Transition zones in railways, marked by abrupt changes in foundation stiffness, lead to differential settlements and amplified dynamic loads, accelerating track degradation. This necessitates a method that accurately relates stiffness ratios while accounting for shear interaction within the soil. Traditional models like the Winkler foundation, which neglect soil interaction, often overestimate dynamic responses in such scenarios. This paper presents a closed-form solution for analyzing transition zones, incorporating shear interaction effects modeled through a Visco-elastic Pasternak foundation of abrupt stiffness. The study extends to examine the dynamic responses of a series of axle loads under varying stiffness ratios and speeds, comparing the behavior of Winkler and Pasternak foundations. Results indicate that the Winkler model overestimates the dynamic response by 24%–28% for displacement and 5%–10% for acceleration, approximately. Additionally, the inclusion of the shear layer in the Pasternak model leads to a higher predicted critical velocity compared to the Winkler model. These findings emphasize the substantial impact of foundation resistance as well as resistance due to shear strain on the dynamic performance of the transition zone. Hence, such models can replicate ground behavior more accurately than the Winkler model, offering improved accuracy over traditional Winkler-based solutions. By analyzing various values of the stiffness ratio r, designers and engineers can make informed decisions regarding the selection and placement of materials with tailored stiffness properties in transition zones. This strategic use of materials with varying stiffness enables the design of effective mitigation measures aimed at smoothing out the abrupt changes in structural rigidity.

The problem of moving sequential loads over beams is a classic example of vehicle-bridge interaction. Many analytical, numerical, and experiments have been conducted in order to study the dynamic behavior of bridges. However, the computational cost involved in traditional methods is very high. The primary novelty of this paper lies in the creation of a non-dimensional mode-superposition to anticipate the bridge's peak dynamic responses, coupled with the application of ANN-based Multi Input Multi-Output metamodeling. The bridge is idealized as a Euler–Bernoulli beam of uniform cross-section subjected to sequential moving loads commonly known as High Speed Load model-B (HSLM-B). The pearson’s correlation coefficient indicates that the most influential parameter affecting the dynamic response of beams under moving loads is the interspatial distance between loads, i.e., ε followed by speed parameter η. Additionally, the comparison of the best-fitted surrogate models has been conducted to evaluate their robustness and efficiency. The results demonstrate an accuracy level of less than 10 percent, highlighting the high precision and reliability of the surrogate models.

This paper introduces a vibration control strategy for bridges that involves the implementation of an inertial amplifier to mitigate train-induced vibrations. The study comprehensively evaluates the effectiveness of two types of vibration absorbers, namely spring-mass resonator (SMR) and inertial amplifiers (IA), using a non-dimensional mechanics-based framework. The study further employs a heuristic search adaptive genetic algorithm (GA) to determine the optimal design parameters for the proposed vibration absorbers. The aim is to minimize the mid-span displacement of the bridge through the optimization process. The theoretical non-dimensional framework and the optimization technique are first validated with existing literature, and further, the efficiency of the optimized IA over the SMR of the same static mass is estimated. The comparative studies elucidate that with a lower mass ratio and higher values of the speed parameter (η) and inter-spatial distance between loads (ϵ), the IA system is more effective in reducing the vibration amplitude due to significant mass amplification. However, for lower values of η and ϵ, the SMR seems effective with a higher mass ratio, consequently resulting in amplified static deflection.

The dynamic interaction between trains, tracks, and bridges is a critical consideration in railway engineering, particularly for designing efficient railway bridges. This interaction holds significant importance, especially in the context of high-speed railways and heavy-haul railways, where optimal bridge design is paramount. Over time, these dynamic loads can lead to fatigue and structural damage, potentially compromising the integrity of the bridge. Vibration control measures help mitigate these dynamic loads, prolonging the lifespan of the bridge and ensuring its structural safety. This paper systematically presents a state-of-the-art review of the vibration control of bridges under the action of high-speed trains in conjunction with bibliometric analysis. Aligning in this direction, an extensive dataset consisting of 2233 research papers was collected from various search engines like Scopus or Web of Knowledge. This provides quantitative insights into research trends, citation patterns, and the impact of scholarly publications within a specific field or discipline. Additionally, a detailed intervention is made based on different vehicle models and methodologies involved in the analysis of vehicle–bridge interaction. This study aids in recognizing emerging topics for research in the domain of vibration control of high-speed railway bridges using different methodologies.

