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.

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).

The auxetic meta-material is a special class of macro-structure designed for exhibiting negative Poisson's ratio. The spatial repetition of the lattice affects the wave propagation and dynamic responses. In this study, a mathematical basis of Bloch analysis for auxetic media have been presented and shaded some important light on the application of the technique. For this design an analysis has been carried out to show how the periodic boundary condition changes with the connectivity, orientation and geometry of unit lattice. The corresponding eigen value problem is developed to obtain the propagation frequency which is the function of mass, stiffness matrix and the wave vector. Mapping of different forms which are associated with the nodal displacements of a unit cell to adjacent cell have been demonstrated and formulated mathematically and observed its effect on the reduced stiffness and mass matrices is studied. Modal analysis has been carried out using Abaqus 6.14 and the transverse nodal displacements obtained from the F.E analysis. The Bloch formulation for revolving-square type auxetic structure has been formulated and validated. Further, we have obtained the changes in auxetic behavior of the structure under different boundary conditions. The periodicity of a given lattice assists in determining the frequency bands within which the propagation of elastic waves is permitted. Further study is proposed for attenuation and transmission band analysis to steer the waves which roots the idea of vibration sink, in which we can damp the mechanical waves effectively at a specific location. The Auxetic meta-materials is envisaged to have a significant role in wave attenuation and wave steering, and can be used effectively for vibration control.

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.