Interacción vehículo-estructura y efectos de resonancia en puentes isostáticos de ferrocarril para líneas de alta velocidad

En esta Tesis se han estudiado diversos aspectos del comportamiento dinámico de Puentes Isostáticos de Ferrocarril situados en Líneas de Alta Velocidad. En primer lugar se ha llevado a cabo un estudio del Estado del Conocimiento en el ámbito de la Dinámica de Puentes de Ferrocarril, con un énfasis particular en lo relativo a cargas verticales sobre puentes isostáticos. El estudio realizado incluye una breve síntesis de la evolución del Cálculo de Puentes desde sus orígenes y de los avances más significativos experimentados por la disciplina en las últimas décadas. Se ha llevado a cabo también un resumen de las hipótesis y formulación matemática de los modelos numéricos más comúnmente empleados para el cálculo dinámico de puentes isostáticos de vía única. Los modelos descritos incluyen el Modelo de Cargas Puntuales, Modelo de Cargas Repartidas y los Modelos de Interacción Completo y Simplificado. Además, de los trabajos de revisión expuestos en los párrafos anteriores, las tareas de investigación más destacables de entre las acometidas en esta Tesis son las siguientes. 1,- Estudio de algunos factores determinantes en la predicción de la respuesta de puentes isostáticos. Dichos factores incluyen el número de modos a considerar en el modelo y el reparto de cargas a través de la vía y elementos estructurales. 2,- Análisis del comportamiento de cuatro tipologías habituales en puentes isostáticos de ferrocarril. Las tipologías analizadas incluyen el puente mixto, dos variantes de puentes de vigas pretensadas y el puente de losa maciza pretensada. A partir de un dimensionamiento basado en un cálculo estático equivalente se ha estudiado el rango de luces en el que estas tipologías resultarían aptas para su uso en líneas de alta velocidad. 3,- Investigación de la posibilidad de aparición de fenómenos de resonancia en líneas con velocidad de explotación inferior o igual a 220 km/h. Valoración de la posibilidad de utilizar el método de cálculo basado en el coeficiente de impacto en dichas líneas. Importancia de la Interacción Vehículo-Estructura en dichas situaciones. 4,- Presentación de la formulación adimensional de las ecuaciones correspondientes al Modelo de Cargas Puntuales y Modelo de Interacción Simplificado. Obtención de Fórmulas de Semejanza Generalizadas en ambos casos. 5,- Estudio de la reducción de la respuesta prevista por los Modelos de Interacción respecto de los Modelos de Cargas Constantes en situación de resonancia. Dicho estudio consta de tres etapas: identificación de los parámetros fundamentales que influyen en la respuesta, determinación de rangos realistas de variación de dichos parámetros y, por último, análisis de la sensibilidad que la reducción de la respuesta presenta ante variaciones de los mismos. 6,- Análisis de las tendencias mostradas por la fueza de interacción rueda-carril en situación de resonancia. Identificación de los factores que podrían favorecer una disminución excesiva de la fuerza de interacción. 7.- Estudio de los efectos de interacción vehículo-estructura al paso de tres composiciones reales de alta velocidad sobre puentes isostáticos. Valoración de la influencia de la interacción en situaciones de resonancia a velocidad inferior a 220 km/h. Las conclusiones generales de la Tesis señalan la importancia de tener en cuenta los fenómenos de resonancia en el cálculo dinámico de puentes isostáticos, así como la conveniencia de emplear para ello Modelos de Interacción

