Modal analysis of buildings : quantification of uncertainties and model updating

Una estructura vibra con la suma de sus infinitos modos de vibración, definidos por sus parámetros modales (frecuencias naturales, formas modales y coeficientes de amortiguamiento). Estos parámetros se pueden identificar a través del Análisis Modal Operacional (OMA). Así, un equipo de investigación de la Universidad Politécnica de Madrid ha identificado las propiedades modales de un edificio de hormigón armado en Madrid con el método Identificación de los sub-espacios estocásticos (SSI). Para completar el estudio dinámico de este edificio, se ha desarrollado un modelo de elementos finitos (FE) de este edificio de 19 plantas. Este modelo se ha calibrado a partir de su comportamiento dinámico obtenido experimentalmente a través del OMA. Los objetivos de esta tesis son; (i) identificar la estructura con varios métodos de SSI y el uso de diferentes ventanas de tiempo de tal manera que se cuantifican incertidumbres de los parámetros modales debidos al proceso de estimación, (ii) desarrollar FEM de este edificio y calibrar este modelo a partir de su comportamiento dinámico, y (iii) valorar la bondad del modelo. Los parámetros modales utilizados en esta calibración han sido; espesor de las losas, densidades de los materiales, módulos de elasticidad, dimensiones de las columnas y las condiciones de contorno de la cimentación. Se ha visto que el modelo actualizado representa el comportamiento dinámico de la estructura con una buena precisión. Por lo tanto, este modelo puede utilizarse dentro de un sistema de monitorización estructural (SHM) y para la detección de daños. En el futuro, podrá estudiar la influencia de los agentes medioambientales, tales como la temperatura o el viento, en los parámetros modales. A structure vibrates according to the sum of its vibration modes, defined by their modal parameters (natural frequencies, damping ratios and modal shapes). These parameters can be identified through Operational Modal Analysis (OMA). Thus, a research team of the Technical University of Madrid has identified the modal properties of a reinforced-concrete-frame building in Madrid using the Stochastic Subspace Identification (SSI) method and a time domain technique for the OMA. To complete the dynamic study of this building, a finite element model (FE) of this 19-floor building has been developed throughout this thesis. This model has been updated from its dynamic behavior identified by the OMA. The objectives of this thesis are to; (i) identify the structure with several SSI methods and using different time blocks in such a way that uncertainties due to the modal parameter estimation are quantified, (ii) develop a FEM of this building and tune this model from its dynamic behavior, and (iii) Assess the quality of the model, the modal parameters used in this updating process have been; thickness of slabs, material densities, modulus of elasticity, column dimensions and foundation boundary conditions. It has been shown that the final updated model represents the structure with a very good accuracy. Thus, this model might be used within a structural health monitoring framework (SHM). The study of the influence of changing environmental factors (such as temperature or wind) on the model parameters might be considered as a future work.

A simplified spectral approachfor impedance-based damage identification of frp-strengthened rc beams

