Análisis del comportamiento a fatiga de uniones adhesivas de acero recubierto

Los adhesivos se conocen y han sido utilizados en multitud de aplicaciones a lo lago de la historia. En la actualidad, la tecnología de la adhesión como método de unión de materiales estructurales está en pleno crecimiento. Los avances científicos han permitido comprender mejor los fenómenos de adhesión, así como, mejorar y desarrollar nuevas formulaciones poliméricas que incrementan el rango de aplicaciones de los adhesivos. Por otro lado, el desarrollo de nuevos materiales y la necesidad de aligerar peso, especialmente en el sector transporte, hace que las uniones adhesivas se introduzcan en aplicaciones hasta ahora reservadas a otros sistemas de unión como la soldadura o las uniones mecánicas, ofreciendo rendimientos similares y, en ocasiones, superiores a los aportados por estas. Las uniones adhesivas ofrecen numerosas ventajas frente a otros sistemas de unión. En la industria aeronáutica y en automoción, las uniones adhesivas logran una reducción en el número de componentes (tales como los tornillos, remaches, abrazaderas) consiguiendo como consecuencia diseños más ligeros y una disminución de los costes de manipulación y almacenamiento, así como una aceleración de los procesos de ensamblaje, y como consecuencia, un aumento de los procesos de producción. En el sector de la construcción y en la fabricación de equipos industriales, se busca la capacidad para soportar la expansión y contracción térmica. Por lo tanto, se usan las uniones adhesivas para evitar producir la distorsión del sustrato al no ser necesario el calentamiento ni la deformación de las piezas cuando se someten a un calentamiento elevado y muy localizado, como en el caso de la soldadura, o cuando se someten a esfuerzos mecánicos localizados, en el caso de montajes remachados. En la industria naval, se están desarrollando técnicas de reparación basadas en la unión adhesiva para distribuir de forma más uniforme y homogénea las tensiones con el objetivo de mejorar el comportamiento frente a fatiga y evitar los problemas asociados a las técnicas de reparación habituales de corte y soldadura. Las uniones adhesivas al no requerir importantes aportes de calor como la soldadura, no producen modificaciones microestructurales indeseables como sucede en la zona fundida o en la zona afectada térmicamente de las uniones soldadas, ni deteriora los recubrimientos protectores de metales de bajo punto de fusión o de naturaleza orgánica. Sin embargo, las uniones adhesivas presentan una desventaja que dificulta su aplicación, se trata de su durabilidad a largo plazo. La primera causa de rotura de los materiales es la rotura por fatiga. Este proceso de fallo es la causa del 85% de las roturas de los materiales estructurales en servicio. La rotura por fatiga se produce cuando se somete al material a la acción de cargas que varían cíclicamente o a vibraciones durante un tiempo prolongado. Las uniones y estructuras sometidas a fatiga pueden fallar a niveles de carga por debajo del límite de resistencia estática del material. La rotura por fatiga en las uniones adhesivas no se produce por un proceso de iniciación y propagación de grieta de forma estable, el proceso de fatiga va debilitando poco a poco la unión hasta que llega un momento que provoca una rotura de forma rápida. Underhill explica este mecanismo como un proceso de daño irreversible de los enlaces más débiles en determinados puntos de la unión. Cuando se ha producido el deterioro de estas zonas más débiles, su área se va incrementando hasta que llega un momento en que la zona dañada es tan amplia que se produce el fallo completo de la unión. En ensayos de crecimiento de grieta realizados sobre probetas preagrietadas en viga con doble voladizo (DCB), Dessureault identifica los procesos de iniciación y crecimiento de grietas en muestras unidas con adhesivo epoxi como una acumulación de microfisuras en la zona próxima al fondo de grieta que, luego, van coalesciendo para configurar la grieta principal. Lo que supone, igualmente, un proceso de daño del adhesivo en la zona de mayor concentración de tensiones que, posteriormente, conduce al fallo de la unión. La presente tesis surge con el propósito de aumentar los conocimientos existentes sobre el comportamiento a fatiga de las uniones adhesivas y especialmente las realizadas con dos tipos de adhesivos estructurales aplicados en aceros con diferentes acabados superficiales. El estudio incluye la obtención de las curvas de tensión frente al número de ciclos hasta el fallo del componente, curvas SN o curvas de Wöhler, que permitirán realizar una estimación de la resistencia a la fatiga de un determinado material o estructura. Los ensayos de fatiga realizados mediante ciclos predeterminados de carga sinusoidales, de amplitud y frecuencia constantes, han permitido caracterizar el comportamiento a la fatiga por el número de ciclos hasta la rotura, siendo el límite de fatiga el valor al que tiende la tensión cuando el número de ciclos es muy grande. En algunos materiales, la fatiga no tiende a un valor límite sino que decrece de forma constante a medida que aumenta el número de ciclos. Para estas situaciones, se ha definido la resistencia a la fatiga (o límite de resistencia) por la tensión en que se produce la rotura para