The Dynamics of High-Speed Railway Bridges: A Review of Design Issues and New Research for Lateral Dynamics

The dynamic effects of high-speed trains on viaducts are important issues for the design of the structures, as well as for the consideration of safe running conditions for the trains. In this work we start by reviewing the relevance of some basic design aspects. The significance of impact factor envelopes for moving loads is considered first. Resonance which may be achieved for high-speed trains requires dynamic analysis, for which some key aspects are discussed. The relevance of performing a longitudinal distribution of axle loads, the number of modes taken in analysis, and the consideration of vehicle-structure interaction are discussed with representative examples. The lateral dynamic effects of running trains on bridges is of importance for laterally compliant viaducts, such as some very tall structures erected in new high-speed lines. The relevance of this study is mainly for the safety of the traffic, considering both internal actions such as the hunting motion as well as external actions such as wind or earthquakes [1]. These studies require three-dimensional dynamic coupled vehicle-bridge models, and consideration of wheel to rail contact, a phenomenon which is complex and costly to model in detail. We describe here a fully nonlinear coupled model, described in absolute coordinates and incorporated into a commercial finite element framework [2]. The wheel-rail contact has been considered using a FastSim algorithm which provides a compromise between accuracy and computational cost, and captures the main nonlinear response of the contact interface. Two applications are presented, firstly to a vehicle subject to a strong wind gust traversing a bridge, showing the relevance of the nonlinear wheel-rail contact model as well as the dynamic interaction between bridge and vehicle. The second application is to a real HS viaduct with a long continuous deck and tall piers and high lateral compliance [3]. The results show the safety of the traffic as well as the importance of considering features such as track alignment irregularities.

Experimental investigation on box-wing configuration for UAS

The range for airframe configurations available for UAS is as diverse as those used for manned aircraft and more since the commercial risk in trying unorthodox solutions is less for the UAS manufacturer. This is principally because the UAS airframes are usually much smaller than the manned aircraft and operators are less likely to have a bias against unconventional configurations. One of these unconventional configurations is the box-wing, which is an unconventional solution for the design of the new UAS generation. The existence of two wings separated in different planes that are, however, significantly close together, means that the aerodynamic analysis by theoretical or computational methods is a difficult task, due to the considerable interference existing. Considering the fact that the flight of most UAS takes place at low Reynolds numbers, it is necessary to study the aerodynamics of the box wing configuration by testing different models in a wind tunnel to be able to obtain reasonable results. In the present work, the study is enhanced by varying not only the sweepback angles of the two wings, but also their position along the models’ fuselage. Certain models have shown being more efficient than others, pointing out that certain relative positions of wing exists that can improve the aerodynamics efficiency of the box wing configuration.

Bridges E-2 and E-3 in the new railway to the Northwest of Spain

During the years 2001 to 2007 it has been constructed in Spain the new railway line of high speed (L. H. S.)that connects Madrid with Valladolid with a length of 179.6 kilometres.

Strengthening and rehabilitation of two damaged bridges in the motorway M-410 in Madrid (Spain)

The new highway M-410 in Madrid was constructed in the year 2007. This motorway near to Parla city crosses the road from Madrid to Toledo. To solve this crossing it was needed to constructed three bridges, the central with two spans over the existing motorway and the other two with one span at each side of the previous one.

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.

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.

Dynamics of high-speed railway bridges: review of design issues and new research for lateral dynamics

Revisión y puesta al día de la publicaciones relacionadas con el diseño de puentes de ferrocarril de alta velocidad y nuevas investigaciones sobre dinámica lateral.

Coupled models for the dynamics of bridges under high-speed rail traffic

The dynamic effects of high-speed trains on viaducts are important issues for the design of the structures, as well as for determining safe running conditions of trains. In this work we start by reviewing the relevance of some basic moving load models for the dynamic action of vertical traffic loads. The study of lateral dynamics of running trains on bridges is of importance mainly for the safety of the traffic, and may be relevant for laterally compliant bridges. These studies require 3D coupled vehicle-bridge models and consideration of wheel to rail contact. We describe here a fully nonlinear coupled model, formulated in absolute coordinates and incorporated into a commercial finite element framework. An application example is presented for a vehicle subject to a strong wind gust traversing a bridge, showing the relevance of the nonlinear wheel-rail contact model as well as the interaction between bridge and vehicle.

Vibrations of Short Span Railway Bridges for High Speed Lines

The physical model based on moving constant loads is widely used for the analysis of railway bridges. Nevertheless, this model is not well-suited for the study of short span bridges (L<=15-20 m), and the results it produces (displacements and accelerations) are much greater than those obtained experimentally. In this paper two factors are analysed which are believed to have an influence in the dynamic behaviour of short bridges. These two factors are not accounted for by the moving loads model and are the following: the distribution of the loads due to the presence of the sleepers and ballast layer, and the train-bridge interaction. Several numerical simulations have been performed in order to decide on their influence, and the results are presented and discussed herein.

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.

Simplified Procedure for the Nonlinear Seismic Analysis of Bridges

The severe accidents suffered by bridges during recent earthquake show that more careful analysis are needed to guarantee their behaviour. In particular simplified non-linear analysis could be useful to bridge the gap between theoretical research and practical applications. This paper presents one of those simplified methods that can be applied for first designs or to retrofitting of groups of bridges.

Efficient sampling from truncated bivariate Gaussians via Box-Muller transformation

Many practical simulation tasks demand procedures to draw samples efficiently from multivariate truncated Gaussian distributions. In this work, we introduce a novel rejection approach, based on the Box-Muller transformation, to generate samples from a truncated bivariate Gaussian density with an arbitrary support. Furthermore, for an important class of support regions the new method allows us to achieve exact sampling, thus becoming the most efficient approach possible. RESUMEN. Método específico para generar muestras de manera eficiente de Gaussianas bidimensionales truncadas con cualquier zona de truncamiento basado en la transformación de Box-Muller.

Rehabilitation of two bridges in construction in the motorway M-410 in Madrid (Spain)

Rehabilitation of two bridges in construction in the motorway M-410 in Madrid (Spain)

Virtual-bound, filamentary and layered states in a box-shaped quantum dot of square potential form the exact numerical solution of the effective mass Schrodinger equation

The effective mass Schrodinger equation of a QD of parallelepipedic shape with a square potential well is solved by diagonalizing the exact Hamiltonian matrix developed in a basis of separation-of-variables wavefunctions. The expected below bandgap bound states are found not to differ very much from the former approximate calculations. In addition, the presence of bound states within the conduction band is confirmed. Furthermore, filamentary states bounded in two dimensions and extended in one dimension and layered states with only one dimension bounded, all within the conduction band which are similar to those originated in quantum wires and quantum wells coexist with the ordinary continuum spectrum of plane waves. All these subtleties are absent in spherically shaped quantum dots, often used for modeling.

Modelization of an experimental solar test box equipped with a water-flow based window

A study on a water- ow window installed in a test box is presented. This window is composed of two glass panes separated by a chamber through water ows. The ow of water comes from an isolated tank which contains heat water. In order to fully evaluate the water- ow window performance for different room and window sizes, locations and weather conditions, a mathematical model of the whole box is needed. The proposed model, in which conduction heat transfer mechanism is the only considered, is one dimensional and unsteady based upon test box energy balance. The effect of the heat water tank, which feeds the water- ow window, is included in the model by means of a time delay in the source term. Although some previous work about moving uid chamber has been developed, air was used as heat transfer uid and no uid storage was considered. Finally a comparison between the numerical solution and the obtained experimental data is done.