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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

Constant moving load models are widely adopted in the dynamic analysis of railway bridges under moving trains. However, the use of this simple model may overestimate the resonant response of simply supported bridges if the vehicle-bridge interaction (VBI) effects are neglected, particularly for short spans. To account for the VBI effects, Eurocode 1 allows engineers to consider an additional amount of structural damping which depends on the bridge span. This method is the so-called Additional Damping Method (ADM), and was formulated in order to provide a conservative prediction of the interaction benefit. Nevertheless, the Additional damping method may sometimes yield to an unsafe prediction of the bridge peak response. Considering the interaction benefits, an alternative analytical approach based on an equivalent VBI model under resonant excitations is presented in this investigation. The key parameters dominating the additional damping problem are subsequently identified. According to the numerical demonstrations supplied, the presented approach provides insights that enable an accurate prediction of the additional amount of damping needed in order to account for VBI effects on short simply-supported railway bridges.

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

In this contribution the vertical response of multi-span single-track simply-supported railway bridges is addressed. The main objective is to assess the influence of the track components and its continuity on the bridge acceleration response under the passage of railway convoys. To this end, a preliminary bidimensional numerical model is presented including a discrete model for the track. The model is calibrated with the proof load test results performed on the structure in the past. A sensitivity analysis is performed showing the effect the track components stiffness and damping considered under resonant and non-resonant conditions. Finally, a recent experimental campaign performed by the authors on an existing bridge is presented and the structural response under two trains is compared with numerical predictions. Preliminary conclusions regarding the effect of the track components and the ballast coupling between adjacent decks are finally extracted.

Ponència presentada al XI International Conference on Structural Dynamics (Eurodyn 2020), del 23 al 26 de novembre de 2020 This paper is devoted to the analysis of rail-bridge interaction effects in railway bridges under the circulation of moving trains. In a first approach, a bidimensional Finite Element model is implemented. The rail and the bridge are represented as Bernouilli-Euler beams, and a three-layer discrete track model accounting for the damping and flexibility of rail pads, ballast and subgrade is considered. In the model, several elastically supported spans are included, coupled by the presence of the track. First a sensitivity analysis is performed on the track parameters. A numerical receptance test is simulated on the rails showing that the track damping parameters influence the response only in the vicinity of the track natural frequencies, which are much higher than the bridge’s. Then, the maximum acceleration of the bridge is evaluated under equidistant trains and consistent conclusions are extracted regarding the track parameters. Last, the number of spans included in the model is evaluated showing that limiting the model to one span does not necessarily lead to the highest response in terms of the bridge acceleration. Finally, the response of an existing two-span single-track bridge belonging to a conventional Spanish line is evaluated under the circulation of the Altaria Talgo train. Numerical predictions are compared to experimental results obtained in a recent campaign. The prediction of the vertical acceleration at the sensors located along the longitudinal symmetry axis is adequate. From the experimental results the coupling effect between the adjacent decks in each span is evident suggesting the need of analyzing this phenomenon with more sophisticated models.

Ponència presentada al XI International Conference on Structural Dynamics (Eurodyn 2020), del 23 al 26 de novembre de 2020 This work is devoted to the experimental evaluation of the dynamic response of railway bridges with common typologies in short-to-medium spans.

