The breaking of axisymmetric slender liquid bridges

Liquids held by surface tension forces can bridge the gap between two solid bodies placed not too far apart from each other. The equilibrium conditions and stability criteria for static, cylindrical liquid bridges are well known. However, the behaviour of an unstable liquid bridge, regarding both its transition toward breaking and the resulting configuration, is a matter for discussion. The dynamical problem of axisymmetric rupture of a long liquid bridge anchored at two equal coaxial disks is treated in this paper through the adoption of one-dimensional theories which are widely used in capillary jet problems

The influence of axial microgravity on the breakage of axisymmetric slender liquid bridges

The dynamics of inviscid, axisymmetric liquid bridges permits a simplified treatment if the bridge is long enough. Under such condition the evolution of the liquid zone is satisfactorily explained through a non-linear one-dimensional model. In the case of breaking, the one-dimensional model fails when the neck radius of the liquid column is close to zero; however, the model allows the calculation of the time variation of the liquid-bridge interface as well as of the fluid velocity field and, because the last part of the evolution is not needed, the overall results such as the breaking time and the volume of each of the two drops resulting after breakage can be calculated. In this paper numerical results concerning the behavior of clinical liquid bridges subjected to a small axial gravitational field are presented.

Stability of slender, axisymmetric liquid bridges between unequal disks

The stability of slender, axisymmetric liquid bridges held by surface tension forces between two coaxial, parallel solid disks having different radii is studied by using standard perturbation techniques. The results obtained show that the behaviour of such configurations becomes similar to that of liquid bridges between equal disks when subject to small axial gravity forces.

One-dimensional self-similar solution of the dynamics of axisymmetric slender liquid bridges

In this paper the dynamics of axisymmetric, slender, viscous liquid bridges having volume close to the cylindrical one, and subjected to a small gravitational field parallel to the axis of the liquid bridge, is considered within the context of one-dimensional theories. Although the dynamics of liquid bridges has been treated through a numerical analysis in the inviscid case, numerical methods become inappropriate to study configurations close to the static stability limit because the evolution time, and thence the computing time, increases excessively. To avoid this difficulty, the problem of the evolution of these liquid bridges has been attacked through a nonlinear analysis based on the singular perturbation method and, whenever possible, the results obtained are compared with the numerical ones.

The dynamics of axisymmetric slender liquid bridges between unequal disks

n this paper the influence of an axial microgravity on the dynamic stability of axisymmetric slender liquid bridges between unequal disks is numerically studied by using a one-dimensional theory. The breaking of such liquid configurations is analyzed and the dependence of some overall characteristics of the breaking process on the value of axial microgravity, the geometry and the volume of the liquid bridge, as well as stability limits are obtained.

Experiments with liquid bridges in simulated microgravity

A feature of stability diagrams of liquid bridges between unequal disks subjected to small axial gravity forces is that, for each separation of disks, there is a value of microgravity for which an absolute minimum volume limit is reached. The dependence of such microgravity values on the liquid bridge geometry has been experimentally checked by using the neutral buoyancy technique, experimental results being in complete agreement with theoretical ones. Analytical background assuring the experimental procedure used is presented, and a second order analytical expression for the equilirium interface is also calculated.

Numerical and experimental study of the dynamics of axisymmetric slender liquid bridges

A one-dimensional inviscid slice model has been used to study numerically the influence of axial microgravity on the breaking of liquid bridges having a volume close to that of gravitationless minimum volume stability limit. Equilibrium shapes and stability limits have been obtained as well as the dependence of the volume of the two drops formed after breaking on both the length and the volume of the liquid bridge. The breaking process has also been studied experimentally. Good agreement has been found between theory and experiment for neutrally buoyant systems

Analysis of the railway track as a spatially periodic structure

This article presents a new and computationally efficient method of analysis of a railway track modelled as a continuous beam of 2N spans supported by elastic vertical springs. The main feature of this method is its important reduction in computational effort with respect to standard matrix methods of structural analysis. In this article, the whole structure is considered to be a repetition of a single one. The analysis presented is applied to a simple railway track model, i.e. to a repetitive beam supported on vertical springs (sleepers). The proposed method of analysis is based on the general theory of spatially periodic structures. The main feature of this theory is the possibility to apply Discrete Fourier Transform (DFT) in order to reduce a large system of q(2N + 1) linear stiffness equilibrium equations to a set of 2N + 1 uncoupled systems of q equations each. In this way, a dramatic reduction of the computational effort of solving the large system of equations is achieved. This fact is particularly important in the analysis of railway track structures, in which N is a very large number (around several thousands), and q = 2, the vertical displacement and rotation, is very small. The proposed method allows us to easily obtain the exact solution given by Samartín [1], i.e. the continuous beam railway track response. The comparison between the proposed method and other methods of analysis of railway tracks, such as Lorente de Nó and Zimmermann-Timoshenko, clearly shows the accuracy of the obtained results for the proposed method, even for low values of N. In addition, identical results between the proposed and the Lorente methods have been found, although the proposed method seems to be of simpler application and computationally more efficient than the Lorente one. Small but significative differences occur between these two methods and the one developed by Zimmermann-Timoshenko. This article also presents a detailed sensitivity analysis of the vertical displacement of the sleepers. Although standard matrix methods of structural analysis can handle this railway model, one of the objectives of this article is to show the efficiency of DFT method with respect to standard matrix structural analysis. A comparative analysis between standard matrix structural analysis and the proposed method (DFT), in terms of computational time, input, output and also software programming, will be carried out. Finally, a URL link to a MatLab computer program list, based on the proposed method, is given

