Fundamentación del uso de software libre en la universidad pública. Enseñando matemática con herramientas alternativas

En el presente trabajo se caracterizará al Software Libre, sus ventajas técnicas, morales y pedagógicas por sobre sus contrapartes privativas. Es mi convicción que la Universidad pública debe enseñar métodos de trabajo y no a utilizar una herramienta en particular; principalmente porque los programas de mayor difusión en el ámbito académico no permiten su distribución ni el estudio de su funcionamiento interno. Se presentarán los principales reemplazos a MATLAB y Maple (SAGE, Python+NumPy y Maxima) y se dará una introducción a estos con ejemplos reales.

Fundamentación del uso de software libre en la universidad pública. Enseñando matemática con herramientas alternativas

En el presente trabajo se caracterizará al Software Libre, sus ventajas técnicas, morales y pedagógicas por sobre sus contrapartes privativas. Es mi convicción que la Universidad pública debe enseñar métodos de trabajo y no a utilizar una herramienta en particular; principalmente porque los programas de mayor difusión en el ámbito académico no permiten su distribución ni el estudio de su funcionamiento interno. Se presentarán los principales reemplazos a MATLAB y Maple (SAGE, Python+NumPy y Maxima) y se dará una introducción a estos con ejemplos reales.

Geochemistry on rocks from Shackleton Range

During the GEISHA expedition (Geologische Expedition in die Shackleton Range 1987/88), the Pioneers Escarpment was visited and sampled extensively for the first time. Most of the rock types encountered represent amphibolite facies metamorphics, but evidence for granulite facies conditions was found in cores of garnet. These conditions must have been at least partly reached during the peak of metamorphism. For the Pioneers Escarpment a varicolored succession of sedimentary and bimodal volcanic origin is typical. It comprises: quartzites muscovite quartzite, sericite quartzite, fuchsite quartzite, garnet-quartz schists etc.; pelites: mica schists and plagioclase or plagioclase-microcline gneisses, aluminous schists; marls and carbonates: grey meta-limestones, carbonaceous quartzites, but also pure white, often fine-grained, saccharoidal marble, or a variety of tremolite marble, olivine (forsterite) marble, diopside-clinopyroxene-tremolite marble, etc.; basic volcanic rocks: amphibole fels, amphibolite schist, garnet amphibolite, and acidic to intermediate volcanic rocks: garnet-biotite schist, epidote-biotite-plagioclase gneiss, microcline gneiss. These rocks are considered to be a supracrustal unit, called the Pioneers Group. In the easternmost parts of the Pioneers Escarpment, e.g. at Vindberget, nonmetamorphic shales, sandstones and greywackes crop out, which are cover rocks of possibly Jurassic age. These metasediments, which represent a quartz-pelite-carbonate (QPC) association, indicate that deposition took place on a stable shelf, i.e. on the submerged rim of a craton. Marine shallow-water sedimentation including marls and aluminous clays form the protoliths. The volcanics may be part of a bimodal volcanics-arkose-conglomerate (BVAC) association. Geochemical analyses support the assumption of volcanic protoliths. This is demonstrated especially by the elevated amounts of the immobile, incompatible high-field-strength elements (HFSE) Nb, Ta, Ti, Y, and Zr encountered in some of the gneisses. Microscopic investigation suggests the existence of ortho-amphibolites. This is confirmed by the geochemistry. A bimodal volcanic association is evident. The amphibolites plot in both the tholeiite and calc-alkaline fields. The acidic volcanics are mainly rhyolitic. The sediments and volcanics were subjected to conditions of 10-11 kbar and 600°C during the peak of metamorphism, i.e. granulite facies metamorphism, which can be deduced from the Fe mole ratios of 0.71-0.73 in the garnet cores. Due to the relatively low temperatures, no anatectic melting took placc. The rims of the garnets show a Fe mole ratio of 0.84-0.86, and the coexisting mineral association garnet-biotite-staurolite-kyanite indicate amphibolite facies. The thermobarometry shows P-T conditions of 5-6 kbar and 570-580°C for this stage. The metamorphic history indicates deep burial at depths down to 35 km (subduction?) i.e. high pressure metamorphism, followed by pressure release due to uplift associated with retrograde metamorphism. This may have happened during a pre-Ross metamorphic event or orogeny. The Ross Orogeny at about 500 Ma probably just led to the weak greenschist facies overprint that is evident in the rocks of the Pioneers Group. Finally, sedimentation resumed in the area of the present Shackleton Range, or at least in the eastern part of the Pioneers Escarpment, probably when detritus from erosion of the basement (Read Group and Pioneers Group) was deposited, forming sandstones and greywackes of possibly Jurassic age. There is no indication that these sediments belong to the former Turnpike Bluff Group.