un número de ciclos predeterminado. Todos estos aspectos permitirán un mejor diseño de las uniones y las condiciones de trabajo de los adhesivos con el fin de lograr que la resistencia a fatiga de la unión sea mucho más duradera y el comportamiento total de la unión sea mucho mejor, contribuyendo al crecimiento de la utilización de las uniones adhesivas respecto a otras técnicas. ABSTRACT Adhesives are well-known and have been used in many applications throughout history. At present, adhesion bonding technology of structural materials is experiencing an important growth. Scientific advances have enabled a better understanding of the phenomena of adhesion, as well as to improve and develop new polymeric formulations that increase the range of applications. On the other hand, the development of new materials and the need to save weight, especially in the transport sector, have promote the use of adhesive bonding in many applications previously reserved for other joining technologies such as welded or mechanical joints, presenting similar or even higher performances. Adhesive bonding offers many advantages over other joining methods. For example, in the aeronautic industry and in the automation sector, adhesive bonding allows a reduction in the number of components (such as bolts, rivets, clamps) and as consequence, resulting in lighter designs and a decrease in handling and storage costs, as well as faster assembly processes and an improvement in the production processes. In the construction sector and in the industrial equipment manufacturing, the ability to withstand thermal expansion and contraction is required. Therefore, adhesion bonding technology is used to avoid any distortion of the substrate since this technology does not require heating nor the deformation of the pieces when these are exposed to very high and localized heating, as in welding, or when are subjected to localized mechanical stresses in the case of riveted joints. In the naval industry, repair techniques based in the adhesive bonding are being developed in order to distribute stresses more uniform and homogeneously in order to improve the performance against fatigue and to avoid the problems associated with standard repair techniques as cutting and welding. Adhesive bonding does not require the use of high temperatures and as consequence they do not produce undesirable microstructural changes, as it can be observed in molten zones or in heat-affected zones in the case of welding, neither is there damage of the protective coating of metals with low melting points or polymeric films. However, adhesive bonding presents a disadvantage that limits its application, the low longterm durability. The most common cause of fractures of materials is fatigue fracture. This failure process is the cause of 85% of the fracture of structural materials in service. Fatigue failure occurs when the materials are subjected to the action of cyclic loads or vibrations for a long period of time. The joints and structures subjected to fatigue can fail at stress values below the static strength of the material. Fatigue failure do not occurs by a static and homogeneous process of initiation and propagation of crack. The fatigue process gradually weakens the bond until the moment in which the fracture occurs very rapidly. Underhill explains this mechanism as a process of irreversible damage of the weakest links at certain points of the bonding. When the deterioration in these weaker zones occurs, their area increase until the damage zone is so extensive that the full failure of the joint occurs. During the crack growth tests performed on precracked double-cantilever beam specimen, (DCB), Dessureault identified the processes of crack initiation and growth in samples bonded with epoxy adhesive as a process of accumulation of microcracks on the zone near the crack bottom, then, they coalesced to configure the main crack. This is a damage process of the adhesive in the zone of high stress concentration that leads to failure of the bond. This thesis aims to further the understanding of the fatigue behavior of the adhesive bonding, primarily those based on two different types of structural adhesives used on carbon-steel with different surface treatments. This memory includes the analysis of the SN or Wöhler curves (stress vs. number of cycles curves up to the failure), allowing to carry out an estimation of the fatigue strength of a specific material or structure. The fatigue tests carried out by means of predetermined cycles of sinusoidal loads, with a constant amplitude and frequency, allow the characterisation of the fatigue behaviour. For some materials, there is a maximum stress amplitude below which the material never fails for any number of cycles, known as fatigue limit. In the other hand, for other materials, the fatigue does not tend toward a limit value but decreases constantly as the number of cycles increases. For these situations, the fatigue strength is defined by the stress at which the fracture occurs for a predetermined number of cycles. All these aspects will enable a better joint design and service conditions of adhesives in order to get more durable joints from the fatigue failure point of view and in this way contribute to increase the use of adhesive bonding over other joint techniques.

