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

Ground maritime structure interaction. Recent failures in inner gravity constructions on the Spanish Coastline

A maritime construction is usually a slender line in the ocean.It is usual to see just its narrow surface strip and not analyse the large amount of submerged material the latter is supporting.Without doubt,it is the ground to which a notable load is transmitted in an environment subjected to periodic,alternating stresses,dynamic forces which the sea's media constitute. Both an outer and inner maritime construction works in a complex fashion.A granular solid(breakwater)breathes with the incident wave flow,dissipating part of the wave energy between its gaps.The backflow tries to extract the different items from the solid block,setting a balance between effective and neutral tensions that follow Terzaghui's principle. On some occasions,fluidification of the armour layer has caused the breakwater to collapse(Sines,Portugal,February 1978).On others,siphoning or liquefaction of sand supporting monoliths(vertical breakwaters)lead them to destruction or collapse(New Barcelona Harbour Mouth,Spain,November 2001). This is why the ground-force-structure interaction is a complicated analysis with joint design tools still in an incipient state. The purpose of this article is to describe two singular failures in inner maritime constructions in Spain deriving from ground problems(Malaga,July 2004and Barcelona,January 2007).They occurred recently and the causes are the subject of reflection and analysis.

Electromagnetic analysis of periodic structures under a waveguide viewpoint

The fundamental objective of this Ph. D. dissertation is to demonstrate that, under particular circumstances which cover most of the structures with practical interest, periodic structures can be understood and analyzed by means of closed waveguide theories and techniques. To that aim, in the first place a transversely periodic cylindrical structure is considered and the wave equation, under a combination of perfectly conducting and periodic boundary conditions, is studied. This theoretical study runs parallel to the classic analysis of perfectly conducting closed waveguides. Under the light shed by the aforementioned study it is clear that, under certain very common periodicity conditions, transversely periodic cylindrical structures share a lot of properties with closed waveguides. Particularly, they can be characterized by a complete set of TEM, TE and TM modes. As a result, this Ph. D. dissertation introduces the transversely periodic waveguide concept. Once the analogies between the modes of a transversely periodic waveguide and the ones of a closed waveguide have been established, a generalization of a well-known closed waveguide characterization method, the generalized Transverse Resonance Technique, is developed for the obtention of transversely periodic modes. At this point, all the necessary elements for the consideration of discontinuities between two different transversely periodic waveguides are at our disposal. The analysis of this type of discontinuities will be carried out by means of another well known closed waveguide method, the Mode Matching technique. This Ph. D. dissertation contains a sufficient number of examples, including the analysis of a wire-medium slab, a cross-shaped patches periodic surface and a parallel plate waveguide with a textured surface, that demonstrate that the Transverse Resonance Technique - Mode Matching hybrid is highly precise, efficient and versatile. Thus, the initial statement: ”periodic structures can be understood and analyzed by means of closed waveguide theories and techniques”, will be corroborated. Finally, this Ph. D. dissertation contains an adaptation of the aforementioned generalized Transverse Resonance Technique by means of which the analysis of laterally open periodic waveguides, such as the well known Substrate Integrated Waveguides, can be carried out without any approximation. The analysis of this type of structures has suscitated a lot of interest in the recent past and the previous analysis techniques proposed always resorted to some kind of fictitious wall to close the structure. vii Resumen El principal objetivo de esta tesis doctoral es demostrar que, bajo ciertas circunstancias que se cumplen para la gran mayoría de estructuras con interés práctico, las estructuras periódicas se pueden analizar y entender con conceptos y técnicas propias de las guías de onda cerradas. Para ello, en un primer lugar se considera una estructura cilíndrical transversalmente periódica y se estudia la ecuación de onda bajo una combinación de condiciones de contorno periódicas y de conductor perfecto. Este estudio teórico y de caracter general, sigue el análisis clásico de las guías de onda cerradas por conductor eléctrico perfecto. A la luz de los resultados queda claro que, bajo ciertas condiciones de periodicidad (muy comunes en la práctica) las estructuras cilíndricas transversalmente periódicas guardan multitud de analogías con las guías de onda cerradas. En particular, pueden ser descritas mediante un conjunto completo de modos TEM, TE y TM. Por ello, ésta tesis introduce el concepto de guía de onda transversalmente periódica. Una vez establecidas las similitudes entre las soluciones de la ecuación de onda, bajo una combinación de condiciones de contorno periódicas y de conductor perfecto, y los modos de guías de onda cerradas, se lleva a cabo, con éxito, la adaptación de un conocido método de caracterización de guías de onda cerradas, la técnica de la Resonancia Transversal Generalizada, para la obtención de los modos de guías transversalmente periódicas. En este punto, se tienen todos los elementos necesarios para considerar discontinuidades entre guías de onda transversalmente periódicas. El analisis de este tipo de discontinuidades se llevará a cabo mediante otro conocido método de análisis de estructuras cerradas, el Ajuste Modal. Esta tesis muestra multitud de ejemplos, como por ejemplo el análisis de un wire-medium slab, una superficie de parches con forma de cruz o una guía de placas paralelas donde una de dichas placas tiene cierta textura, en los que se demuestra que el método híbrido formado por la Resonancia Transversal Generalizada y el Ajuste Modal, es tremendamente preciso, eficiente y versátil y confirmará la validez de el enunciado inicial: ”las estructuras periódicas se pueden analizar y entender con conceptos y técnicas propias de las guías de onda cerradas” Para terminar, esta tésis doctoral incluye también una modificación de la técnica de la Resonancia Transversal Generalizada mediante la cual es posible abordar el análisis de estructuras periódica abiertas en los laterales, como por ejemplo las famosas guías de onda integradas en sustrato, sin ninguna aproximación. El análisis de este tipo de estructuras ha despertado mucho interés en los últimos años y las técnicas de análisis propuestas hasta ix el momento acostumbran a recurrir a algún tipo de pared ficticia para simular el carácter abierto de la estructura.