Railway induced vibrations on short-to-medium span simply-supported (SS) bridges is addressed in this contribution. Such structures may experience high levels of vertical acceleration at the platform, leading to adverse consequences such as a premature degradation of the ballast layer and passenger discomfort. In the present study, the evolution of the bridge dynamic response when soil-structure interaction (SSI) is taken into account is investigated. To this end a coupled three-dimensional (3D) Boundary Element-Finite Element model (BEM-FEM) formulated in the time domain is implemented to reproduce the soil and structural behaviour, respectively. First, a set of soil-bridge systems of interest is defined, covering a wide range of lengths and natural frequencies for the structures, and an interval of expectable elastic properties and damping levels for the soil. Then, different types of analyses are performed on the soil-bridge systems extracting conclusions regarding the effect of including SSI in numerical models for predicting the bridge behaviour under railway traffic. In particular natural frequencies and modal damping levels are identified, and the structure amplification after the passage of a moving load in free vibration is investigated. Conclusions regarding how resonance and cancellation conditions may be affected by soil properties are extracted. Finally, the dynamic response of a real bridge, belonging to the Spanish railway network, is evaluated under the circulation of trains that induce second and third resonances of the bridge fundamental mode. The effect of the soil flexibility, soil material damping and the bridge resonance order are evaluated. Conclusions regarding the appropriateness of the results provided by common models which do not include SSI effects are extracted Ministerio de Economía y Competitividad BIA2013-43085-P Ministerio de Economía y Competitividad BIA2016-75042-C2 Centro Informático Científico de Andalucía (CICA)

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

In this contribution the authors include results and conclusions from an experimental and numerical analysis of a railway bridge belonging to the Madrid-Sevilla High-Speed railway line in Spain. This structure is monitored due to its short length and typology, which make it susceptible to experience high transverse vibration levels. During the in-situ tests the soil properties at the site were obtained. Also, the response of the structure under the circulation of railway convoys was measured at several points of the deck and at the abutments. From the experimental measurements the modal parameters of the bridge are identified. Finally the experimental results are compared to those provided by a finite element numerical model in the time and frequency domains. Conclusions are extracted regarding the structure performance and the adequacy of the numerical model implemented.

This work is devoted to the analysis of the railway-induced vertical vibrations of simply-supported double track bridges composed by pre-stressed concrete girder decks. Despite the low torsional stiffness that this particular deck configuration exhibits, several structures of this type do exist in both conventional and high-speed railway lines in Spain. Even though railway administrators recommend the construction of transverse or end beams bracing the longitudinal girders at the supports in girder bridges, in several occasions these elements are not built in order to accelerate the construction process. The aim of this study is to evaluate the beneficial effect of installing these transverse beams on the vertical dynamic response of the aforementioned structures and to determine what particular bridges are most affected by the presence of these elements. To this end, a representative ensemble of girder bridges covering a range of span lengths L between 10 m and 25 m has been predimensioned and their dynamic behaviour has been predicted by a finite element model that adopts common assumptions in engineering practice. Conclusions show that installing these elements is particularly relevant in the case of short (10–12.5 m) oblique bridges with a low number of longitudinal girders for a particular deck bending stiffness, leading to an important increase of the first torsion and first transverse bending natural frequencies and to a reduction of the structural response. Finally, experimental measurements on a real bridge belonging to the Madrid-Sevilla high-speed line are included in the final section to illustrate the theoretical derivations. Ministerio de Economía y Competitividad (España) BIA2016-75042-C2 Andalusian Scientific Computing Centre (CICA) and Universitat Jaume I UJI-A2018-06

This work is devoted to the experimental evaluation of the dynamic response of railway bridges with common typologies in short-to-medium span lengths. An extensive experimental campaign is performed in several railway bridges belonging to the High-Speed (HS) and conventional Spanish railway network. The main objectives are to (i) characterise the structures main features affecting their dynamic behaviour, (ii) determine the soil properties at the structures respective locations; and (iii) analyse the bridge dynamic responses under different operating conditions. All the bridges are composed by simply-supported (S-S) spans except the last one which is a continuous beam bridge. The structures present different steel, concrete and steel–concrete composite typologies. Five bridges have been experimentally investigated. The five bridges are nowadays at full operation. The study includes the identification of the bridges modal parameters and dynamic soil properties at the sites, a discussion on the identified structural damping in all the bridges, the measurement of the vibration levels induced by railway traffic under operational conditions in the first four bridges, and under construction operation machinery in the fifth case, and a final analysis on the differences found in the structural behaviour of the different typologies for similar traffic. This paper summarizes a vast experimental campaign. The data is available and may be useful to other researchers in order to estimate the response in similar cases and to validate numerical models. Ministerio de Economía y Competitividad BIA2016-75042-C2 Ministerio de Ciencia, Innovación PID2019-109622RB-C21 Consejería de Economía y Conocimiento of Junta de Andalucía (Spain) US-1264916 Generalitat Valenciana AICO2019/175