Examples of PDEs all whose points are characteristic

Let π : FM ! M be the bundle of linear frames of a manifold M. A basis Lijk , j < k, of diffeomorphism invariant Lagrangians on J1 (FM) was determined in [J. Muñoz Masqué, M. E. Rosado, Invariant variational problems on linear frame bundles, J. Phys. A35 (2002) 2013-2036]. The notion of a characteristic hypersurface for an arbitrary first-order PDE system on an ar- bitrary bred manifold π : P → M, is introduced and for the systems dened by the Euler-Lagrange equations of Lijk every hypersurface is shown to be characteristic. The Euler-Lagrange equations of the natural basis of Lagrangian densities Lijk on the bundle of linear frames of a manifold M which are invariant under diffeomorphisms, are shown to be an underdetermined PDEs systems such that every hypersurface of M is characteristic for such equations. This explains why these systems cannot be written in the Cauchy-Kowaleska form, although they are known to be formally integrable by using the tools of geometric theory of partial differential equations, see [J. Muñoz Masqué, M. E. Rosado, Integrability of the eld equations of invariant variational problems on linear frame bundles, J. Geom. Phys. 49 (2004), 119-155]

On the structure of the floating zone in melting

Floating zone melting is used in crystal growth and purification of high melting materials. The use of a reduced gravity environment will remove the constraint imposed on the length of the zone by the hydrostatic pressure. The equilibrium of the fioatmg zone may involve, (1)Hydrostatic forces, when the zone rotates as a whole. (2)Convective driving forces, when the zone is stationary but fluid property gradients appear.(3) Hydrodynamic forces, when some parts of the zone are set into motion with respect to others. The last effects are considered in this paper. The flow pattern of a floating zone held between two discs in relative motion is complicated, and thence the solution of the problem is difficult even assuming a constant property-newtonian liquid Nevertheless, when a small parameter appears m the problem, the complete flow field can be split into zones where simple solutions are found. To illustrate this approach, the spin up from rest of an initially cylindrical floating zone is considered with detail. Here the small parameter is the time elapsed from the impulsive starting of motion. Since the problem which has been considered, as well as some others which can be tackled by use of similar methods, concern the viscous layer close to either plate, they can be simulated experimentally in the ground laboratory with short floating zones. Procedures to produce these zones are indicated.

The Minimum Number of Points Taking Part in k-Sets in Sets of Unaligned Points

En este trabajo se da un ejemplo de un conjunto de n puntos situados en posición general, en el que se alcanza el mínimo número de puntos que pueden formar parte de algún k-set para todo k con 1menor que=kmenor quen/2. Se generaliza también, a puntos en posición no general, el resultado de Erdõs et al., 1973, sobre el mínimo número de puntos que pueden formar parte de algún k-set. The study of k- sets is a very relevant topic in the research area of computational geometry. The study of the maximum and minimum number of k-sets in sets of points of the plane in general position, specifically, has been developed at great length in the literature. With respect to the maximum number of k-sets, lower bounds for this maximum have been provided by Erdõs et al., Edelsbrunner and Welzl, and later by Toth. Dey also stated an upper bound for this maximum number of k-sets. With respect to the minimum number of k-set, this has been stated by Erdos el al. and, independently, by Lovasz et al. In this paper the authors give an example of a set of n points in the plane in general position (no three collinear), in which the minimum number of points that can take part in, at least, a k-set is attained for every k with 1 ≤ k < n/2. The authors also extend Erdos’s result about the minimum number of points in general position which can take part in a k-set to a set of n points not necessarily in general position. That is why this work complements the classic works we have mentioned before.

Optimal fits of diffusion constants from single-time data points of Brownian trajectories

Experimental methods based on single particle tracking (SPT) are being increasingly employed in the physical and biological sciences, where nanoscale objects are visualized with high temporal and spatial resolution. SPT can probe interactions between a particle and its environment but the price to be paid is the absence of ensemble averaging and a consequent lack of statistics. Here we address the benchmark question of how to accurately extract the diffusion constant of one single Brownian trajectory. We analyze a class of estimators based on weighted functionals of the square displacement. For a certain choice of the weight function these functionals provide the true ensemble averaged diffusion coefficient, with a precision that increases with the trajectory resolution.

Decelerator elements for ramp transfer points in fruit packing lines

Two different decelerator elements used to reduce impacts on fruits on ramp transfer points in fruit packing lines were designed and tested. The performance of these elements, a powered decelerator and a multiple curtain, was compared to commercial decelerators (blankets). A ramp of length 60 cm was placed at an angle of 30º in an experimental fruit packing line between a roller transporter and a conveyor. The decelerators were placed on top of the ramp. Different tests were carried out to study the performance of the decelerators using instrumented spheres (IS 100) of various sizes. Results showed that decelerators can reduce the impact intensity down to safe thresholds. The powered decelerator was the most effective because it reduced the speed of fruits and did not cause retention of the fruit, when correctly regulated.

