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This paper is devoted to track-bridge interaction phenomena in railway bridges of short simply-supported (SS) spans composed by ballasted tracks. These structures may experience high vertical acceleration levels under operating conditions. In particular, the coupling effect exerted by the ballast track shared by structural parts that are theoretically independent, such as consecutive simply-supported spans or twin adjacent single-track decks, is investigated. Experimental evidence shows that in these cases there may be an important vibration transmission from the loaded to the unloaded track, and that the interlocked ballast granules couple some of the lowest modes of vibration to an important extent. To this end a detailed three-dimensional (3D) Finite Element (FE) model of an existing bridge is implemented where the ballast in weakly connected regions is simulated as transversely isotropic material, in order to represent in a simplified manner the degraded state due to the relative motion between the disconnected structural parts. First, the bridge numerical model is updated from the ambient vibration response of the structure previously measured by the authors. Second, a sensitivity analysis is performed on the properties of the degraded ballast and their effect on the first five modes of vibration of the bridge is discussed. Finally, the response of the bridge under operating conditions is computed numerically, compared with the response measured experimentally in the time and frequency domains and conclusions are extracted regarding the model adequacy. Spanish Ministry of Science and Innovation PID2019-109622RB FEDER Andalucía 2014–2020 Operational Program US-126491 Generalitat Valenciana, Spain and Universitat Jaume I, Spain AICO2019/175 Generalitat Valenciana, Spain and Universitat Jaume I, Spain UJI/A2008/06

Número especial Bulletin of Earthquake Engineering, Ag. 2021: S.I. : SOIL-STRUCTURE INTERACTION EFFECTS ON THE DYNAMICS OF STRUCTURES. // Artículo Open Access CCBY 4.0. Disponible online 3 agosto 2021 A novel numerical methodology is presented to solve the dynamic response of railway bridges under the passage of running trains, considering soil–structure interaction. It is advantageous compared to alternative approaches because it permits, (i) consideration of complex geometries for the bridge and foundations, (ii) simulation of stratifed soils, and, (iii) solving the train-bridge dynamic problem at minimal computational cost. The approach uses sub-structuring to split the problem into two coupled interaction problems: the soil–foundation, and the soil–foundation–bridge systems. In the former, the foundation and surrounding soil are discretized with Finite Elements (FE), and padded with Perfectly Match Layers to avoid boundary refections. Considering this domain, the equivalent frequency dependent dynamic stifness and damping characteristics of the soil–foundation system are computed. For the second sub-system, the dynamic response of the structure under railway trafc is computed using a FE model with spring and dashpot elements at the support locations, which have the equivalent properties determined using the frst subsystem. This soil–foundation–bridge model is solved using complex modal superposition, considering the equivalent dynamic stifness and damping of the soil–foundation corresponding to each natural frequency. The proposed approach is then validated using both experimental measurements and an alternative Finite Element–Boundary Element (FE– BE) methodology. A strong match is found and the results discussed Ministerio de Ciencia, Innovación y Universidades PID2019-109622RB Universidad de Sevilla US-126491 Generalitat Valenciana AICO2019/175 Centro Informático Científico de Andalucía (CICA)

In this paper the authors investigate the energy harvesting in railway bridges and analyse the performance under different operational conditions. An approximation based on modal superposition is proposed for the computation of the energy harvested from train-induced bridge vibration. This approach is consistent with the analytical modal solutions of the simply-supported Bernouilli-Euler beam transverse response under moving loads. The influence of the bridge maximum dynamic response and cancellation phenomena, the tuning effect of the harvester device and the relevance of different modal contributions on the harvested energy are studied using a single-degree of freedom system as a simplistic mechanical approach. Later, a piezoelectrically coupled lumped parameter model is used to investigate the available energy due to High-Speed train passages at different circulating speeds. Finally, the feasibility of energy harvesting is evaluated from the experimental data measured by the authors in a railway bridge from the Madrid-Sevilla High-Speed line. The obtained results allow quantifying the harvested energy in a time window of three and a half hours and twenty train passages. Ministerio de Economía y Competitividad (España) BIA2016-75042-C2 Ministerio de Ciencia, Innovación (España) PID2019-109622RB-C21 Consejería de Economía y Conocimiento of Junta de Andalucía (España) US-1264916 Generalitat Valenciana (España) AICO2019/175