The objective of this study is to evaluate the vibratory response of two-span continuous beams subjected to moving loads and, in particular, to investigate the maximum resonance and cancellation of resonance phenomena. The main practical interest is the evaluation of the maximum acceleration response in railway bridges, which is one of the most demanding Serviceability Limit States for traffic safety according to current regulations. Two-span continuous bridges, in their simplest version (i.e. uniform identical spans), present antisymmetric and symmetric modes with closely spaced natural frequencies, leading to a more involved dynamic behaviour than that of simply-supported bridges. First, the free vibration response of a Bernoulli-Euler two-span beam after the passage of a single load at constant speed is formulated analytically, and non-dimensional speeds leading to cancellation or maximum response in free vibration are obtained for each mode. Then, these conditions are equated to resonant speeds induced by equidistant load series, and span length-to-characteristic distance ratios causing cancelled out resonances, or remarkably prominent ones, are obtained. Based on the previous derivations, a methodology for detecting which could be the most aggressive trains for a particular structure based on pure geometrical considerations is discussed. Finally, the applicability of the theoretical derivations is shown through the numerical analysis of two real bridges belonging to the Swedish railway network.

In this paper the dynamic response of a particular type of high-speed railway bridge common in the Spanish railway system is analysed with the aim of evaluating the levels of vertical vibrations experienced at the platform. To this end, Bracea I bridge which belongs to the Madrid-Sevilla High Speed railway line is selected. The bridge is composed by two identical short simply supported spans. The pre-stressed concrete girders deck dimensions and level of obliquity make this structure prone to (i) experience important vertical accelerations under railway traffic and (ii) present a dynamic response with a high participation of modes different from the longitudinal bending one. Therefore the structure is not expected to behave as a beam-type structure. The results of an experimental campaign recently performed at the site are presented with the objective of characterising the soil dynamic properties and the structure response under ambient vibration conditions and under railway traffic. The experimental response of the bridge is then compared in the time and frequency domains to numerical predictions given by two Finite Element models which adopt common assumptions in engineering practice. The study provides interesting conclusions regarding the structure experimental response under resonant and not resonant conditions. Additionally, conclusions regarding the adequacy of the numerical models for predicting the bridge response and assessing the Serviceability Limit State of vertical acceleration in ballasted railways are presented. Ministerio de Economía y Competitividad BIA2013-43085-P y BIA2016-75042-C2 Universitat Jaume I PI-1B2015-54 CICA PI-1B2015-54

This paper investigates the seismic performance of an existing steel cable-stayed bridge located in a high seismic zone. In 1988 the structure experienced the failure of one of its anchorage plates needing closure and structural repair as a consequence of seismic activity. In this study, the possibility of retrofitting the original bridge with different passive supplemental damping and seismic isolation systems is proposed and assessed, in order to improve the response of the structure in its longitudinal direction. To this end a Finite Element model of the bridge is developed and the structural response is evaluated through non-linear dynamic response analyses under a set of historical ground motions of different intensities, including a near field record. Strength degradation capabilities are introduced in the model, allowing the occurrence of brittle failure in all the members. Seismic performance indices referred to the dynamic response of the unretrofitted structure and to the results of a pushover analysis are defined and used to compare the proposed innovative solutions. The major improvement on the overall response of the bridge is shown and conclusions regarding the most appropriate retrofit alternative for the particular case study are determined. The authors express their gratitude to the Spanish Ministry of Economics and Competitiveness (Ministerio de Economía y Competitividad, MINECO), for the financial support received in the framework of the program “José Castillejo” with reference number JC2011-0304 for mobility of researchers.

