‐PIM method performs nonstationary random vibration analysis of time‐dependent coupled vehicle‐bridge systems efficiently and accurately.

The purpose of this paper is to present a practical and efficient iterative method for predicting vehicle-induced response of bridge.

The vehicle-bridge interaction (VBI) problem is generalized mathematically and a computational algorithm for VBI is proposed. This method rests on an iterative procedure, which utilizes the whole interaction process for iteration. By this means, vehicle and bridge become totally uncoupled and are only linked by the contact force history. This method provides flexibility to choose simplified or refined vehicle and bridge models for the VBI problem, as well as open options for different commercial FEM software without specialized codes.

The method is verified through two numerical examples. The first example uses a simple 1D beam bridge model, which illustrates the procedure of this method and demonstrates its fast convergence in several iterations. The second example employs a realistic full 3D finite element bridge model, which shows that the method easily connects complex FEM bridge models in ABAQUS with a calibrated vehicle model in Matlab. The dynamic response of the bridge is reliably calculated within only a few iterations.

The proposed iterative method separates vehicle and bridge into independent subsystems in the computational process, thus providing more flexibility to utilize commercial FEM softwares. Its efficiency is realized through choosing the whole interaction force process for iteration, which considerably reduces the iteration steps.

According to relevant research, non-uniform speed has a significant impact on the vehicle-track systems. Up to now, research work on it is still very limited. In this paper, the PEM is adopted to further transform it into a deterministic process to solve the vehicle’s problem of running at a non-uniform speed.

The multi-body vehicle model has 10 degrees of freedom and the track is regarded as a finite long beam supported by lumped sleepers and ballast blocks. They are connected via linear Hertz springs. The vertical track irregularity is a Gaussian stationary process in the space domain. It is transformed into a uniformly modulated nonstationary random process in the time domain with respect to the non-uniform vehicle speed. By solving the equation of motion of the coupled vehicle-track system with the pseudo-excitation method, the pseudo-response and consequently the power spectral density and the standard deviation of the structural response can be obtained.

Two kinds of vehicle braking programs are taken in the numerical example and some beneficial conclusions are drawn.

The pseudo-excitation method (PEM) was used to perform the random vibration analysis of a coupled non-uniform speed vehicle-track system. Transforming the track irregularity into a uniformly modulated nonstationary random process in time domain with respect to the non-uniform vehicle speed was undertaken. The pseudo-response of the coupled system is solved by applying the Newmark algorithm with constant space integral steps. The random vibration transfer mechanism of the coupled system is fully discussed.

Based on the aerodynamic loads and dynamic performances of trains, this study aims to investigate the effect of crosswinds and raindrops on intercity trains operating on viaducts to ensure the safe operation of intercity railways in metropolitan areas.

An approach coupled with the Euler multiphase model as well as the standard k-ɛ turbulence model is used to investigate the coupled flow feature surrounding trains and viaducts, including airflow and raindrops, and the numerical results are validated with those of the wind tunnel test. Additionally, the train’s dynamic response and the operating safety region in different crosswind speeds and rainfall is investigated based on train’s aerodynamic loads and the train wheel–rail dynamics simulation.

The aerodynamic loads of trains at varying running speeds exhibit an increasing trend as the increase of wind speed and rainfall intensity. The motion of raindrop particles demonstrates a significant similarity with the airflow in wind and rain environments, as a result of the dominance of airflow and the supplementary impacts of droplets. As the train’s operating speed ranged between 120 and 200 km/h and within a rainfall range of 20–100 mm/h, the safe operating region of trains decreased by 0.56%–7.03%, compared with the no-rain condition (0 mm/h).

The impact of crosswind speeds and rainfall on the train’s aerodynamic safety is studied, including the flow feature of crosswind and different particle-sized raindrops around the train and viaduct, aerodynamic loads coefficients suffered by the intercity train as well as the operating safety region of intercity trains on the viaduct.

This paper aims to study the influence of aerodynamics force of trains passing each other on the dynamic response of vehicle bridge coupling system based on numerical simulation and multi-body dynamics and put forward the speed threshold for safe running of train under different crosswind speeds.

The computational fluid dynamics method is adopted to simulate the aerodynamic force in the whole process of train passing each other by using dynamic grid technology. The dynamic model of vehicle-bridge coupling system is established considering the effects of aerodynamic force of train passing each other under crosswind, the dynamic response of train intersection on the bridge under crosswind is computed and the running safety of the train is evaluated.