This study investigates the parametric optimization of multiple-tuned mass dampers (MTMDs) deployed along the length of a tower and monopile structure subjected to stochastic wind and wave forces. The structural components, comprising the tower and monopile, are conceptualized as Euler–Bernoulli beams. The interaction with the soil is modeled through viscoelastic springs distributed along the monopile. The rotor nacelle assembly (RNA) and blades are abstracted into a concentrated mass at the tower's apex. The MTMDs are characterized as spring–mass–dashpot systems strategically positioned at intervals along the tower and monopile. The investigation involves a random vibration analysis under wind and wave loads, employing the Kaimal spectrum for wind and the JONSWAP spectrum for waves. The study focuses on optimizing the TMD parameters using H2 optimization techniques, with the optimization criteria being the minimization of the standard deviation of the tower's top displacement response. Additionally, meta-heuristic algorithms like the genetic algorithm (GA) are utilized to refine the determination of these optimal parameters. A key aspect of the research includes a parametric study that reveals variations in optimal parameters as the number of TMDs is altered, maintaining a consistent total mass across the MTMDs.

A hybrid model that incorporates an artificial neural network (ANN) and non-dimensional numerical analysis has been developed to predict the displacement response of an elastically supported (ES) beam under the action of sequential moving loads in opposite directions. The dataset acquired from non-dimensional numerical modeling was utilized for training multi-layered feed-forward ANN, resulting in the development of surrogate models. The input parameters include the beam and load parameters, whereas the beam's displacement is the output parameter. The robustness and efficiency of the hybrid models have been highlighted using statistical metrics, which show that training and validating data produce promising predictions. Further, the relationship between input and output parameters was represented using Pearson's correlation. Results indicated that the effectiveness of the ES beam depends on the critical combination of stiffness parameter κ and interspatial distance parameter ϵ under particular speed parameter R. To bypass the computational cost, a user-friendly interface has been developed to assess the displacement response of elastically-supported beams under the action of one-way and two-way moving loads. Further, the proposed methodology has wide application in analyzing and designing short to medium-span bridges in critical locations such as canal/road crossings under the action of opposite moving loads using elastic support conditions.

This paper presents the evaluation of the dynamic stiffness coefficient (the stiffness and damping coefficient) of a rigid and massless foundation embedded in a layered elastic half-space. Linear hysteric material damping is introduced in the model using the correspondence principle. Based on the strength of the material approach with one-dimensional wave propagation in cones (cone model), horizontal and vertical dynamic stiffness coefficients were evaluated. To check the accuracy of the model, the dynamic stiffness coefficient of foundations resting on and/or embedded in layered half-space was evaluated using a cone model and validated with published results based on rigorous analysis. A parametric study is also carried out to investigate the influence of shear wave velocity, depth of embedment, and thickness of the top layer on the dynamic response of the foundation embedded in layered half-space. The results of the cone model analyses are presented in terms of stiffness coefficient K(ao) and damping coefficient C(ao) varying with dimensionless frequency (ao) for both horizontal and vertical modes of vibration. The results of the cone model provide physical insight with sufficient generality, making it convenient to use for various foundation vibration problems.