To reduce the resonant response of high-speed railway bridges, semi-active magnetorheological dampers are proposed in this study. The elements are connected to the structure in a double beam configuration. An H ∞ control algorithm to drive magnetorheological damping forces of MR dampers is derived. Feasible solutions for an uncertain time-delay model are obtained by using standard linear matrix inequality techniques. Weight functions as a loop shaping procedure are also introduced in the feedback controllers to improve the tracking ability of magnetorheological damping forces. To this end, the effectiveness of magnetorheological dampers controlled by the proposed scheme, along with the effects of the uncertain and the time-delay parameters on the models, are evaluated and compared with the performance of fluid viscous dampers in similar applications reported in previous research through numerical simulations.

Traffic induced vibrations in railway bridges has become an issue of main concern among scientists and engineers due to the extensive construction of new High-Speed railway lines and the upgrading of existing lines for higher operating velocities [1, 2]. In this context, short to medium-span bridges (10–25 m) composed by simply-supported elements are especially critical, due to their usually associated low masses, and may experience considerably high vertical acceleration levels at the platform area [3]. As a result, the transverse acceleration in such structures is one of the most demanding Serviceability Limit States according to present regulations [4]. As a consequence, there is a need to realistically predict the behavior of railway structures in the design phase and along the bridge’s life. In this contribution the authors include results and conclusions from an experimental and numerical analysis of Arroyo Bracea II railway bridge, located in the Madrid-Sevilla High-Speed railway line in Spain. This structure is monitored due to its short length and typology, which make it susceptible to experience high transverse vibration levels. During the experimental campaign the soil properties at the site were obtained. Also, the response of the structure under the circulation of railway convoys travelling at speeds over 260 km/h was measured at several points of the deck and at the abutments. From the experimental measurements the modal parameters of the bridge are identified. Finally the experimental results are compared to those provided by a finite element numerical model in the time and frequency domains. Conclusions are extracted regarding the structure performance and the adequacy of the numerical model implemented for the particular soil and loading conditions.

This article addresses the dynamic behaviour of double track simply supported bridges of short to medium span lengths (10 m < L < 25 m) belonging to conventional railway lines. These structures are susceptible to experience inadmissible levels of vertical vibrations when traversed by trains at high speeds, and in certain cases their dynamic performance may require to be re-evaluated in case of an increase of the traffic velocity above 200 km/h. In engineering consultancies, these structures have been traditionally analysed under the passage of trains at different speeds using planar models, neglecting the contribution of transverse vibration modes and also the flexibility of the elastomeric bearings. The study presented herein endeavours to evaluate the influence of these two aspects in the verification of the Serviceability Limit State of vertical accelerations, which is of great interest in order to guarantee a conservative prediction of the dynamic behaviour. In the present study, the dynamic response of representative slab and girder bridges has been evaluated using an orthotropic plate finite element model, leading to practical conclusions regarding the circumstances under which the above mentioned factors should be considered in order to adequately evaluate the transverse vibration levels of the deck.

This work deals with the optimization of fluid viscous damper systems (FVDs) to reduce the resonant dynamic structural response of high-speed railway bridges by algebraic and numerical approaches. The presented method chooses the objective function based on the H ∞ norm over the frequency band of interest. This function allows taking into account structural damping properties and minimizing simultaneously the structural response associated with multiple modes. Especially, the proposed objective function may also be extended to nonlinear problems to determine optimal parameters of nonlinear fluid viscous dampers which may be an interesting solution in applications where high force levels are expected in the dampers. Finally, the proposed method is validated through numerical simulations. The simulation results show that the optimal FVD coefficients obtained by using the presented method are more exact than those by the previous method. Besides, the effectiveness of the method for solving the problems with the contribution of high modes and the consideration of nonlinear FVDs is also proved.

