Abstract 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 stratified 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 reflections. Considering this domain, the equivalent frequency dependent dynamic stiffness and damping characteristics of the soil–foundation system are computed. For the second sub-system, the dynamic response of the structure under railway traffic is computed using a FE model with spring and dashpot elements at the support locations, which have the equivalent properties determined using the first sub-system. This soil–foundation–bridge model is solved using complex modal superposition, considering the equivalent dynamic stiffness 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.
A significant number of railway bridges composed by simply-supported (SS) spans are present in existing railway lines. Special attention must be paid to short to medium span length structures, as they are prone to experience high vertical acceleration levels at the deck, due to their low weight and damping, compromising the travelling comfort and the structural integrity. The accurate prediction of the dynamic response of these bridges is a complex issue since it is affected by uncertain factors such as structural damping and complex interaction mechanisms such as vehicle-bridge, soil-structure or track-bridge interaction. Concerning track-bridge interaction, experimental evidences of a dynamic coupling exerted by the ballasted track between subsequent SS spans and also between structurally independent single-track twin adjacent decks have been reported in the literature [1, 2]. Nevertheless, this phenomenon is frequently disregarded due to the computational cost of models including the track and due to the uncertainties in the mechanical parameters that define the track system. The present work contributes to the study of the coupling effect exerted by the ballasted track between independent structures in railway bridges. With this purpose two 3D finite element (FE) track-bridge interaction models are implemented. The former includes a continuous representation of the track components meshing the sleepers, ballast and sub-ballast with solid FE. In the latter, the track is represented as a 2D discrete three-layer model where the mass, stiffness and damping of the components are concentrated at the sleepers locations. The numerical models are updated with experimental measurements performed on an existing railway bridge in a view to evaluate (i) the influence of the track continuity on the bridge modal parameters and on the train-induced vibrations; (ii) the adequacy of the implemented numerical models and (iii) the importance of the track-bridge interaction for an accurate prediction of the vertical acceleration levels under operating conditions.
J.M. Portolés, E. Moliner, V. AlberoUniversitat Jaume I, Department of Mechanical Engineering and Construction (SPAIN)
This contribution investigates the vertical coupling exerted by ballasted tracks on the vertical response of bridges composed either of (i) several successive simply-supported spans with weak coupling between them due to the continuous track; or (ii) adjacent single-track decks conforming a double-track bridge, in which interaction effects are induced due to the transverse continuity of the ballast layer. To this end, 2 D and 3 D track-bridge interaction Finite Element models are implemented, which consider a three-layer discrete and explicit idealization of the track. The 2 D track-bridge interaction model is used to perform sensitivity analyses on the track parameters, which have revealed that the ballast shear mechanisms along the track may significantly affect the train-induced vibrations under resonant conditions. Then, the influence of the ballast coupling on the response of twin adjacent decks is investigated with a 3 D track-bridge interaction model. To this end, this model is updated based on the results of an experimental campaign performed on a real bridge composed of two SS spans and two single track twin adjacent decks. The numerical-experimental comparison shows an evident dynamic vertical coupling between the bridge decks and reveals the importance of including the ballasted track in the modelling process of these structures.
This chapter presents a numerical formulation within the finite element method in order to computationally simulate thermoelectric devices. For this purpose, a theoretical formulation based on nonequilibrium thermodynamics with historical notes is previously outlined. Then, a brief description of the finite element is reported to express the thermodynamics governing equations in an amenable form to be numerically discretized. Finally, several applications of cooling thermoelectrics are performed to highlight the benefits of the finite element method. In particular, a commercial thermoelectric device is simulated and several variables such as extracted heat, voltage drop, and temperature distributions inside the thermoelements are represented for different operating conditions. In conclusion, the present numerical tool could be used as a virtual laboratory for the design and optimization of Peltier cells.
This paper investigates the influence of track-bridge interaction (TBI) in the comparison of dynamic effects of actual (or envisaged) high-speed trains vs. load models prescribed by national or international standards.The focus is set on concentrated load models of high-speed vehicles travelling over simple bridges, following a general methodology previously presented by the authors (Museros, P., A. Andersson, V. Martí, and R. Karoumi.Dynamic behaviour of bridges under critical articulated trains: Signature and bogie factor applied to the review of some regulations included in en 1991-2.J. Rail and Rapid Transit, 1-21, 2020).For such comparison, two variables named exceedance (in amplitude) and required speed increase were used to analyse whether a real train is or is not duly covered by a model prescribed in a standard.Two particular cases are analysed here of one regular and one conventional train, both compliant with Annex E in EN1991-2, which are compared vs model HSLM-A in two slab-type bridges of spans 10.8 m and 25.2 m.Two different mathematical models are considered for each bridge, characterised by very different levels of refinement.The frequencies of the bridges are selected intentionally low, close to the limit of the frequency band defined in EN1991-2, section 6.4.4; therefore, it is of interest to note how the resonant speeds are also low, particularly for the second example.The main conclusions of this work are two.First,
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.
This paper investigates the optimal design of 3D printed energy harvesters for railway bridges. The type of harvester studied is a cantilever bimorph beam with a mass at the tip and a load resistance. These parameters are adjusted to find the optimal design that tunes the harvester to the fundamental frequency of the bridge. An analytical model based on a variational formulation to represent the electromechanical behaviour of the device is presented. The optimisation problem is solved using a genetic algorithm with constraints of geometry and structural integrity. The proposed procedure is implemented in the design and manufacture of an energy harvesting device for a railway bridge on an in-service high-speed line. To do so, first the methodology is validated experimentally under laboratory conditions and shown to offer strong performance. Next the in-situ railway bridge is instrumented using accelerometers and the results used to evaluate energy harvesting performance. The results show the energy harvested in a time window of three and a half hours (20 train passages) is E=109.32mJ. The proposed methodology is particularly useful for bridges with fundamental mode shapes above 4.5Hz, however optimal design curves are also presented for the most common railway bridges found in practice. A novelty of this work is the use of additive manufacturing to 3D print energy harvesters, thus maximising design flexibility and energy performance.
The work presented herein is devoted to the analysis of the vertical acceleration response of high speed railway bridges composed by multiple simply-supported spans of short to medium length.In this regard, the investigation focuses on the adequacy of using highly detailed three-dimensional finite element models of the bridge for the prediction of the structural dynamic response under operational conditions.A particular bridge configuration is evaluated: pre-stressed concrete simply-supported girder bridges with high levels of obliquity.The presented bridge numerical model include: (i) a detailed discretisation of the track platform; (ii) transverse diaphragms at the span ends; and (iii) successive oblique simply-supported spans weakly coupled through the ballast track layer.To this end, digital twins of two real bridges of 15 and 25 meters span length are implemented and calibrated with experimental measurements.Different approaches for the railway vehicle are assumed to quantify the agreement between experimental and numerical predictions: (i) the simple moving load model; (ii) a multibody three-dimensional vehicle model accounting for the vehicle-bridgeinteraction effect and the track irregularities.Conclusions regarding the dynamic performance and the influence of vehicle-bridge-interaction effect are finally presented.