Perfect imaging of three object points with only two analytic lens surfaces in two dimensions

In this work, a new two-dimensional analytic optics design method is presented that enables the coupling of three ray sets with two lens profiles. This method is particularly promising for optical systems designed for wide field of view and with clearly separated optical surfaces. However, this coupling can only be achieved if different ray sets will use different portions of the second lens profile. Based on a very basic example of a single thick lens, the Simultaneous Multiple Surfaces design method in two dimensions (SMS2D) will help to provide a better understanding of the practical implications on the design process by an increased lens thickness and a wider field of view. Fermat?s principle is used to deduce a set of functional differential equations fully describing the entire optical system. The transformation of these functional differential equations into an algebraic linear system of equations allows the successive calculation of the Taylor series coefficients up to an arbitrary order. The evaluation of the solution space reveals the wide range of possible lens configurations covered by this analytic design method. Ray tracing analysis for calculated 20th order Taylor polynomials demonstrate excellent performance and the versatility of this new analytical optics design concept.

Passing or stopping by: meeting points on the fly

In traditional nomadic societies, social life was created around mobile points rekindled in different places each time. After the settled urbanization period, where social life centred on fixed attractions, we are opening a new era, where thanks to technology, we are able to create meeting points on the fly. Contemporary public space for passer-by users will be again based on traces instead of lines, reflecting current reality far more accurately.

Analytical Calculation of Stall-inception and Surge Points for an Axial-flow Compresor Rotor

Recently, a theoretical criterion to calculate the stability of an axial-flow compressor rotor has been presented in the scientific literature. This theoretical criterion was used for determining the locus of the stability line over the rotor map and for predicting the post-stall evolution of the constant-speed line of a rotor. The main objective of this paper is to improve the predictions of such a model. To do that, the paper proposes a different characterization of the characteristic azimuthal length and a calculation of the ratio of specific heats based on a polytropic exponent. Thanks to these new values, the model predicts two bifurcation points in the behaviour of the flow: the inception point of the instability and the surge point. Experimental data from a pure axial compressor are used to validate the model showing that the prediction of the flow coefficient at the surge point has an error inferior to 5%. For the rotor studied, the paper provides a quantitative and qualitative description of the inception of the instability and of the mechanism involved in the instable region of the compressor map. The paper also discusses the role of rotor efficiency in the position of the bifurcations and gives a sensitivity analysis of its position. Finally, it presents a discussion about how the model can explain the different behaviours exhibited by the same rotor when the flow coefficient is reduced

Meromorphic continuation of functions and arbitrary distribution of interpolation points

We characterize the region of meromorphic continuation of an analytic function ff in terms of the geometric rate of convergence on a compact set of sequences of multi-point rational interpolants of ff. The rational approximants have a bounded number of poles and the distribution of interpolation points is arbitrary.

Sharp imaging of Multiple object pointS: how and why

Is it possible to sharply image M object points with N surfaces when N menor que M? Under what conditions? Why is it interesting for optimization? What is the role of the SMS method?

Concept of operations for ATM by managing uncertainty through multiple metering points

This paper presents an operational concept for Air Traffic Management, and in particular arrival management, in which aircraft are permitted to operate in a manner consistent with current optimal aircraft operating techniques. The proposed concept allows aircraft to descend in the fuel efficient path managed mode and with arrival time not actively controlled. It will be demonstrated how the associated uncertainty in the time dimension of the trajectory can be managed through the application of multiple metering points strategically chosen along the trajectory. The proposed concept does not make assumptions on aircraft equipage (e.g. time of arrival control), but aims at handling mixed-equipage scenarios that most likely will remain far into the next decade and arguably beyond.

Double ion implantation and pulsed laser melting processes for third generation solar cells

In the framework of the third generation of photovoltaic devices, the intermediate band solar cell is one of the possible candidates to reach higher efficiencies with a lower processing cost. In this work, we introduce a novel processing method based on a double ion implantation and, subsequently, a pulsed laser melting (PLM) process to obtain thicker layers of Ti supersaturated Si. We perform ab initio theoretical calculations of Si impurified with Ti showing that Ti in Si is a good candidate to theoretically form an intermediate band material in the Ti supersaturated Si. From time-of-flight secondary ion mass spectroscopy measurements, we confirm that we have obtained a Ti implanted and PLM thicker layer of 135 nm. Transmission electron microscopy reveals a single crystalline structure whilst the electrical characterization confirms the transport properties of an intermediate band material/Si substrate junction. High subbandgap absorption has been measured, obtaining an approximate value of 104 cm−1 in the photons energy range from 1.1 to 0.6 eV.