The aerodynamic force of trains' intersection has little effects on the derailment factor, lateral wheel-rail force and vertical acceleration of train, but it increases the offload factor of train and significantly increases the lateral acceleration of train. The crosswind has a significant effect on increasing the derailment factor, lateral wheel-rail force and offload factor of train. The offload factor of train is the key factor to control the threshold of train speed. The impact of the aerodynamic force of trains' intersection on running safety cannot be ignored. When the extreme values of crosswind wind speed are 15 m·s⁻¹, 20 m·s⁻¹ and 25 m·s⁻¹, respectively, the corresponding speed thresholds for safe running of train are 350 km·h⁻¹, 275 km·h⁻¹ and 200 km·h⁻¹, respectively.

The research can provide a more precise numerical method to study the running safety of high-speed trains under the aerodynamic effect of trains passing each other on bridge in crosswind.

Develops a general five‐axle vehicle model to study the dynamic interactions between the moving mass and the bridge structural components. Two‐axle, three‐axle, or four‐axle sprung loads, and the limiting load conditions such as a moving constant force, a moving alternating force, a moving unsprung mass, and combinations thereof, can be treated as special cases of the more general case presented. Further, its integration with the versatile finite element modelling has enhanced the practical applicability of such a theoretical development. The physical characteristics of the bridge and the vehicle, such as the bridge geometry, mechanical properties, profile of the road surface, the vehicle parameters including the distance between axles, leaf springs suspension and the total weight, are considered explicitly in the present model. The dynamic equations of equilibrium in time are integrated using the Newmark integration scheme. Verifies the accuracy of the algorithm by comparing the numerical results obtained from the present formulation with the experimental results.

This study aims to propose a vertical coupling dynamic analysis method of vehicle–track–substructure based on forced vibration and use this method to analyze the influence on the dynamic response of track and vehicle caused by local fastener failure.

The track and substructure are decomposed into the rail subsystem and substructure subsystem, in which the rail subsystem is composed of two layers of nodes corresponding to the upper rail and the lower fastener. The rail is treated as a continuous beam with elastic discrete point supports, and spring-damping elements are used to simulate the constraints between rail and fastener. Forced displacement and forced velocity are used to deal with the effect of the substructure on the rail system, while the external load is used to deal with the reverse effect. The fastener failure is simulated with the methods that cancel the forced vibration transmission, namely take no account of the substructure–rail interaction at that position.

The dynamic characteristics of the infrastructure with local diseases can be accurately calculated by using the proposed method. Local fastener failure will slightly affect the vibration of substructure and carbody, but it will significantly intensify the vibration response between wheel and rail. The maximum vertical displacement and the maximum vertical vibration acceleration of rail is 2.94 times and 2.97 times the normal value, respectively, under the train speed of 350 km·h⁻¹. At the same time, the maximum wheel–rail force and wheel load reduction rate increase by 22.0 and 50.2%, respectively, from the normal value.

This method can better reveal the local vibration conditions of the rail and easily simulate the influence of various defects on the dynamic response of the coupling system.

The nuclear purpose of this research paper is to analyse representative bridges around the world as a tourist attraction and iconic element through destination marketing organisations’ (DMOs’) tourism official websites where these are localised and three online travel agencies’ (OTAs’) websites.

This research used a mixed method. The author carried out Google research (13 March 2023) that included the following search word string “iconic bridges around the world” and “the most famous bridges worldwide” to select the most relevant bridges around the globe. Moreover, this research used a content analysis to examine how Expedia, Booking and Orbitz OTAs promote the bridges through their websites in terms of a tourist attraction, iconic element, tourist package, images and information.

Findings suggest that the most representative bridges analysed in this study are promoted as iconic element and tourist attraction through DMOs’ websites. Nevertheless, Booking, Expedia and Orbitz OTAs promote and sell products and services related to bridges selected, except in the case of the Millau Viaduct in France, the Si-O-Se-Pol bridge in Iran, the Danyang Kunshan Grand bridge in China and the Royal Gorge in the USA. Furthermore, results support that OTAs need to enhance the quality and variety of products and services that are linked to iconic bridges sightseeing tours because at the moment, there is a great uniformity in the promotion of products and services provided.

This paper contributes to broader debates in the importance of bridges as a tourist attraction and iconic element to attract tourists through tourism promotion websites.