The vibrational response of railway bridges is an issue of main concern, especially since the advent of High-Speed traffic. In the case of short-to-medium lengths and simply-supported spans excessive transverse acceleration levels may be induced at the platform, with detrimental consequences for passengers and infrastructures. The orthotropic plate has proven to be an appropriate model for the prediction of the response of certain typologies in the aforementioned cases such as multiple girder decks, solid or voided slabs or filler-beam multiple-track decks. In this contribution, the vibrational response of orthotropic plates, simply and elastically supported, circulated by vertical moving loads is investigated. First, maximum free vibration and cancellation conditions are derived analytically. From these, bridge span length-characteristic distance ratios leading to maximum and minimum resonances under series of equidistant loads are depicted. Second, the applicability of these ratios in oblique decks is analysed for the most common first three mode shapes: first longitudinal bending, first torsion and first transverse bending modes, and the errors in relation to the straight reference case are bounded. To this end, an extensive bridge catalogue of girder bridges is designed in the range of lengths of interest, covering flexural stiffnesses typical from both conventional and High-Speed railway lines. Finally, the applicability of the previous theoretical results is exemplified with experimental measurements performed on a bridge from the Spanish railway network. Spanish Ministries of Economy and Competitiveness (Ministerio de Economía y Competitividad, España) BIA2016-75042-C2 Spanish Ministries of Education (Ministerio de Educación, España) CAS18/00080 Generalitat Valenciana (España) AICO/2019/175

This contribution investigates the application of Passive Control techniques to reduce the severe transverse vibrations that railway bridges of moderate lengths may experience under resonant conditions. The proposed solution consists in connecting the slab to a series of auxiliary beams clamped between the bridge abutments through a set of fluid viscous dampers. A particular configuration minimising the space occupied by the devices and the auxiliary beams under the bridge deck is proposed for two typical typologies in the aforementioned lengths: slabs and girder bridges. First, the dynamic response of a double-beam analytical model is obtained in closed-form under harmonic excitation in order to detect the main governing parameters, capturing the essence of the response at resonance of the main beam fundamental mode. Then conditions are obtained for the optimal damper constants that minimise the main beam amplification. Finally the effectiveness of the solution and the adequacy of the expressions derived from the harmonic case are proven under railway traffic excitation taking into account the three-dimensional deformation of the deck. Throughout the study special attention is given to the beneficial effect arising from clamping the auxiliary beam supports when compared to the simply-supported case, analysed by the authors in previous works. Partial rotational restrictions are admitted to take into consideration the expectable deviation from ideally clamped conditions. Two case studies are presented showing that the auxiliary beams size, if partially clamped, could be significantly reduced for the same main beam vibration mitigation level. If the beams are to be installed under a railway bridge deck in a practical application, this is a crucial issue in order to minimise the free space occupied with the retrofit.

The advent of high-speed railways has raised many concerns regarding the behaviour of bridges. Particularly, the analysis of the free vibrations generated by each load is of great interest because they can possibly accumulate and create resonance phenomena. Regarding simply supported beams, earlier contributions showed that the free vibrations created by a single moving force are of maximum or zero amplitude (cancellation) for certain speeds. In the present paper new closed-form expressions are given for the cancellation speeds of a generic mode, as well as for the most representative points of maximum amplitude. Similar new results are provided for elastically supported beams as well. A simpler, closed-form approximate expression of the cancellation condition for an elastically supported beam is also derived from the analysis of a single passing load; this approximate formula is in good agreement with the exact results. Knowing a priori the speeds of maximum free vibrations or cancellation is of great interest for experimental tests on bridges, particularly as regards the evaluation of amplitude-dependent magnitudes such as structural damping. Regarding the resonance phenomena, if the resonance speeds coincide with either a maximum free vibration or a cancellation speed, then a maximum resonance or a cancellation of resonance will occur. The most relevant cases thereof have been investigated, and new expressions which allow predicting them for a generic mode are given. Finally, a new approximate formula is proposed for estimating the maximum acceleration of simply supported bridges caused by resonances of the fundamental mode. After extensive numerical testing, the formula has proved to be a useful tool for a first assessment of simply supported bridges according to building codes such as Eurocodes. (C) 2012 Elsevier Ltd. All rights reserved., The authors acknowledge the financial support of the State Secretariat for Research of the Spanish Ministry of Science and Innovation (Secretaria de Estado de Investigacion, Ministerio de Ciencia e Innovacion, MICINN) in the framework of the Research Project BIA2008-04111.