Comportamiento hidrológico de cuencas de media montaña españolas: efectos de los procesos de acumulación / fusión de nieve en terrenos permeables sobre la infiltración y régimen de caudales Alto Tajo

La infiltración de agua en el suelo y la recarga profunda del agua subterránea contenida en los acuíferos es un proceso lento en relación con otros fenómenos hidrológicos. La redacción de esta tesis ha pretendido contribuir al estudio de la influencia que el almacenamiento de la precipitación sólida en forma de manto de nieve y su eventual fusión puedan tener sobre dicho proceso en áreas de media montaña (1.000 – 2.000 m.) en las que con gran frecuencia se sitúan las cabeceras de los ríos peninsulares. Para ello se ha partido del análisis de las diferentes variables intervinientes durante un determinado periodo temporal y sobre un espacio geográfico concreto, por lo que su metodología es de naturaleza empírica. La extensión del periodo (2002/03 a 2010/11) ha venido condicionada por la disponibilidad de los valores de algunas de sus principales variables, como han sido el equivalente en agua de la nieve acumulada y los caudales procedentes de su fusión. Éstos se han obtenido como resultado de la aplicación del modelo ASTER, desarrollado en el programa de Evaluación de los Recursos Hídricos procedentes de la Innivación (ERHIN), calibrado – entre otros- con datos de precipitaciones, temperatura y caudales provenientes a su vez del Sistema Automático de Información Hidrológica (SAIH). Ambos programas fueron implantados por la Administración en las diferentes Confederaciones Hidrográficas y en determinados Organismos de cuenca actuales, en cuyo desarrollo participó el autor de esta tesis. En cuanto a la zona de estudio se ha procedido a su elección considerando las posibles áreas de media montaña en las que la presencia de la nieve fuera hidrológicamente significativa y estuvieran constituidas litológicamente por afloramientos permeables que no impidieran la infiltración en el terreno y la formación de acuíferos de cierta relevancia. El interés se centró discrecionalmente en la cuenca del Tajo, tanto por el carácter estratégico de la misma -como suministradora en la actualidad de excedentes a otras cuencas deficitarias- como por el valor representativo de sus condiciones climáticas y orográficas en relación con otras cuencas hidrográficas peninsulares. Para ello se partió de las cabeceras de ríos identificadas por el programa ERHIN por su interés nivológico para la implantación del modelo ASTER y de las Masas de Agua Subterráneas MASb (antes Unidades Hidrogeológicas UUHH) definidas en los planes hidrológicos. La intersección en el territorio de ambos criterios condujo, finalmente, a la zona del Alto Tajo, en la que se cumplen ambos requisitos. El tramo quedó concretado en el comprendido entre las cabeceras de los ríos Tajo y Guadiela y la cola de los embalses de Entrepeñas y Buendía respectivamente, puntos de cierre para la calibración llevada a cabo en la modelización ASTER. Gran parte de éste discurre, en su parte alta, sobre rocas carbonatadas (calizas y dolomías del Jurásico y Cretácico), relacionados con las MASb de Tajuña-Montes Universales, Molina de Aragón y Sigüenza-Maranchón. Los valores diarios de las reservas de agua en forma de nieve, evapotranspiración y caudales procedentes de la fusión se han obtenido a partir de los resultados del mencionado modelo, procediéndose al cálculo de la infiltración por balance hídrico durante el periodo de estudio considerado, teniendo en cuenta los valores de precipitación, evapotranspiración y aportaciones de caudales. Esto ha requerido el estudio previo de las condiciones hidrogeológicas de la zona seleccionada con objeto de conocer las posibles interconexiones subterráneas que pudieran alterar los saldos entre las variables intervinientes anteriormente citadas. Para ello se ha llevado a cabo la recopilación y análisis de la información hidrogeológica correspondiente a la documentación de los planes hidrológicos del Tajo (Plan Hidrológico de la cuenca del Tajo RD 1664/1998 y el actual Plan Hidrológico de la parte española de la Demarcación Hidrográfica del Tajo RD 270/2014) y de los estudios previos realizados por el organismo de cuenca y el Instituto Geológico y Minero de España (lGME) fundamentalmente. En relación con la MASb Tajuña-Montes Universales -cuya extensión supera la zona seleccionada- dichos estudios consideran su estructura geológica y distribución litológica, con intercalaciones impermeables que actúan como barreras, dividiendo a éstas en Subunidades e identificando las zonas de drenaje de sus respectivos acuíferos. También se ha considerado la documentación y estudios previos del Plan Hidrológico Nacional sobre las Unidades Hidrogeológicas compartidas entre ámbitos geográficos de diferentes planes hidrológicos. Se concluye que las divisorias hidrográficas de las cabeceras son sensiblemente coincidentes o abarcan las Subunidades Montes Universales meridionales, Priego, Cifuentes, Zaorejas, u Montes Universales septentrionales, que