The design of high-speed simply supported bridges in critical conditions, such as road or canal crossings, is a matter of concern, particularly under two-way crossings with sequential wheel loads. Contrarily to simple classical support, elastic bearings can serve towards vibration mitigation under high speed. In this paper, a non-dimensional framework is developed to understand the impact mechanism of an elastically supported (ES) beam under the action of single as well as opposite traversing loads. A good agreement with the available literature has been confirmed for the one-way crossing using the present methodology. Moreover, a parametric study is conducted for an ES beam, in which the effects of speed parameter (η), speed parameter ratio between two trains (R), interspatial distance between loads to the length of the bridge (ϵ), damping ζ, stiffness parameter (κ), and traversing time difference between two trains (tos) are investigated. The theoretical results suggest the effective use of the ES beam under higher values of η for one-way and R for two-way traffic. Additionally, various resonances and cancellation speed ratios under particular values of ϵ have been identified under varying values of κ.

Keeping in view the design of short to medium-span bridges in critical locations such as road/river crossings under the action of oppositely moving high-speed loads, this paper presents a hybrid model for the prediction of dynamic displacement employing a theoretical non-dimensional framework aided by an artificial neural network (ANN). The introduction of such a hybrid model reduces parametric space and time. The feed-forward ANN is implemented to train the comprehensive data set obtained from the non-dimensional theoretical scheme. The dimensionless input to ANN comprises the bridge and load parameters, whereas maximum dynamic displacement is the output parameter. The robustness and efficiency of the proposed surrogate ANN framework in terms of computational efficiency are compared with the conventional mode-superposition method formulated in dimensionless form. The training of test and validated data sets results in best-fit models with optimistic statistical metrics and accuracy ≤ 6%. Moreover, the sensitivity of different parameters to the displacement response is highlighted using Pearson's correlation and Quantile-Quantile plots. To incorporate the best-fit models into the design by bypassing the high-fidelity model, a user-friendly interface is developed, confirming the standards of the high-speed rating code (TZY2014-232 2014). Such interfaces have the potential for wide application in the preliminary design of short-to medium-span bridges under opposite moving loads in critical locations such as crossing valleys, rivers, and railroads.

The prediction of the design parameters of short to medium-span supported bridges in critical locations (such as canal/road crossings) under the action of high-speed trains has been investigated in this article. An artificial neural network (ANN)-based MIMO (multiple-input multiple-output) metamodels is proposed in conjunction with the semi-analytical framework of simply-supported bridges. Three cases, namely single moving load, series of moving loads at equal spacing (HSLM-B), and as per conventional train configuration (HSLM-A) recommended in Eurocode1: EN 1991-2 (2003), are considered. The prime novelty of the article is to develop a dimensionless semi-analytical framework to train and validate a MIMO metamodel implementing ANN for predicting the multiple dynamic responses of bridges under high-speed loads. The dependency of the maximum dynamic responses, that is, displacement, shear force, and bending moment, on the governing parameters (structural and loading) have been elucidated using Pearson's correlation matrix for the three different train configurations. Further, the robustness and efficiency of the best-fitted metamodels have been compared, and a user interface has been developed for ease of implementation. This platform evaluates the responses such as displacement, shear force, bending moment, and structural safety confirming the standards of Eurocode EN 1990:2002 + A1:2005 (E).

This paper explores the design parameters for elastically supported (ES) bridges, particularly for short to medium under the influence of high-speed trains. It introduces a non-dimensional mathematical framework that conceptualizes the ES as a EulerBernoulli beam supported by elastic bearings at its ends and subjected to evenly spaced moving loads. The framework highlights various resonances and speed ratios for cancelling out specific effects based on the stiffness parameter and the distance between loads. The analysis indicates that most of the maximum displacement occurs near the beam's midpoint. Additionally, it shows that lower resonance speeds coupled with higher stiffness parameter values can result in significant amplification of displacement response due to cumulative forces acting on the system. This amplification is a consequence of the cumulative forces acting on the system. Hence, this research provides valuable insights for designers and engineers to optimize foundation design, thereby reducing structure-borne vibrations transmitted to the ground.