[EN] In this article, the resonant response of plates traversed by moving loads is addressed being its main application the dynamic performance of railway bridges under high-speed traffic. An innovative alternative to reduce the deck inadmissible oscillations that may appear in short simply supported structures in resonant conditions is proposed, based on artificially increasing the superstructure damping by retrofitting the deck with fluid viscous dampers. A particular auxiliary structure transforming the deck vertical deflection into relative movement within the devices is envisaged, being the main objectives of the study to optimise the retrofitting system parameters and to prove its efficiency under the action of railway vehicles. For these purposes, the retrofitted deck behaviour is first investigated using an orthotropic plate model under harmonic excitation. On the basis of an analytical approach, a dimensionless version of the equations of motion is presented, the governing parameters are extracted and an intensive sensitivity analysis of the plate response is performed. Finally, analytical closed-form expressions for the optimal dampers constants are derived and their adequacy is numerically evaluated. To this end, an existing bridge belonging to the Spanish Railway network is analysed using a three-dimensional finite element code specifically programmed by the authors for this application. In the end the controlling effect of the retrofitting system and the applicability of the optimal parameters analytical expressions are proven for a wide range of circulating velocities. (C) 2010 Elsevier Ltd. All rights reserved., The authors acknowledge the financial support of the Spanish Ministry of Public Works, in the framework of the National Programme for Construction (Area of Transportation and Construction) of the National Plan for Scientific Research, Development and Technological Innovation 2004-2007, under research project no. 80021/A04.

[EN] In this paper, the dynamic performance of a certain kind of existing bridge under the action of highspeed railway traffic is addressed. Short-to-medium-span simply supported structures are susceptible to experiencing harmful transverse vibrations under resonant conditions, leading to excessive levels of vertical acceleration, the subsequent premature deconsolidation and degradation of the ballast layer, passenger discomfort and high maintenance costs of the corresponding lines. This dynamic problem, which can require the reduction of the design velocity or the temporary interruption of the railway service to undertake corrective actions, has been reported in Europe, China and Japan during the last decades (European Rail Research Institute (2000) [13], Duan (1995) [30], Ishibashi (2004) [15]). In particular, single-track simply supported short bridges appear to be quite critical structures in this regard. In what follows, the authors present an evaluation of the dynamic performance of three real bridges on the Spanish railway network, located in double-track branches but composed of structurally independent decks. The objective of the investigation is to compare their performance with that of hypothetical modified double-track versions of the original decks. An orthotropic plate finite element model, whose properties are updated from experimental tests performed on the bridges in the past, is used to predict the structural dynamic responses in the time domain. Finally, the predominant effect of the increase in the mass of the bridges over the increase in the eccentricity of the tracks, the reduction in the natural frequency experienced by the torsion mode, and the relevance of three-dimensional modal contributions is proven, leading to remarkable reductions of the maximum acceleration levels in the multiple-track modified structures. © 2010 Elsevier Ltd. All rights reserved., The authors express their gratitude to the Spanish Ministry of Science and Innovation (Ministerio de Ciencia e Innovacion, MICINN), for the financial support received in the framework of Research Project number BIA2008-04111.

[EN] This paper deals with the application of Passive Control techniques to mitigate the excessive vibrations that short simply supported railway bridges may undergo under the circulation of High-Speed trains. A possible solution to reduce inadmissible levels of deck vertical acceleration, based on retrofitting the bridge with fluid viscous dampers connected to the slab and to an auxiliary structure, is proposed and evaluated. To this end, two real bridges belonging to the Spanish railway network are analysed using an orthotropic plate Finite Element model, which properties are updated from experimental tests performed on the structures in the past. A possible conditioning of the respective lines for higher design velocities than the current ones is considered, leading to inadmissible performances of the bridges. A particular retrofit is proposed for each structure in order to accomplish the Serviceability Limit State of vertical acceleration, and the controlling effect of the proposed system is shown for a wide range of trains and circulating velocities. In order to realistically assess the technical feasibility of the alternative, special attention is given to practical aspects related to the auxiliary structure and dampers installation. (C) 2009 Elsevier Ltd. All rights reserved., The authors acknowledge the financial Support of the Spanish Ministry of Public Works (Ministerio de Fomento), in the framework of the National Program for Construction (Area of Transportation and Construction) of the National Plan for Scientific Research, Development and Technological Innovation 2004-2007, under research project No. 80021/A04. Also, the technical information provided by Mr. Jorge Nasarre, from the Fundacion Caminos de Hierro, and by the Subdireccion General de Construccion (Ministry of Public Works) is gratefully acknowledged.