Benthic foraminiferal biofacies and stable isotopic record of St. Stephens Quarry, Alabama

We integrate upper Eocene-lower Oligocene lithostratigraphic, magnetostratigraphic, biostratigraphic, stable isotopic, benthic foraminiferal faunal, downhole log, and sequence stratigraphic studies from the Alabama St. Stephens Quarry (SSQ) core hole, linking global ice volume, sea level, and temperature changes through the greenhouse to icehouse transition of the Cenozoic. We show that the SSQ succession is dissected by hiatuses associated with sequence boundaries. Three previously reported sequence boundaries are well dated here: North Twistwood Creek-Cocoa (35.4-35.9 Ma), Mint Spring-Red Bluff (33.0 Ma), and Bucatunna-Chickasawhay (the mid-Oligocene fall, ca. 30.2 Ma). In addition, we document three previously undetected or controversial sequences: mid-Pachuta (33.9-35.0 Ma), Shubuta-Bumpnose (lowermost Oligocene, ca. 33.6 Ma), and Byram-Glendon (30.5-31.7 Ma). An ~0.9 per mil d18O increase in the SSQ core hole is correlated to the global earliest Oligocene (Oi1) event using magnetobiostratigraphy; this increase is associated with the Shubuta-Bumpnose contact, an erosional surface, and a biofacies shift in the core hole, providing a first-order correlation between ice growth and a sequence boundary that indicates a sea-level fall. The d18O increase is associated with a eustatic fall of ~55 m, indicating that ~0.4 per mil of the increase at Oi1 time was due to temperature. Maximum d18O values of Oi1 occur above the sequence boundary, requiring that deposition resumed during the lowest eustatic lowstand. A precursor d18O increase of 0.5 per mil (33.8 Ma, midchron C13r) at SSQ correlates with a 0.5 per mil increase in the deep Pacific Ocean; the lack of evidence for a sea-level change with the precursor suggests that this was primarily a cooling event, not an ice-volume event. Eocene-Oligocene shelf water temperatures of ~17-19 °C at SSQ are similar to modern values for 100 m water depth in this region. Our study establishes the relationships among ice volume, d18O, and sequences: a latest Eocene cooling event was followed by an earliest Oligocene ice volume and cooling event that lowered sea level and formed a sequence boundary during the early stages of eustatic fall.

Vegetation, soil and site characteristics of samples taken along the Yamal Transet in 2007-2008