Influence of the Second Flexural Mode on the Response of High-Speed Bridges

This paper deals with the assessment of the contribution of the second flexural mode to the dynamic behaviour of simply supported railway bridges. Alluding to the works of other authors, it is suggested in some references that the dynamic behaviour of simply supported bridges could be adequately represented taking into account only the contribution of the fundamental flexural mode. On the other hand, the European Rail Research Institute (ERRI) proposes that the second mode should also be included whenever the associated natural frequency is lower than 30 Hz]. This investigation endeavours to clarify the question as much as possible by establishing whether the maximum response of the bridge, in terms of displacements, accelerations and bending moments, can be computed accurately not taking account of the contribution of the second mode. To this end, a dimensionless formulation of the equations of motion of a simply supported beam traversed by a series of equally spaced moving loads is presented. This formulation brings to light the fundamental parameters governing the behaviour of the beam: damping ratio, dimensionless speed $\alpha$=VT/L, and L/d ratio (L stands for the span of the beam, V for the speed of the train, T represents the fundamental period of the bridge and d symbolises the distance between consecutive loads). Assuming a damping ratio equal to 1%, which is a usual value for prestressed high-speed bridges, a parametric analysis is conducted over realistic ranges of values of $\alpha$ and L/d. The results can be extended to any simply supported bridge subjected to a train of equally spaced loads in virtue of the so-called Similarity Formulae. The validity of these formulae can be derived from the dimensionless formulation mentioned above. In the parametric analysis the maximum response of the bridge is obtained for one thousand values of speed that cover the range from the fourth resonance of the first mode to the first resonance of the second mode. The response at twenty-one different locations along the span of the beam is compared in order to decide if the maximum can be accurately computed with the sole contribution of the fundamental mode

Influence of the Second Bending Mode on the Response of High-Speed Bridges at Resonance

This paper deals with the assessment of the contribution of the second bending mode to the dynamic behavior of simply supported railway bridges. Traditionally the contributions of modes higher than the fundamental have been considered of little importance for the computation of the magnitudes of interest to structural engineers (vertical deflections, bending moments, etc.). Starting from the dimensionless equations of motion of a simply supported beam subjected to moving loads, the key parameters governing the dynamic behavior are identified. Then, a parametric study over realistic ranges of values of those parameters is conducted, and the influence of the second mode examined in detail. The main purpose is to decide whether the second mode should be taken into account for the determination of the maximum displacement and acceleration in high-speed bridges. In addition, the reasons that cause the contribution of the second bending mode to be relevant in some situations are highlighted, particularly with regard to the computation of the maximum acceleration

Moving loads on railway bridges: The Spanish Code approach

This paper presents the results of part of the research carried out by a committee in charge of the elaboration of the new Spanish Code of Actions in Railway Bridges. Following the work developed by the European Rail Research Institute (ERRI), the dynamic effects caused by the Spanish high-speed train TALGO have been studied and compared with other European trains. A simplified envelope of the impact coefficient is also presented. Finally, the train-bridge interactions has been analysed and the results compared with those obtained from simple models based on moving loads

Free vibrations of simply-supported beam bridges under moving loads: Maximum resonance, cancellation and resonant vertical acceleration

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.Museros Romero, P.; Moliner, E.; Martinez-Rodrigo, M. (2013). Free vibrations of simply-supported beam bridges under moving loads: Maximum resonance, cancellation and resonant vertical acceleration. Journal of Sound and Vibration. 332(2):326-345. https://doi.org/10.1016/j.jsv.2012.08.008326345332

Dynamic performance of existing double track railway bridges at resonance with the increase of the operational line speed

[EN] 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.Moliner, E.; Martínez-Rodrigo, M.; Museros Romero, P. (2017). Dynamic performance of existing double track railway bridges at resonance with the increase of the operational line speed. Engineering Structures. 132:98-109. doi:10.1016/j.engstruct.2016.11.031S9810913

Dynamic behaviour of bridges under critical articulated trains: Signature and bogie factor applied to the review of some regulations included in EN 1991-2