drenan hacia el Tajo/Guadiela (bien directamente, bien a través de afluentes como el Gallo, Ablanquejo, Cabrillas, Cuervo…), MASb Molina de Aragón, que drena al Tajo a través del río Gallo y MASb Sigüenza—Maranchón, que drena su parte correspondiente hacia el Tajo a través del Ablanquejo. Se descartan – salvo la pequeña salvedad del manantial de Cifuentes- las conexiones hidrogeológicas con otras MASb o Subunidades por lo que las cabeceras del Tajo y del Guadiela pueden considerarse como un Sistema independiente donde las precipitaciones no evaporadas escurren superficialmente o se infiltran y descargan hacia los embalses de Entrepeñas y Buendía. La cuantificación diaria y acumulada de los balances hídricos ha permitido calcular la evolución aproximada de las reservas de agua subterránea desde la fecha inicial. Originalmente los balances se realizaron de forma separada en las cabeceras del Tajo y del Guadiela, cuyos valores acumulados manifestaron una tendencia creciente en la primera y decreciente en la segunda. Dicha situación se equilibra cuando el balance se practica conjuntamente en ambas, apreciándose en la variación del volumen de agua subterránea una evolución acorde hidrológicamente con los ciclos de verano/invierno y periodos de sequía, manteniéndose sus valores medios a largo/medio plazo, poniendo en evidencia la existencia de interconexiones subterráneas entre ambas cuencas. El balance conjunto, agregando la cabecera del Tajuña (que también comparte los materiales permeables de la MASb Tajuña-Montes Universales) no reveló la existencia de nuevas interrelaciones hidrogeológicas que influyeran en los balances hídricos realizados Tajo/Guadiela, confirmando las conclusiones de los estudios hidrogeológicos anteriormente analizados. Se ha procedido a confrontar y validar los resultados obtenidos de la evolución de las reservas de agua subterránea mediante los siguientes procedimientos alternativos: - Cálculo de los parámetros de desagüe de la curva de agotamiento correspondiente al volumen de agua subterránea drenante hacia el Tajo/Guadiela. Éste se ha realizado a partir de las aportaciones mensuales entrantes en los embalses de Entrepeñas y Buendía durante los meses de junio, julio, agosto y septiembre, cuyos valores responden al perfil típico de descargas de un acuífero. A partir de éstos se ha determinado el volumen drenante correspondiente al primero de junio de cada año de la serie histórica considerada. - Determinación del caudal base por el método Wallingford y deducción de los volúmenes drenantes. Estimación de las recarga anuales - Cuantificación de la recarga anual por el método Sanz, Menéndez Pidal de Navascués y Távara. Se obtuvieron valores de recarga muy aproximados entre los calculados por los dos últimos procedimientos citados. Respecto a las reservas de agua subterránea almacenadas siguen una evolución semejante en todos los casos, lo que ha permitido considerar válidos los resultados conseguidos mediante balance hídrico. Confirmada su solidez, se han buscado correlaciones simples entre el volumen de las reservas subterráneas (como indicador estimativo del efecto de la infiltración) y los volúmenes procedentes de la fusión. La conclusión es que estos últimos no tienen un efecto determinante a escala anual sobre la infiltración,recarga y variación de los volúmenes de agua subterránea, frente al peso de otras variables (precipitación y evapotranspiración). No obstante se ha encontrado una buena correlación múltiple entre la recarga estimada y la precipitación eficaz (precipitación menos evapotranspiración) y fusión, que ha permitido cuantificar la contribución de esta última. Posteriormente se ha recurrido a la selección de los episodios más intensos de acumulación /fusión en las cabeceras del Tajo y Guadiela. Y se procedió a la comparación entre los resultados obtenidos por aplicación del modelo de simulación en los mismos periodos (normalmente de varios días de duración) con datos reales y con datos ficticios de temperatura que anularan o disminuyeran la presencia de nieve, apreciándose una gran sensibilidad del efecto de la temperatura sobre la evapotranspiración y estableciéndose nuevamente correlaciones lineales entre los volúmenes de fusión y el incremento de reservas subterráneas. Las mismas confirman el efecto “favorecedor” de la acumulación de agua en forma de nieve y su posterior licuación, sobre sobre la infiltración de agua en el suelo y almacenamiento subterráneo. Finalmente se establecieron varios escenarios climáticos (+1ºC; +3ºC; +1ºC y – 10% precipitación; y 3ºC – 10% precipitación) compatibles con las previsiones del IPCC para mediados y finales del presente siglo, determinándose mediante simulación ASTER los correspondientes valores de fusión. La correlación establecida a escala anual ha permitido evaluar el efecto de la disminución del volumen de fusión - en los diferentes escenarios – sobre la recarga, pronosticando un descenso de los caudales de estiaje y la desaparición del “efecto nieve” sobre la infiltración y recarga con