The overarching goal of the Yamal portion of the Greening of the Arctic project is to examine how the terrain and anthropogenic factors of reindeer herding and resource development combined with the climate variations on the Yamal Peninsula affect the spatial and temporal patterns of vegetation change and how these changes are in turn affecting traditional herding of the indigenous people of the region. The purpose of the expeditions was to collect groundobservations in support of remote sensing studies at four locations along a transect that traverses all the major bioclimate subzones of the Yamal Peninsula. This data report is a summary of information collected during the 2007 and 2008 expeditions. It includes all the information from the 2008 data report (Walker et al. 2008) plus new information collected at Kharasavey in Aug 2008. The locations included in this report are Nadym (northern taiga subzone), Laborovaya (southern tundra = subzone E of the Circumpolar Arctic Vegetation Map (CAVM), Vaskiny Dachi (southern typical tundra = subzone D), and Kharasavey (northern typical tundra = subzone C). Another expedition is planned for summer 2009 to the northernmost site at Belyy Ostrov (Arctic tundra = subzone B). Data are reported from 10 study sites - 2 at Nadym, 2 at Laborovaya, and 3 at Vaskiny Dachi and 3 at Kharasavey. The sites are representative of the zonal soils and vegetation, but also include variation related to substrate (clayey vs. sandy soils). Most of the information was collected along 5 transects at each sample site, 5 permanent vegetation study plots, and 1-2 soil pits at each site. The expedition also established soil and permafrost monitoring sites at each location. This data report includes: (1) background for the project, (2) general descriptions and photographs of each locality and sample site, (3) maps of the sites, study plots, and transects at each location, (4) summary of sampling methods used, (5) tabular summaries of the vegetation data (species lists, estimates of cover abundance for each species within vegetation plots, measured percent ground cover of species along transects, site factors for each study plot), (6) summaries of the Normalized Difference Vegetation Index (NDVI) and leaf area index (LAI) along each transect, (7) soil descriptions and photos of the soil pits at each study site, (8) summaries of thaw measurements along each transect, and (9) contact information for each of the participants. One of the primary objectives was to provide the Russian partners with full documentation of the methods so that Russian observers in future years could repeat the observations independently.

Matriz de equilibrio de estructuras trianguladas de barras articuladas con cargas en los nodos

El texto describe la forma de ensamblar la matriz de equilibrio de estructuras de barras articuladas en los nodos, en 3D. Se explica previamente los conceptos teóricos y luego se implementa dentro del software comercial Maple.

The Learning of the Mathematical Models to Aid Decision Making in the High Level Engineering Schools?

At present, in the University curricula in most countries, the decision theory and the mathematical models to aid decision making is not included, as in the graduate program like in Doctored and Master´s programs. In the Technical School of High Level Agronomic Engineers of the Technical University of Madrid (ETSIA-UPM), the need to offer to the future engineers training in a subject that could help them to take decisions in their profession was felt. Along the life, they will have to take a lot of decisions. Ones, will be important and others no. In the personal level, they will have to take several very important decisions, like the election of a career, professional work, or a couple, but in the professional field, the decision making is the main role of the Managers, Politicians and Leaders. They should be decision makers and will be paid for it. Therefore, nobody can understand that such a professional that is called to practice management responsibilities in the companies, does not take training in such an important matter. For it, in the year 2000, it was requested to the University Board to introduce in the curricula an optional qualified subject of the second cycle with 4,5 credits titled " Mathematical Methods for Making Decisions ". A program was elaborated, the didactic material prepared and programs as Maple, Lingo, Math Cad, etc. installed in several IT classrooms, where the course will be taught. In the course 2000-2001 this subject was offered with a great acceptance that exceeded the forecasts of capacity and had to be prepared more classrooms. This course in graduate program took place in the Department of Applied Mathematics to the Agronomic Engineering, as an extension of the credits dedicated to Mathematics in the career of Engineering.

Implementación de algoritmos para la manipulación de curvas concoides en diseño geométrico