The dynamic transverse response of beam type bridges under railway traffic is addressed in this contribution. In particular, how soil-structure interaction may affect the critical or resonant velocities and the associated vibratory amplitudes is evaluated in detail. Resonance in beams, due to the circulation of equidistant loads, is highly influenced by the free vibration response that every single load leaves after traversing the structure. On this basis a numerical investigation is carried out analysing the effects of the wave propagation problem on the free vibration response of simply-supported beams in a wide range of travelling velocities. To this end a coupled three-dimensional boundary element-finite element model formulated in the time domain is used to reproduce the soil and structural behaviour, respectively. A catalogue of bridge deck typologies is defined, covering lengths, associated linear masses and fundamental frequencies that may experience high levels of transverse accelerations under resonant conditions, for nowadays existing trains and design velocities. Lengths ranging from 12.5 to 25 m are evaluated, along with fundamental frequencies covering most common typologies. A homogeneous soil is considered with shear wave velocities in the interval 150 to 365 m/s. From the single load free vibration parametric analysis conclusions are derived regarding the conditions of maximum free vibration and cancellation of the deck response. These conclusions are used afterwards to justify how resonant amplitudes of the bridge under the circulation of railway convoys may be affected by the soil properties, leading to substantially amplified responses or to almost imperceptible ones, and a numerical example is included to show the aforementioned situations. The first two authors would like to acknowledge the financial support provided by Universitat Jaume I under the research project P1··1B2015-54. The third and fourth authors would like to acknowledge the financial support provided by the Spanish Ministry of Economy and Competitiveness (Ministerio de Economía y Competitividad) under the research project [BIA2013-43085-P]. The authors also wish to acknowledge the support provided by the Andalusian Scientific Computing Centre (CICA).

This paper presents a study on the energy-absorbing capacities of viscoelastic dampers (VEDs) for reducing the resonant vibrations of simply supported high-speed railway bridges of short to medium span. The proposed solution is based on retrofitting the bridge with a set of discrete VEDs connected to the slab and to an auxiliary structure, placed underneath the bridge deck and resting on the abutments. In this investigation attention is focused on mitigating flexural vibrations; therefore, both the bridge and the auxiliary structure are modelled as simply supported beams with Bernoulli-Euler (B-E) behavior, whereas a discrete fractional derivative model simulates the behavior of the damping material. Firstly, a parametric study of this planar model is carried out, which has led to a dimensioning procedure of the dissipative system. The technical feasibility of this particular retrofit design is numerically evaluated by applying it to a numerical model of a simply supported railway bridge with inadmissible vertical accelerations. Numerical results show that the dynamic response of the structure can be significantly reduced in resonance with the proposed damping system. © 2012 Elsevier Ltd., The authors wish to express their gratitude to the Spanish Ministry of Public Works for the financial support received in the framework of Research Project number 80021/A04.

A new base-isolation mechanism corresponding to a variance of the stepping A-shaped frame is proposed and its seismic performance is investigated numerically for strong ground accelerations with peak values in the range from 0.5 to 1g. In its simplest two-dimensional form, the system consists of a frame with two telescoping legs pinned at the apex at a sharp angle. The legs are attached to the foundation through a spring and a damper acting in parallel. Both the springs and viscous dampers have bilinear characteristics that make them very stiff in compression but very soft in tension. As the structure rocks sideways, the length of the loaded leg remains essentially constant while the length of the unloaded leg increases. When the ground acceleration changes direction, the process is reversed. The resulting system has three main characteristics: (i) as the structure steps on a rigid leg, the maximum acceleration that can be transmitted to the superstructure is limited to a value which is approximately independent of the amplitude of the ground motion; (ii) there is a systematic lifting of the superstructure with kinetic energy being systematically transformed into potential energy during the strong phase of the ground motion; and (iii) the system is slowly self-centering at the end of the earthquake. The seismic performance of the system is evaluated for a tall bridge pier and for a smaller frame that could be used in a multi-story building. The results obtained for the 1940 El Centro ground motion scaled to 1g and for the near-field Rinaldi ground motion recorded during the Northridge earthquake show that substantial reductions of the absolute acceleration can be obtained with reasonable relative displacements of the superstructure and small strokes in the isolation devices.