un aumento de 3ºC de temperatura. Teniendo en cuenta las condiciones de representatividad de la zona elegida, resulta verosímil la extensión de las anteriores conclusiones a otras cabeceras fluviales enclavadas en áreas de media montaña situadas entre 1000 a 2000m y sus efectos aguas abajo.Water infiltration into the soil and groundwater recharge deep water in aquifers is slow relative to other hydrological phenomena. The wording of this thesis aims to contribute to the study of the influence that the storage of solid precipitation as snow cover and its eventual melting may have on this process in mid-mountain areas (1000 - 2,000 m) where very often the headwaters of the peninsular rivers are located. For this party analysis of the different variables involved has over a given time period and a particular geographical area, so that their methodology is empirical in nature. The extension of the period (2002/03 to 2010/11) has been conditioned by the availability of the values of some of its key variables, as were the water equivalent of the snow and flows from melting. These have been obtained as a result of the application of ASTER model, developed in the program Evaluation of Water Resources from the Innivation (ERHIN), calibrated - among others data of rainfall, temperature and flow from turn System Automatic Hydrological Information (SAIH). Both programs were implemented by the Administration in the different Water Boards and to undertakings for current basin, in which the author participated development of this thesis. As for the study area has proceeded at its option considering the possible areas of midmountain in the presence of snow outside hydrological meaningful and they were lithology consisting of permeable outcrops that did not prevent infiltration into the ground and forming aquifers of some significance. We were interested discretion in the Tagus basin, therefore the strategic nature of it, as currently supplying surplus to other basins deficit- as the representative value of its climate and terrain conditions in relation to other peninsular river basins . To do this we started from the headwaters identified by the ERHIN program for its implementation snow interest to the ASTER model and Ground Water Bodies MASb (before UUHH Hydrogeological Units) defined in hydrological plans. The intersection in the territory of both criteria led eventually to the Alto Tajo, in which both requirements are met. The section was finalized in the period between the headwaters of the Tagus and Guadiela rivers and reservoirs end Entrepeñas and Buendia respectively checking points for calibration performed in ASTER modeling. Much of it runs on carbonate rocks (limestones and dolomites of Jurassic and Cretaceous) related MASb of Tajuña -Montes Universal, Molina de Aragón and Sigüenza-Maranchón. The daily values of water reserves in the form of snow, evapotranspiration and flow from melting were obtained from the results of this model, proceeding to the calculation of infiltration water balance during the study period considered, taking into account values of precipitation, evapotranspiration and input flow. This has required the prior examination of the hydrogeological conditions of your required in order to know the possible underground interconnections that could alter the balance between the intervening variables aforementioned area. For this we have carried out the collection and analysis of hydrogeological information relevant documentation Tagus river management plans (Hydrological Plan Tajo Basin RD 1664/1998 and the current Hydrological Plan of the Spanish part of the River Basin Tagus RD 270/2014) and previous studies by the basin organization and the Geological Survey of Spain (IGME) mainly. Regarding the MASb Tajuña- Montes Universal - whose length exceeds the area selected - these studies consider its geological structure and lithology distribution with waterproof collations that act as barriers, dividing it into subunits and identifying areas draining their respective aquifers. It has also considered the documentation and previous studies of the National Hydrological Plan on shared among different geographical areas management plans Hydrogeological Units. We conclude that river dividing the headers are substantially coincident or covering Subunits southern Universal Montes, Priego Cifuentes, Zaorejas and northern Universal Mounts, which drain into the Tagus / Guadiela (either directly or through tributaries such as Gallo, Ablanquejo , whitecaps , Raven ...), MASb Molina de Aragón which drains through the Tajo del Gallo and MASb Sigüenza- Maranchón river that drains into the Tagus using the Ablanquejo . Discarded - except the small exception of spring Cifuentes -hydrogeological connections with other MASb or Subunits so the headwaters of the Tagus and Guadiela be considered as a separate system, where rainfall not evaporated runs on surface or infiltrates and eventually discharged into reservoirs Entrepeñas and Buendia. The daily and cumulative quantification of water