Este proyecto se enmarca dentro de la Computación Simbólica y de los fundamentos matemáticos del Diseño Geométrico Asistido por ordenador (CAGD). Se abordara uno de los problemas principales en el ámbito del CAGD y que es la manipulación de las Curvas Concoide. La importancia del avance en la manipulación de las curvas concoide radica en el papel fundamental que desempeñan en múltiples aplicaciones en la actualidad dentro de campos de diversa índole tales como la medicina, la óptica, el electromagnetismo, la construcción, etc. El objetivo principal de este proyecto es el diseño e implementación de algoritmos para el estudio, cálculo y manipulación de curvas concoides, utilizando técnicas propias del Calculo Simbólico. Esta implementación se ha programado utilizando el sistema de computación simbólica Maple. El proyecto consiste en dos partes bien diferenciadas, una parte teórica y otra más practica. La primera incluye la descripción geométrica y definición formal de curvas concoide, así como las ideas y propiedades básicas. De forma más precisa, se presenta un estudio matemático sobre el análisis de racionalidad de estas curvas, explicando los algoritmos que serán implementados en las segunda parte, y que constituye el objetivo principal de este proyecto. Para cerrar esta parte, se presenta una pequeña introducción al sistema y a la programación en Maple. Por otro lado, la segunda parte de este proyecto es totalmente original, y en ella el autor desarrolla las implementaciones en Maple de los algoritmos presentados en la parte anterior, así como la creación de un paquete Maple que las recoge. Por último, se crean las paginas de ayudas en el sistema Maple para la correcta utilización del paquete matemático anteriormente mencionado. Una vez terminada la parte de implementación, se aplican los algoritmos implementados a una colección de curvas clásicas conocidas, recogiendo los datos y resultados obtenidos en un atlas de curvas. Finalmente, se presenta una recopilación de las aplicaciones más destacadas en las que las concoides desempeñan un papel importante así como una breve reseña sobre las concoides de superficies, objeto de varios estudios en la actualidad y a los que se considera que el presente proyecto les puede resultar de gran utilidad. Abstract This project is set up in the framework of Symbolic Computation as well as in the implementation of algebraic-geometric problems that arise from Computer Aided Geometric Design (C.A.G.D.) applications. We address problems related to conchoid curves. The importance of these curves is the fundamental role that they play in current applications as medicine, optics, electromagnetism, construction, etc. The main goal of this project is to design and implement some algorithms to solve problems in studying, calculating and generating conchoid curves with symbolic computation techniques. For this purpose, we program our implementations in the symbolic system “Maple". The project consists of two differentiated parts, one more theoretical part and another part more practical. The first one includes the description of conchoid curves as well as the basic ideas about the concept and its basic properties. More precisely, we introduce in this part the mathematical analysis of the rationality of the conchoids, and we present the algorithms that will be implemented. Furthermore, the reader will be brie y introduced in Maple programming. On the other hand, the second part of this project is totally original. In this more practical part, the author presents the implemented algorithms and a Maple package that includes them, as well as their help pages. These implemented procedures will be check and illustrated with some classical and well known curves, collecting the main properties of the conchoid curves obtained in a brief atlas. Finally, a compilation of the most important applications where conchoids play a fundamental role, and a brief introduction to the conchoids of surfaces, subject of several studies today and where this project could be very useful, are presented.

