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.
J.M. Portolés, E. Moliner, V. AlberoUniversitat Jaume I, Department of Mechanical Engineering and Construction (SPAIN)
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 paper discusses the dynamic behavior of twin-box girder bridges under high-speed railway traffic. On the basis of several representative examples derived from recently built high-speed bridges, this contribution examines the effects of transverse bending in the upper slab of these structures and evaluates the bending moments in resonance conditions. The analysis was carried out according to one of the reference norms for the assessment of dynamic effects in high-speed bridges (Eurocode). The results demonstrate that the predicted dynamic response for shorter-span bridges can be unexpectedly higher than the static effects caused by the design loads as a result of transverse resonances induced by the absence of transverse diaphragms between the box girders and the movement of the sliding supports. Moreover, these strong impact coefficients may occur even when the maximum level of vertical vibrations in the deck is not severe.
Increasing the operating speed of the trains on modern networks necessitates performing dynamic analyses to assess the performance of bridges under passage of trains. The detailed investigation of their responses requires constructing complex computational models capable to take the train–track–bridge interaction effects into account. Such models have successfully been developed; however, employing those elaborated models for practical engineering applications, or to perform studies that require a large number of analyses may become infeasible. Among such situations are conducting probabilistic investigations, screening of entire networks, or sensitivity analyses. These concerns have been addressed by employing simplified models mostly relying on moving load modeling strategy which disregards the train–track–bridge interaction effects. Those neglected contributions can be compensated by implementing additional correction factors. The distribution of loads within track is one of those disregarded effects where a reduction factor is recommended by design guidelines to take its contribution into account. It has been shown that the existing relationship for these reduction factors delivers an acceptable performance for vertical accelerations, while showing a less favorable performance for displacements. Then, a data-driven strategy is adopted in this study to propose easy-to-apply relationships for reduction factors of deflections, due to load distribution within the track. In this context, three different distributive lengths of triangular load footprints have been considered, namely 2.0, 2.5 and 3.0[Formula: see text]m. The procedure employed has trained and tested for more than 1[Formula: see text]200 train configurations, comprising conventional, articulated and regular vehicles, and including several tens of thousand data points for each distributive length. The performance observed in the new models revealed a considerable improvement with respect to the existing relationship.
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.
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.
Energy harvesters are a promising technology for powering infrastructure condition monitoring systems without batteries. When deployed on railway bridges they are typically tuned to the bridge's natural frequency, however due to the dominance of train-induced forced vibration of the structure, this results in sub-optimal energy harvesting. As a solution, this paper presents a novel tuning strategy for energy harvesters on railway bridges. The strategy is based on a statistical analysis of the mechanical energy generated in the bridge during train passage and involves four steps: (i) measurement of bridge response due to train traffic, (ii) calculation of mechanical energy during train passage, (iii) statistical characterisation of the energy distribution, and finally, (iv) calculation of the tuning frequency. A case study is presented to compare the potential of the proposed strategy against tuning based upon the bridge natural frequency. First, an in-service railway bridge is monitored to determine its natural frequency and response to train traffic. Combining the field data with the proposed tuning strategy, the design of energy harvesters for the bridge is optimised. The design of harvesters tuned to natural frequencies is also studied. The underlying harvester type is a cantilever bimorph beam with a mass at the tip and load resistance. Additive manufacturing is used for the substructure, which is formed from PAHT-CF15 (High Temperature Polyamide carbon fibre reinforcement). The harvesters are manufactured and deployed on the bridge subject to live railway traffic. Field results show the devices designed using the new tuning strategy harvest up to 300% more energy. The energy harvested in a time window of three hours (18 train passages) is 7.65mJ.
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,