[EN] The information contained in this paper will be of interest not only to bridge engineers, but also to train manufacturers. The article provides practical insight into the degree of coverage of realarticulated trains(ATs) that Eurocode EN1991-2 guarantees. In both the design of new railway bridges, as well as in the assessment of existing ones, the importance of a detailed knowledge of thelimits of validityofload modelscannot be overemphasised. Being essential components of the rail transportation system, the capacity of bridges to withstand future traffic demands will be determined precisely by the load models. Therefore, accurate definition of the limits of validity of such models reveals crucial when increased speeds and/or increased axle loads are required by transportation pressing priorities. The most relevant load model for a significant portion of the bridges in high-speed railway lines is the so-called HSLM-A model, defined in EN1991-2. Their limits of validity are described in Annex E of such code. For its singular importance, the effects of vibrations induced by HSLM-A are analysed in this paper with attention to the response ofsimply supported bridges. This analysis is carried out in a view to determine whether the limits of validity given in Annex E of EN1991-2 cover the largest part of cases of interest. Specifically, the vibration effects of HSLM-A are compared with those of the ATs described in such Annex E, and the response is analysed in depth for simply supported bridges, which are structures especially sensitive to passing trains at high speeds. New theoretical approaches have been developed in order to undertake this investigation, including a novel, simplified expression of thetrain signaturefor ATs that is convenient for its low computational cost. The mathematical proofs are included in the first part of the paper and two separate appendices.The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was partially developed during a stay performed by Pedro Museros at the KTH Royal Institute of Technology, within the Division of Structural Engineering and Bridges (Stockholm, Sweden). The financial support of the Generalitat Valenciana, through the program BEST2019 for research stays (Subvenciones para estancias de personal investigador doctor en centros de investigacion radicados fuera de la Comunitat Valenciana), as well as the permission obtained from the Universitat Politecnica de Valencia to carry out such stay, are gratefully acknowledged.Museros Romero, P.; Andersson, A.; Marti, V.; Karoumi, R. (2021). Dynamic behaviour of bridges under critical articulated trains: Signature and bogie factor applied to the review of some regulations included in EN 1991-2. Proceedings of the Institution of Mechanical Engineers. Part F, Journal of rail and rapid transit (Online). 235(5):655-675. https://doi.org/10.1177/0954409720956476S655675235

Finite element modeling of energy harvesters: application to vibrational devices

[ES] En este capítulo se presenta el conjunto de ecuaciones de gobierno para estudiar el comportamiento de los materiales activos, los cuales tienen una capacidad intrínseca para acoplar varias ramas de la Física y, en consecuencia, son comúnmente utilizados para la fabricación de cosechadoras. Una vez definidas las ecuaciones, se desarrolla una formulación numérica basada en el método de los elementos finitos para modelar estos materiales. En particular, en este capítulo se estudia la producción de energía a partir de las vibraciones mecánicas presentes en puentes ferroviarios de alta velocidad. Para ello, se hace un repaso de los parámetros básicos de estos puentes, sus vibraciones, frecuencias y las características dinámicas. A continuación, se simulan cosechadores en voladizo fabricados con materiales piezoeléctricos y piezomagnéticos bajo vibraciones mecánicas típicas y se destacan varias conclusiones.[EN] This chapter presents the set of governing equations to study the behavior of active materials, which have an intrinsic ability for coupling several branches of Physics and, consequently, are commonly used for manufacturing harvesters. Once the equations are defined, a numerical formulation based on the finite element method is developed in order to model these materials. In particular, this chapter studies the energy production from mechanical vibrations present in high-speed railway bridges. For this purpose, a review of the basic parameters of these bridges, their vibrations, frequencies and the dynamic characteristics are highlighted. Then, cantilever harvesters made out of piezoelectric and piezomagnetic materials are simulated under typical mechanical vibrations and several conclusions are highlighted.Palma, R.; Pérez-Aparicio, JL.; Museros Romero, P. (2018). Finite element modeling of energy harvesters: application to vibrational devices. En Energy Harvesting for Wireless Sensor Networks: Technology, Components and System Design. De Gruyter. 3-33. https://doi.org/10.1515/9783110445053-00133