Transport and mixing enhancement in fluid-thermal microsystems

En esta tesis se investiga de forma experimental el transporte pasivo de magnitudes físicas en micro-sistemas con carácter de inmediata aplicación industrial, usando métodos innovadores para mejorar la eficiencia de los mismos optimizando parámetros críticos del diseño o encontrar nuevos destinos de posible aplicación. Parte de los resultados obtenidos en estos experimentos han sido publicados en revistas con un índice de impacto tal que pertenecen al primer cuarto del JCR. Primero de todo se ha analizado el efecto que produce en un intercambiador de calor basado en micro-canales el hecho de dejar un espacio entre canales y tapa superior para la interconexión de los mismos. Esto genera efectos tridimensionales que mejoran la exracción de calor del intercambiador y reducen la caída de presión que aparece por el transcurso del fluido a través de los micro-canales, lo que tiene un gran impacto en la potencia que ha de suministrar la bomba de refrigerante. Se ha analizado también la mejora producida en términos de calor disipado de un micro-procesador refrigerado con un ampliamente usado plato de aletas al implementar en éste una cámara de vapor que almacena un fluido bifásico. Se ha desarrollado de forma paralela un modelo numérico para optimizar las nuevas dimensiones del plato de aletas modificado compatibles con una serie de requerimientos de diseño en el que tanto las dimensiones como el peso juegan un papel esencial. Por otro lado, se han estudiado los fenomenos fluido-dinámicos que aparecen aguas abajo de un cuerpo romo en el seno de un fluido fluyendo por un canal con una alta relación de bloqueo. Los resultados de este estudio confirman, de forma experimental, la existencia de un régimen intermedio, caracterizado por el desarrollo de una burbuja de recirculación oscilante entre los regímenes, bien diferenciados, de burbuja de recirculación estacionaria y calle de torbellinos de Karman, como función del número de Reynolds del flujo incidente. Para la obtención, análisis y post-proceso de los datos, se ha contado con la ayuda de un sistema de Velocimetría por Imágenes de Partículas (PIV). Finalmente y como adición a este último punto, se ha estudiado las vibraciones de un cuerpo romo producidas por el desprendimiento de torbellinos en un canal de alta relación de bloqueo con la base obtenida del estudio anterior. El prisma se mueve con un movimiento armónico simple para un intervalo de números de Reynolds y este movimiento se transforma en vibración alrededor de su eje a partir de un ciero número de Reynolds. En relación al fluido, el régimen de desprendimiento de torbellinos se alcanza a menores números de Reynolds que en el caso de tener el cuerpo romo fijo. Uniendo estos dos registros de movimientos y variando la relación de masas entre prisma y fluido se obtiene un mapa con diferentes estados globales del sistema. Esto no solo tiene aplicación como método para promover el mezclado sino también como método para obtener energía a partir del movimiento del cuerpo en el seno del fluido. Abstract In this thesis, experimental research focused on passive scalar transport is performed in micro-systems with marked sense of industrial application, using innovative methods in order to obtain better performances optimizing critical design parameters or finding new utilities. Part of the results obtained in these experiments have been published into high impact factor journals belonged to the first quarter of the Journal Citation Reports (JCR). First of all the effect of tip clearance in a micro-channel based heat sink is analyzed. Leaving a gap between channels and top cover, letting the channels communicate each other causes three-dimensional effects which improve the heat transfer between fluid and heat sink and also reducing the pressure drop caused by the fluid passing through the micro-channels which has a great impact on the total cooling pumping power needed. It is also analyzed the enhancement produced in terms of dissipated heat in a micro-processor cooling system by improving the predominantly used fin plate with a vapour chamber based heat spreader which contains a two-phase fluid inside. It has also been developed at the same time a numerical model to optimize the new fin plate dimensions compatible with a series of design requirements in which both size and wight plays a very restrictive role. On the other hand, fluid-dynamics phenomena that appears downstream of a bluff body in the bosom of a fluid flow with high blockage ratio has been studied. This research experimentally confirms the existence of an intermediate regime characterized by an oscillating closed recirculation bubble intermediate regime between the steady closed recirculation bubble regime and the vortex shedding regime (Karman street like regime) as a function of the incoming flow Reynolds number. A particle image velocimetry technique (PIV) has been used in order to obtain, analyze and post-process the fluid-dynamic data. Finally and as an addition to the last point, a study on the vortexinduced vibrations (VIV) of a bluff body inside a high blockage ratio channel has been carried out taking advantage of the results obtained with the fixed square prism. The prism moves with simple harmonic motion for a Reynolds number interval and this movement becomes vibrational around its axial axis after overcoming at definite Reynolds number. Regarding the fluid, vortex shedding regime is reached at Reynolds numbers lower than the previous critical ones. Merging both movement spectra and varying the square prism to fluid mass ratio, a map with different global states is reached. This is not only applicable as a mixing enhancement technique but as an energy harvesting method.

Técnicas de interpolación para la reconstrucción del espectro de irradiación en la superficie de Marte a partir de medidas hechas por fotodiodos