Dynamic stabilization of L2 periodic orbits using attitude-orbit coupling effects

Numerical explorations show how the known periodic solutions of the Hill problem are modified in the case of the attitude-orbit coupling that may occur for large satellite structures. We focus on the case in which the elongation is the dominant satellite’s characteristic and find that a rotating structure may remain with its largest dimension in a plane parallel to the plane of the primaries. In this case, the effect produced by the non-negligible physical length is dynamically equivalent to the perturbation produced by an oblate central body on a mass-point satellite. Based on this, it is demonstrated that the attitude-orbital coupling of a long enough body may change the dynamical characteristics of a periodic orbit about the collinear Lagrangian points.

Dynamic stabilization of L2 periodic orbits using attitude-orbit coupling effects

Numerical explorations show how the known periodic solutions of the Hill problem are modified in the case of the attitude-orbit coupling that may occur for large satellite structures. We focus on the case in which the elongation is the dominant satellite?s characteristic and find that a rotating structure may remain with its largest dimension in a plane parallel to the plane of the primaries. In this case, the effect produced by the non-negligible physical dimension is dynamically equivalent to the perturbation produced by an oblate central body on a masspoint satellite. Based on this, it is demonstrated that the attitude-orbital coupling of a long enough body may change the dynamical characteristics of a periodic orbit about the collinear Lagrangian points.

Unearthing the roots of degradation of Quercus pyrenaica coppices: an integrative perspective from clonal structure to carbon budgets