The dynamic response of a multi-story steel moment resisting frame (MRF) equipped with fluid viscous (VS) dampers and subjected to seismic loads is investigated numerically. The structure is retrofitted with two fluid VS dampers per story in its middle bay. Its dynamic response is analyzed when retrofitted with linear and nonlinear VS dampers. Two performance indices are developed in order to evaluate by means of a simple procedure the adequacy of each retrofitting option. The different options are evaluated and an optimum design is selected. The main objective of this numerical research is to build a simple methodology leading to an optimum retrofitting option with nonlinear fluid VS dampers. A secondary objective of the study is to compare the structure response retrofitted with linear and nonlinear VS dampers and finding an optimum retrofit strategy attending to two performance indices that are developed. The seismic behavior of a six-story steel structure is analyzed and it is found that the maximum force experienced by the dampers in the nonlinear case may be reduced in more than a 35% in comparison with the linear retrofitting case with a similar structural seismic performance.

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.

Ponència presentada al XI International Conference on Structural Dynamics (Eurodyn 2020), del 23 al 26 de novembre de 2020 In the present contribution the effect of the continuity of the ballasted track on the dynamic response of simply-supported railway bridges composed by structurally independent adjacent slabs at each span is addressed. Previous research works and experimental campaigns performed on simply-supported structures have shown that the presence of the ballast layer and other track components (rails, sleepers) may induce a dynamic coupling effect between the bridge spans or adjacent decks. In this study the influence of this effect on the train-induced vibrations is assessed. With this purpose a preliminary three-dimensional finite element (FE) model that includes the track components as a set of discrete mass, stiffness and damping elements has been implemented to numerically evaluate the influence of the continuity of the track components on the prediction of the bridge acceleration response under the passage of railway vehicles. The numerical model is calibrated with the load test results performed on a simply-supported railway bridge composed by several adjacent slabs. Finally the measured structural response of the bridge under train induced vibrations is compared with the numerical predictions. Preliminary conclusions regarding the importance of considering the continuity of the track components for the prediction and the assessment of the Serviceability Limit State of vertical acceleration in ballasted simply-supported railway bridges are presented.

In the present contribution, the dynamic behaviour of beams traversed by moving loads including soil–structure interaction (SSI) is investigated. The main application of the study is to analyse the effects of SSI on the resonant response of bridges caused by railway traffic. As this phenomenon is highly influenced by the free vibration response of the deck, a numerical investigation is carried out by analysing the effects of the wave propagation problem on the transverse-free vibration response of beams under moving loads in a wide range of velocities. To this end, a coupled three-dimensional boundary element-finite element model formulated in the time domain is used to reproduce the soil and structural behaviour, respectively. A subset of bridges is defined considering span lengths ranging from 12.5 to 25 m and fundamental frequencies covering associated typologies. A homogeneous soil is considered with shear wave velocities ranging from 150 to 365 m/s. From the single load-free vibration parametric analysis, conclusions are derived regarding the conditions of maximum free vibration and cancellation of the response. These conclusions are used afterwards to justify how resonant amplitudes of the bridge under the circulation of railway convoys are affected by the soil properties, leading to substantially amplified responses or to almost cancelled ones, and numerical examples are included to show the aforementioned situations. The first two authors would like to acknowledge the financial support provided by Universitat Jaume I under the research project P1 1B2015-54. The third and fourth authors would like to acknowledge the financial support provided by the Spanish Ministry of Economy and Competitiveness (Ministerio de Econom´ıa y Competitividad) under the research project [BIA2013-43085-P]. The authors also wish to acknowledge the support provided by the Andalusian Scientific Computing Centre (CICA).