Este trabajo fin de grado es un estudio sobre la reconstrucción del espectro de irradiancia solar en la superficie de Marte y de la radiación solar recibida en lo alto de la atm´osfera. Se llevará a cabo a partir de los datos recogidos por “arrays” de fotodiodos, que se integran en unos sensores, y miden la intensidad de la radiación recibida del cuerpo negro (el Sol), en un rango de longitudes de onda del espectro electromagnético. Para lograr esta reconstrucción, se ha necesitado desarrollar técnicas de interpolación y modelos matemáticos. Estos m´etodos los he implementado con el lenguaje de programación Matlab y me he ayudado de Maple para conseguir distintos resultados. Estos procedimientos serán aplicados a tres configuraciones de sondas en las que cada una cuenta con un número determinado de fotodiodos. El objetivo es reconstruir este espectro de irradiancia aproximándolo lo máximo posible a unos conjuntos de datos estimados, según modelos de transferencia radiativa, que me han sido proporcionados para el cuerpo negro y que miden la radiación solar recibida en la superficie y en lo alto de la atmósfera del Planeta rojo. Este trabajo está basado en un proyecto de investigación que se está llevando a cabo desde hace varios años por un equipo de investigadores de varias universidades de Madrid, conjuntamente con el I.N.T.A. (Instituto Nacional de Técnica Aeroespacial), entre los que se encuentra mi tutor.

Transverse galloping of two-dimensional bodies having a rhombic cross-section

Transverse galloping is a type of aeroelastic instability characterized by oscillations perpendicular to wind direction, large amplitude and low frequency, which appears in some elastic two-dimensional bluff bodies when they are subjected to an incident flow, provided that the flow velocity exceeds a threshold critical value. Understanding the galloping phenomenon of different cross-sectional geometries is important in a number of engineering applications: for energy harvesting applications the interest relies on strongly unstable configurations but in other cases the purpose is to avoid this type of aeroelastic phenomenon. In this paper the aim is to analyze the transverse galloping behavior of rhombic bodies to understand, on the one hand, the dependence of the instability with a geometrical parameter such as the relative thickness and, on the other hand, why this cross-section shape, that is generally unstable, shows a small range of relative thickness values where it is stable. Particularly, the non-galloping rhombus-shaped prism?s behavior is revised through wind tunnel experiments. The bodies are allowed to freely move perpendicularly to the incoming flow and the amplitude of movement and pressure distributions on the surfaces is measured.

Determination of Maximum Mechanical Energy Efficiency in Energy Galloping Systems

Transverse galloping is a type of aeroelastic instability characterized by large amplitude, low frequency, normal to wind oscillations that appear in some elastic two-dimensional bluff bodies when subjected to a fluid flow, provided that the flow velocity exceeds a threshold critical value. Such an oscillatory motion is explained because of the energy transfer from the flow to the two-dimensional bluff body. The 7 amount of energy that can be extracted depends on the cross section of the galloping prism. Assuming that the Glauert-Den Hartog quasistatic criterion for galloping instability is satisfied in a first approximation, the suitability of a given cross section for energy harvesting is evaluated by analyzing the lateral aerodynamic force coefficient, fitting a function with a power series in tan a (a being the angle of attack) to 10 available experimental data. In this paper, a fairly large number of simple prisms (triangle, ellipse, biconvex, and rhombus cross sections, as well 11 as D-shaped bodies) is analyzed for suitability as energy harvesters. The influence of the fitting process in the energy harvesting efficiency evaluation is also demonstrated. The analysis shows that the more promising bodies are those with isosceles or approximate isosceles cross sections.

Rational conchoid and offset constructions: algorithms and implementation

This paper is framed within the problem of analyzing the rationality of the components of two classical geometric constructions, namely the offset and the conchoid to an algebraic plane curve and, in the affirmative case, the actual computation of parametrizations. We recall some of the basic definitions and main properties on offsets (see [13]), and conchoids (see [15]) as well as the algorithms for parametrizing their rational components (see [1] and [16], respectively). Moreover, we implement the basic ideas creating two packages in the computer algebra system Maple to analyze the rationality of conchoids and offset curves, as well as the corresponding help pages. In addition, we present a brief atlas where the offset and conchoids of several algebraic plane curves are obtained, their rationality analyzed, and parametrizations are provided using the created packages.