Axisymmetric long liquid bridges in a time-dependent microgravity field

This paper deals with the dynamics of liquid bridges when subjected to an oscillatory microgravity field. The analysis has been performed by using a one-dimensional slice model, already used in liquid bridge problems, which allows to calculate not only the resonance frequencies of a wide range of such fluid configurations but also the dependence of the dynamic response of the liquid bridge on the frequency on the imposed perturbations. Theoretical results are compared with experimental ones obtained aboard Spacelab-Dl, the agreement between theoretical and experimental results being satisfactory

Axisymmetric long liquid bridges stability and resonances

In this paper mathematical expressions for minimum-volume stability limits and resonance frequencies of axisymmetric long liquid bridges are presented. These expressions are valid for a wide range of liquid bridge configurations, accounting for ef-fects like unequal disks and axial microgravity in the case of minimum-volume stability limits,and unequal disks, axial microgravity,non-zero viscosity and liquid bridge volume different from the cylindrical one in the case of resonance frequencies.

The Future of the Technologies of Shell and spatial Structures. Bridges

The objective of this lecture is try to predict the future of this important type of spatial structures. In this way the activities of the different IASS Technical Working Groups can be stimulated and coordinated in order to play a more relevant role in this future. To grasp a possible evolution of bridges it is convenient a reflection on the bridge history and on their present situation, particularly in relation to the different existing achievements.

Dynamic behaviour of underspanned suspension road bridges under traffic loads

Underspanned suspension bridges are structures with important economical and aesthetic advantages, due to their high structural efficiency. However, road bridges of this typology are still uncommon because of limited knowledge about this structural system. In particular, there remains some uncertainty over the dynamic behaviour of these bridges, due to their extreme lightness. The vibrations produced by vehicles crossing the viaduct are one of the main concerns. In this work, traffic-induced dynamic effects on this kind of viaduct are addressed by means of vehicle-bridge dynamic interaction models. A finite element method is used for the structure, and multibody dynamic models for the vehicles, while interaction is represented by means of the penalty method. Road roughness is included in this model in such a way that the fact that profiles under left and right tyres are different, but not independent, is taken into account. In addition, free software {PRPgenerator) to generate these profiles is presented in this paper. The structural dynamic sensitivity of underspanned suspension bridges was found to be considerable, as well as the dynamic amplification factors and deck accelerations. It was also found that vehicle speed has a relevant influence on the results. In addition, the impact of bridge deformation on vehicle vibration was addressed, and the effect on the comfort of vehicle users was shown to be negligible.

Railway Rapid Transit timetables with variable and elastic demand.

This paper focuses on the design of railway timetables considering a variable elastic demand profile along a whole design day. Timetabling is the third stage in the classical hierarchical railway planning process. Most of previous works on this topic consider a uniform demand behavior for short planning intervals. In this paper, we propose a MINLP model for designing non-periodic timetables on a railway corridor where demand is dependent on waiting times. In the elastic demand case, long waiting times lead to a loss of passengers, who may select an alternative transportation mode. The mode choice is modeled using two alternative methods. The first one is based on a sigmoid function and can be used in case of absence of information for competitor modes. In the second one, the mode choice probability is obtained using a Logit model that explicitly considers the existence of a main alternative mode. With the purpose of obtaining optimal departure times, in both cases, a minimization of the loss of passengers is used as objective function. Finally, as illustration, the timetabling MINLP model with both mode choice methods is applied to a real case and computational results are shown.

Análisis de registros de aceleraciones verticales en caja de grasa y correlación con la infraestructura