balances allowed us to compute the approximate evolution of groundwater reserves from its initial date. Initially balances were performed separately in the headwaters of the Tagus and Guadiela, whose cumulative values showed an increasing trend in the first and decreasing in the second. This situation is balanced when the balance is practiced together in both , appreciating the change in volume of groundwater hydrological evolution commensurate with the cycles of summer / winter and drought periods , keeping their average long / medium term values and putting in shows the existence of underground interconnections between the two basins. The overall balance, adding header Tajuña (which also shares the permeable materials MASb Tajuña -Montes Universal ) did not reveal the existence of new hydrogeological interrelationships that influenced water balances made Tajo / Guadiela, confirming the findings of the hydrogeological studies previously analyzed. We proceeded to confront and validate the results of the evolution of groundwater reserves by the following alternative procedures: - Calculate the parameters drain depletion curve corresponding to the volume of groundwater draining into the Tajo / Guadiela. This has been made from monthly inflows in the reservoirs of Entrepeñas and Buendia during the months of June, July, August and September, whose values match the typical profile of an aquifer discharges. From these has been determined for the first of June each year of the time series considered drainage volume - Determination of base flow by Wallingford method and deduction of drainage volumes. Estimate of annual recharge - Quantification of the annual recharge by the method Sanz Menéndez Pidal of Navascués and Távara. Very approximate values recharge between calculated for the last two mentioned methods were obtained. Concerning groundwater reserves stored follow a similar pattern in all cases, allowing consider valid the results achieved through water balance. Confirmed its robustness, simple correlations were sought between the volume of groundwater reserves (as estimated indicator of the effect of infiltration) and volumes from the melting. The conclusion is that the latter do not have a decisive effect on the annual scale infiltration, recharge and variation in volumes of groundwater, against the weight of other variables (precipitation and evapotranspiration). However found a good multiple correlation between the estimated recharge and effective precipitation (precipitation minus evapotranspiration) and fusion, which allowed quantify the contribution of the latter. Subsequently it has resorted to the selection of the most intense episodes of accumulation / melting in the headwaters of the Tagus and Guadiela. And we proceeded to the comparison between the results obtained by application of the simulation model in the same periods (usually several days) with real data and fictitious temperature data to annul or decrease the presence of snow, appreciating a great sensitivity of the effect of temperature on evapotranspiration and establishing linear correlations between the volumes of melting and increased groundwater reserves again. They confirm the “flattering " effect of water accumulation as snow and subsequent liquefaction of the infiltration of water into the soil and underground storage. Finally various climate scenarios (+1ºC; +3ºC; +1ºC y – 10% precipitation; y 3ºC – 10% precipitation) were established consistent with IPCC projections for mid - to late - century, determined through simulation ASTER corresponding values of melting. The correlation established on an annual scale has allowed to evaluate the effect of decreasing the volume of melt - in different scenarios - on recharge, predicting a decline in low flows and the disappearance of "snow effect" on infiltration and recharge with an increase of 3°C temperature. Given the conditions of representativeness of the chosen area, plausible extension of the above findings to other landlocked headwaters in mid-mountain areas located between 1000 to 2000m and its downstream effects.

Hysteresis in transverse galloping: the role of the inflection points

Transverse galloping is here considered as a one-degree-of-freedom oscillator subjected to aerodynamic forces, which are described by using the quasi-steady hypothesis. The hysteresis of transverse galloping is also analyzed. Approximate solutions of the model are obtained by assuming that the aerodynamic and damping forces are much smaller than the inertial and stiffness ones. The analysis of the approximate solution, which is obtained by means of the method of Krylov–Bogoliubov, reveals the existing link between the hysteresis phenomenon and the number of inflection points at the aerodynamic force coefficient curve, Cy(α)Cy(α); CyCy and αα being, respectively, the force coefficient normal to the incident flow and the angle of attack. The influence of the position of these inflection points on the range of flow velocities in which hysteresis takes place is also analyzed.