Quercus pyrenaica es una especie rebrotadora de raíz intensa e históricamente aprovechada en monte bajo para la obtención de leñas, carbón y pastos. Debido al éxodo rural y a la aparición de nuevas fuentes energéticas, este aprovechamiento fue abandonado en la década de 1970. Desde entonces, las bajas producciones de madera y bellota y el puntisecado de los pies evidencian el generalizado estancamiento de estas masas. Uno de los mayores retos actuales de la selvicultura en el ámbito mediterráneo es encontrar usos alternativos para estos montes abandonados, siendo la conversión a monte alto una de las alternativas preferidas. Se han realizado resalveos de conversión, sin embrago, éstos se aplican sin un conocimiento integral de las causas de la degradación. En esta tesis doctoral, estudiamos un hipotético desequilibrio entre la parte radical y la parte aérea (R:S) de las cepas de rebollo como causa subyacente de su decaimiento. En una parcela experimental, aprovechada al menos desde el siglo XII, se realizaron análisis genéticos a priori para elucidar la estructura genética del rodal, y así estudiar la influencia del tamaño clonal en el funcionamiento de las cepas. Las cepas de mayor tamaño presentaron un menor crecimiento diametral de sus pies, así como mayores tasas de respiración radical, estimadas a partir de flujos internos de CO2 a través del xilema (FT) y de los flujos de CO2 del suelo. Estos resultados sugieren que el desequilibrio R:S aumenta con el tamaño clonal, dado que la eliminación periódica de órganos aéreos, al mismo tiempo que las raíces permanecen intactas, da lugar a un gran desarrollo del sistema radical que consume gran parte de los carbohidratos no estructurales (NSC) en respiración de mantenimiento, comprometiendo así el desarrollo de órganos aéreos. Se excavaron y pesaron dos cepas compuestas por cuatro y ocho pies, las cuales mostraron ratios R:S (0.5 y 1, respectivamente) superiores a los registrados en pies de origen sexual. Al igual que en otras especies rebrotadoras de raíz, se observaron altas concentraciones de NSC en las raíces (> 20% en primavera) y una gran proporción de albura en el sistema radical (52%) que alberga una notable reserva de NSC (87 kg en la cepa de mayor tamaño). En el sistema radical de dicha cepa, estimada mediante dataciones radiocarbónicas en 550 años de edad, se contaron 248 uniones radicales. La persistencia de sistemas radicales grandes, viejos, y altamente interconectados sugiere que la gran cantidad de recursos almacenados y consumidos en las raíces compensan un pobre desarrollo aéreo con una alta resiliencia vegetativa. Para un mejor entendimiento de los balances de carbono y del agotamiento de NSC en las cepas de rebollo, se midieron los flujos internos y externos de CO2 en troncos y los flujos de CO2 del suelo, y se estimó la respiración de órganos aéreos (RS) y subterráneos (RR). Estacionalmente, RS y RR reflejaron las dinámicas de flujo de savia y de crecimiento del tronco, y estuvieron determinadas principalmente por los flujos externos de CO2, dada la escasa contribución de FT a RS y RR (< 10% y < 2%, respectivamente). En una escala circadiana, la contribución de FT a RS aumentó hasta un 25% en momentos de alta transpiración. Las bajas concentraciones de CO2 en el xilema ([CO2] hasta un 0.11%) determinaron comparativamente unos bajos FT, probablemente causados por una limitada respiración del xilema y una baja resistencia a la difusión radial del CO2 impuestos por la sequía estival. Los pulsos de [CO2] observados tras las primeras lluvias de otoño apoyan esta idea. A lo largo del periodo vegetativo, el flujo medio de CO2 procedente del suelo (39 mol CO2 day-1) fue el mayor flujo respiratorio, tres y cuatro veces superior a RS (12 mol CO2 day-1) y RR (8-9 mol CO2 day-1), respectivamente. Ratios RR/RS menores que la unidad evidencian un importante peso de la respiración aérea como sumidero de carbono adicional. Finalmente, se ensayó el zanjado de raíces y el anillamiento de troncos como tratamientos selvícolas alternativos con el objetivo de aumentar las reservas de NSC en los troncos de las cepas. Los resultados preliminares desaconsejan el zanjado de raíces por el alto coste derivado posiblemente de la cicatrización de las heridas. El anillado de troncos imposibilitó el transporte de NSC a las raíces y aumentó la concentración de almidón por encima de la zona anillada, mientras que sistema radical se mantiene por los pies no anillados de la cepa. Son necesarias más mediciones y datos adicionales para comprobar el mantenimiento de esta respuesta positiva a largo plazo. Para concluir, destacamos la necesidad de estudios multidisciplinares que permitan una comprensión integral