Vortex-induced vibrations on bridges : the interaction mechanism in complex sections and a new proposed semi-empirical model

El presente trabajo de investigación se ocupa del estudio de las vibraciones verticales inducidas por vórtices (VIV) en aquellos puentes que, por sus características geométricas y propiedades dinámicas, muestran cierta sensibilidad este tipo de fenómeno aeroelástico. El objeto principal es el análisis del mecanismo de interacción viento-estructura sobre secciones no fuseladas de geometría simple, con objeto de realizar una adecuada caracterización del problema y poder abordar posteriormente el análisis de otras secciones de geometría más compleja, representativas de los principales elementos estructurales de los puentes, como arcos, tableros, torres y pilas. Este aspecto es fundamental durante la fase de diseño del puente, donde deberán tenerse en cuenta también una serie de detalles que pueden influir significativamente su sensibilidad ante problemas aerodinámicos, como la morfología y dimensiones principales de la sección transversal del tablero, la disposición de barreras de seguridad y barreras cortaviento, o las riostras que unen diferentes elementos estructurales. La configuración de dos elementos en tándem o la construcción de un puente en las inmediaciones de otro existente son otros aspectos a considerar respecto a la sensibilidad frente a efectos aeroelásticos. El estudio se ha llevado a cabo principalmente mediante la implementación de simulaciones numéricas que reproducen la interacción entre la corriente de aire y secciones representativas de modelos estructurales, a partir de un código CFD basado en el método de las partículas de vórtices (VPM), siguiendo por tanto un esquema Lagrangiano. Los resultados han sido validados con datos experimentales existentes, valores procedentes de ensayos en túnel de viento y registros reales a partir de diferentes casos de estudio: Alconétar (2006), Niterói (1980), Trans- Tokyo Bay (1995) y Volgogrado (2010). Finalmente, se propone un modelo semi-empírico para la estimación del rango de velocidades críticas y amplitudes de oscilación basado en la utilización de las derivadas de flameo de Scanlan, y la densidad espectral de las fuerzas aerodinámicas en el dominio de la frecuencia. The present research work concerns the study of vertical vortex-induced vibrations (VIV) in bridges which show certain sensitivity to this type of aeroelastic phenomenon. It focuses on the analysis of the wind-structure interaction mechanism on bluff sections, with the objective of making a good characterisation of the problem and subsequently addressing the analysis of sections with a complex geometry, which are representative of the bridge structural elements, such as arches, decks, towers and piers. This issue is of relative importance during the bridge design phase, since minor details of the aforementioned elements can significantly influence its sensitivity to aerodynamic problems. The shape and main dimensions of the deck cross section, the addition of safety barriers and windshields, the presence of braces to enhance the structure mechanical properties, the utilisation of cross sections in tandem arrangement, or the erection of a new bridge in the vicinity of another existing one are some of the aspects to be considered regarding the sensitivity to the aeroelastic effects. The study has been carried out mainly through the implementation of numerical simulations that reproduces the interaction between the airflow and the representative cross section of a structural bridge model, by the use of a CFD code based on the vortex particle method (VPM), thus following a Lagrangian scheme. The results have been validated with existing experimental data, values from wind tunnel tests and full scale observations from the different case studies: Alconétar (2006), Niterói (1980), Trans-Tokyo Bay (1995) and Volgograd (2010). Finally, a new semi-empirical model is proposed for the estimation of the critical wind velocity ranges and oscillation amplitudes based on the use of the Scanlan’s flutter derivatives and the power spectral density of aerodynamic force time history in the frequency domain.

Accurate integration of forced and damped oscillators

The new methods accurately integrate forced and damped oscillators. A family of analytical functions is introduced known as T-functions which are dependent on three parameters. The solution is expressed as a series of T-functions calculating their coefficients by means of recurrences which involve the perturbation function. In the T-functions series method the perturbation parameter is the factor in the local truncation error. Furthermore, this method is zero-stable and convergent. An application of this method is exposed to resolve a physic IVP, modeled by means of forced and damped oscillators. The good behavior and precision of the methods, is evidenced by contrasting the results with other-reputed algorithms implemented in MAPLE.