El sector ferroviario ha experimentado en los últimos años un empuje espectacular acaparando las mayores inversiones en construcción de nuevas líneas de alta velocidad. Junto a esta inversión inicial no se debe perder de vista el coste de mantenimiento y gestión de las mismas y para ello es necesario avanzar en el conocimiento de los fenómenos de interacción de la vía y el material móvil. En los nuevos trazados ferroviarios, que hacen del ferrocarril un modo de transporte competitivo, se produce un notable aumento en la velocidad directamente relacionado con la disminución de los tiempos de viaje, provocando por ello elevados esfuerzos dinámicos, lo que exige una elevada calidad de vía para evitar el rápido deterioro de la infraestructura. Resulta primordial controlar y minimizar los costes de mantenimiento que vienen generados por las operaciones de conservación de los parámetros de calidad y seguridad de la vía férrea. Para reducir las cargas dinámicas que actúan sobre la vía deteriorando el estado de la misma, debido a este aumento progresivo de las velocidades, es necesario reducir la rigidez vertical de la vía, pero igualmente este aumento de velocidades hace necesarias elevadas resistecias del emparrillado de vía y mejoras en las plataformas, por lo que es necesario buscar este punto de equilibrio en la elasticidad de la vía y sus componentes. Se analizan las aceleraciones verticales medidas en caja de grasa, identificando la rigidez vertical de la vía a partir de las frecuencias de vibración vertical de las masas no suspendidas, correlacionándola con la infraestructura. Estas aceleraciones verticales se desprenden de dos campañas de medidas llevadas a cabo en la zona de estudio. En estas campañas se colocaron varios acelerómetros en caja de grasa obteniendo un registro de aceleraciones verticales a partir de las cuales se ha obteniendo la variación de la rigidez de vía de unas zonas a otras. Se analiza la rigidez de la vía correlacionándola con las distintas tipologías de vía y viendo la variación del valor de la rigidez a lo largo del trazado ferroviario. Estos cambios se manifiestan cuando se producen cambios en la infraestructura, de obras de tierra a obras de fábrica, ya sean viaductos o túneles. El objeto principal de este trabajo es profundizar en estos cambios de rigidez vertical que se producen, analizando su origen y las causas que los provocan, modelizando el comportamiento de los mismos, para desarrollar metodologías de análisis en cuanto al diseño de la infraestructura. Igualmente se analizan los elementos integrantes de la misma, ahondando en las características intrínsecas de la rigidez vertical global y la rigidez de cada uno de los elementos constituyentes de la sección tipo ferroviaria, en cada una de las secciones características del tramo en estudio. Se determina en este trabajo si se produce y en qué medida, variación longitudinal de la rigidez de vía en el tramo estudiado, en cada una de las secciones características de obra de tierra y obra de fábrica seleccionadas analizando las tendencias de estos cambios y su homogeneidad a lo largo del trazado. Se establece así una nueva metodología para la determinación de la rigidez vertical de la vía a partir de las mediciones de aceleraciones verticales en caja de grasa así como el desarrollo de una aplicación en el entorno de Labview para el análisis de los registros obtenidos. During the last years the railway sector has experienced a spectacular growth, focusing investments in the construction of new high-speed lines. Apart from the first investment the cost of maintaining and managing them has to be considered and this requires more knowledge of the process of interaction between track and rolling stock vehicles. In the new high-speed lines, that make of the railway a competitive mode of transport, there is a significant increase in speed directly related to the shorten in travel time, and that produces high dynamic forces. So, this requires a high quality of the track to avoid quickly deterioration of infrastructure. It is essential to control and minimize maintenance costs generated by maintenance operations to keep the quality and safety parameters of the railway track. Due to this gradual increase of speed, and to reduce the dynamic loads acting on the railway track causing its deterioration, it is necessary to reduce the vertical stiffness of the track, but on the other hand this speed increase requires high resistance of the railway track and improvements of the railway platform, so we must find the balance between the elasticity of the track and its components. Vertical accelerations in axle box are measured and analyzed, identifying the vertical stiffness of the railway track obtained from the vertical vibration frequency of the unsprung masses, correlating with the infrastructure. These vertical accelerations are the result of two measurement campaigns carried out in the study area with the placement of several accelerometers located in the axle box. From these vertical accelerations the variation of the vertical stiffness from one area to another is obtained. The track stiffness is analysed relating with the different types of infrastructure and the change in the value of the stiffness along the railway line. These changes are revealed when changes in infrastructure occurs, for instance; earthworks to bridges or tunnels. The main purpose of this paper is to examine these vertical stiffness changes, analysing its origins and causes, modelling their behaviour, developing analytical methodologies for the design of infrastructure. In this thesis it is also reviewed the different elements of the superstructure, paying special attention to the vertical stiffness of each one. In this study is determined, if it happens and to what extent, the longitudinal variation in the stiffness of track along the railway line studied in every selected section; earthwork, bridges and tunnels. They are also analyzed trends of these changes and homogeneity along the path. This establishes a new method for determining the vertical stiffness of the railway track from the vertical accelerations measured on axle box as well as an application developed in LabView to analyze the recordings obtained.

Minimum volume stability limits for axisymmetric liquid bridges subject to steady axial acceleration

In this paper the influence of an axial microgravity on the minimum volume stability limit of axisymmetric liquid bridges between unequal disks is analyzed both theoretically and experimentally. The results here presented extend the knowledge of the static behaviour of liquid bridges to fluid configurations different from those studied up to now (almost equal disks). Experimental results, obtained by simulating microgravity conditions by the neutral buoyancy technique, are also presented and are shown to be in complete agreement with theoretical ones.