Wheel-Rail Contact Forces in High-Speed Simply Supported Bridges at Resonance

The response of high-speed bridges at resonance, particularly under flexural vibrations, constitutes a subject of research for many scientists and engineers at the moment. The topic is of great interest because, as a matter of fact, such kind of behaviour is not unlikely to happen due to the elevated operating speeds of modern rains, which in many cases are equal to or even exceed 300 km/h ( [1,2]). The present paper addresses the subject of the evolution of the wheel-rail contact forces during resonance situations in simply supported bridges. Based on a dimensionless formulation of the equations of motion presented in [4], very similar to the one introduced by Klasztorny and Langer in [3], a parametric study is conducted and the contact forces in realistic situations analysed in detail. The effects of rail and wheel irregularities are not included in the model. The bridge is idealised as an Euler-Bernoulli beam, while the train is simulated by a system consisting of rigid bodies, springs and dampers. The situations such that a severe reduction of the contact force could take place are identified and compared with typical situations in actual bridges. To this end, the simply supported bridge is excited at resonace by means of a theoretical train consisting of 15 equidistant axles. The mechanical characteristics of all axles (unsprung mass, semi-sprung mass, and primary suspension system) are identical. This theoretical train permits the identification of the key parameters having an influence on the wheel-rail contact forces. In addition, a real case of a 17.5 m bridges traversed by the Eurostar train is analysed and checked against the theoretical results. The influence of three fundamental parameters is investigated in great detail: a) the ratio of the fundamental frequency of the bridge and natural frequency of the primary suspension of the vehicle; b) the ratio of the total mass of the bridge and the semi-sprung mass of the vehicle and c) the ratio between the length of the bridge and the characteristic distance between consecutive axles. The main conclusions derived from the investigation are: The wheel-rail contact forces undergo oscillations during the passage of the axles over the bridge. During resonance, these oscillations are more severe for the rear wheels than for the front ones. If denotes the span of a simply supported bridge, and the characteristic distance between consecutive groups of loads, the lower the value of , the greater the oscillations of the contact forces at resonance. For or greater, no likelihood of loss of wheel-rail contact has been detected. The ratio between the frequency of the primary suspension of the vehicle and the fundamental frequency of the bridge is denoted by (frequency ratio), and the ratio of the semi-sprung mass of the vehicle (mass of the bogie) and the total mass of the bridge is denoted by (mass ratio). For any given frequency ratio, the greater the mass ratio, the greater the oscillations of the contact forces at resonance. The oscillations of the contact forces at resonance, and therefore the likelihood of loss of wheel-rail contact, present a minimum for approximately between 0.5 and 1. For lower or higher values of the frequency ratio the oscillations of the contact forces increase. Neglecting the possible effects of torsional vibrations, the metal or composite bridges with a low linear mass have been found to be the ones where the contact forces may suffer the most severe oscillations. If single-track, simply supported, composite or metal bridges were used in high-speed lines, and damping ratios below 1% were expected, the minimum contact forces at resonance could drop to dangerous values. Nevertheless, this kind of structures is very unusual in modern high-speed railway lines

Free vibration of viscoelastically supported beam bridges under moving loads: Closed-form formula for maximum resonant response

[EN] In this paper, a closed-form approximate formula for estimating the maximum resonant response of beam bridges on viscoelastic supports (VS) under moving loads is proposed. The methodology is based on the discrete approximation of the fundamental vertical mode of a non-proportionally damped Bernoulli-Euler beam, which allows the derivation of closed-form expressions for the fundamental modal characteristics and maximum amplitude of free vibration at the mid-span of VS beams. Finally, an approximate formula to estimate maximum resonant acceleration of VS beams under passage of articulated trains has been proposed. Verification studies prove that the approximate closed-form formula estimates the resonant peaks with good accuracy and is a useful tool for preliminary assessment of railway beam bridges considering the effect of soil-structure interaction at resonance. In combination with the use of full train signatures through the Residual Influence Line (LIR) method, the proposed solution yields good results also in the lower range of speeds, where resonant sub-harmonics are more intensely reduced by damping.This research was partly sponsored by the Swedish Research Council FORMAS and has also received funding from the Shift2Rail Joint Undertaking under the European Union's Horizon 2020 research and innovation program under grant agreement No 826255 which are gratefully acknowledged.Zangeneh, A.; Museros Romero, P.; Pacoste, C.; Karoumi, R. (2021). Free vibration of viscoelastically supported beam bridges under moving loads: Closed-form formula for maximum resonant response. Engineering Structures. 244:1-11. https://doi.org/10.1016/j.engstruct.2021.112759S11124