de la degradación de los rebollares ibéricos para poder aplicar a posteriori una gestión adecuada en estos montes bajos abandonados. ABSTRACT Quercus pyrenaica is a vigorous root-resprouting species intensively and historically coppiced for firewood, charcoal and woody pastures. Due to the rural exodus and the appearance of new energy sources, coppicing was abandoned towards 1970. Since then, tree overaging has resulted in stand stagnation displayed by slow stem growth, branch dieback, and scarce acorn production. The urgent need to find new alternative uses for abandoned coppices is recognized as one of the biggest challenges which currently faces Mediterranean silviculture; conversion into high forest by thinning is one of the preferred alternatives. For this aim, thinning has been broadly applied and seldom tested, although without a comprehensive understanding of the causes of stand stagnation. In this PhD study, we test the hypothesis of an imbalance between above- and below-ground organs, result of long term coppicing, as the underlying cause of Q. pyrenaica decay. In an experimental plot coppiced since at least the 12th century, genetic analyses were performed a priori to elucidate inconspicuous clonal structure of Q. pyrenaica to evaluate how clonal size affects the functioning of these multi-stemmed trees. Clonal size negatively affected diametric stem growth, whereas root respiration rates, measured by internal fluxes of CO2 through xylem (FT) and soil CO2 efflux, increased with clonal size. These results suggest root-to-shoot (R:S) imbalance intensifying with clonal size: periodic removal of aboveground organs whilst belowground organs remain undisturbed may have led to massive root systems which consume a great proportion of non-structural carbohydrates (NSC) for maintenance respiration, thus constraining aboveground performance. Furthermore, excavation of two multi-stemmed trees, composed by four and eight stems, revealed R:S ratios (0.5 and 1, respectively) greater than those reported for sexually regenerated trees. Moreover, as similarly observed in several root-resprouting species, NSC allocation to roots was favored ([NSC] > 20% in spring): a large proportion of sapwood maintained throughout the root system (52%) stored a remarkable NSC pool of 87 kg in the case of the largest clone. In this root system of the eight-stemmed tree, 248 root connections were counted and, by radiocarbon dating, its age was estimated to be 550-years-old. Persistence of massive, old and highly interconnected root systems suggests that enhanced belowground NSC storage and consumption reflects a trade-off between vegetative resilience and aboveground development. For a better understanding of tree carbon budget and the potential role of carbon starvation in Q. pyrenaica decay, internal and external stem CO2 fluxes and soil CO2 effluxes were monitored to evaluate respiratory costs above- and below-ground. On a seasonal scale, stem and root respiration (RS and RR) mirrored sap flow and stem growth dynamics. Respiration was determined to the greatest extent by external fluxes of CO2 to the atmosphere or soil, since FT accounted for a low proportion of RS and RR (< 10% and < 2%, respectively). On a diel scale, the contribution of FT to RS increased up to 25% at high transpiration rates. Comparatively low FT was determined by the low concentration of xylem CO2 registered ([CO2] as low as 0.11%), likely as a consequence of constrained xylem respiration and reduced resistance to CO2 radial diffusion imposed by summer drought. Xylem [CO2] pulses following first autumn rains support this idea. Averaged over the growing season, soil CO2 efflux was the greatest respiratory flux (39 mol CO2 day-1), three and four times greater than RS (12 mol CO2 day-1) and RR (8-9 mol CO2 day-1), respectively. Ratios of RR/RS below one evidence an additional and important weight of aboveground respiration as a tree carbon sink. Finally, root trenching and stem girdling were tested as complimentary treatments to thinning as a means to improve carbon reserves in stems of clonal trees. Preliminary results discouraged root trenching due to the high cost likely incurred for wound closure. Stem girdling successfully blocked NSC translocation downward, increasing starch concentrations above the girdled zone whilst the root system is fed by non-girdled stems within the clone. Further measurements and ancillary data are necessary to verify that this positive effect hold over time. To conclude, the need of multidisciplinary approaches for an integrative understanding on the functioning of abandoned Q pyrenaica coppices is highlighted for an appropriate management of these stands.