Hoy en día, el refuerzo y reparación de estructuras de hormigón armado mediante el pegado de bandas de polímeros reforzados con fibras (FRP) se emplea cada vez con más frecuencia a causa de sus numerosas ventajas. Sin embargo, las vigas reforzadas con esta técnica pueden experimentar un modo de fallo frágil a causa del despegue repentino de la banda de FRP a partir de una fisura intermedia. A pesar de su importancia, el número de trabajos que abordan el estudio de este mecanismo de fallo y su monitorización es muy limitado. Por ello, el desarrollo de metodologías capaces de monitorizar a largo plazo la adherencia de este refuerzo a las estructuras de hormigón e identificar cuándo se inicia el despegue de la banda constituyen un importante desafío a abordar. El principal objetivo de esta tesis es la implementación de una metodología fiable y efectiva, capaz de detectar el despegue de una banda de FRP en una viga de hormigón armado a partir de una fisura intermedia. Para alcanzar este objetivo se ha implementado un procedimiento de calibración numérica a partir de ensayos experimentales. Para ello, en primer lugar, se ha desarrollado un modelo numérico unidimensional simple y no costoso representativo del comportamiento de este tipo vigas de hormigón reforzadas con FRP, basado en un modelo de fisura discreta para el hormigón y el método de elementos espectrales. La formación progresiva de fisuras a flexion y el consiguiente despegue en la interface entre el hormigón y el FRP se formulan mediante la introducción de un nuevo elemento capaz de representar ambos fenómenos simultáneamente sin afectar al procedimiento numérico. Además, con el modelo propuesto, se puede obtener de una forma sencilla la respuesta dinámica en altas frecuencias de este tipo de estructuras, lo cual puede hacer muy útil su uso como herramienta de diagnosis y detección del despegue en su fase inicial mediante una monitorización de la variación de las características dinámicas locales de la estructura. Un método de evaluación no destructivo muy prometedor para la monitorización local de las estructuras es el método de la impedancia usando sensores-actuadores piezoeléctricos (PZT). La impedancia eléctrica de los sensores PZT se puede relacionar con la impedancia mecánica de las estructuras donde se encuentran adheridos Ya que la impedancia mecánica de una estructura se verá afectada por su deterioro, se pueden implementar indicadores de daño mediante una comparación del espectro de admitancia (inversa de la impedancia) a lo largo de distintas etapas durante el periodo de servicio de una estructura. Cualquier cambio en el espectro se podría interpretar como una variación en la integridad de la estructura. La impedancia eléctrica se mide a altas frecuencias con lo cual esta metodología debería ser muy sensible a la detección de estados de daño incipiente local, tal como se desea en la aplicación de este trabajo. Se ha implementado un elemento espectral PZT-FRP como extensión del modelo previamente desarrollado, con el objetivo de poder calcular numéricamente la impedancia eléctrica de sensores PZT adheridos a bandas de FRP sobre una viga de hormigón armado. El modelo, combinado con medidas experimentales captadas mediante sensores PZT, se implementa en el marco de una metodología de calibración de modelos para detectar cuantitativamente el despegue en la interfase entre una banda de FRP y una viga de hormigón. El procedimiento de optimización se resuelve empleando el método del enjambre cooperativo con un algoritmo bagging. Los resultados muestran una gran aproximación en la estimación del daño para el problema propuesto. Adicionalmente, se ha desarrollado también un método adaptativo para el mallado de elementos espectrales con el objetivo de localizar las zonas dañadas a partir de los resultados experimentales, el cual contribuye a aumentar la robustez y efectividad del método propuesto a la hora de identificar daños incipientes en su aparición inicial. Finalmente, se ha llevado a cabo un procedimiento de optimización multi-objetivo para detectar el despegue inicial en una viga de hormigón a escala real reforzada con FRP a partir de las impedancias captadas con una red de sensores PZT instrumentada a lo largo de la longitud de la viga. Cada sensor aporta los datos para definir cada una de las funciones objetivo que definen el procedimiento. Combinando el modelo previo de elementos espectrales con un algoritmo PSO multi-objetivo el procedimiento de detección de daño resultante proporciona resultados satisfactorios considerando la escala de la estructura y todas las incertidumbres características ligadas a este proceso. Los resultados obtenidos prueban la viabilidad y capacidad de los métodos antes mencionados y también su potencial en aplicaciones reales. Abstract Nowadays, the external bonding of fibre reinforced polymer (FRP) plates or sheets is increasingly used for the strengthening and retrofitting of reinforced concrete (RC) structures due to its numerous advantages. However, this kind of strengthening often leads to brittle failure modes being the most dominant failure mode the debonding induced by an intermediate crack (IC). In spite of its importance, the number of studies regarding the IC debonding mechanism and bond health monitoring is very limited. Methodologies able to monitor the long-term efficiency of bonding and successfully identify the initiation of FRP debonding constitute a challenge to be met. The main purpose of this thesisis the implementation of a reliable and effective methodology of damage identification able to detect intermediate crack debonding in FRP-strengthened RC beams. To achieve this goal, a model updating procedure based on numerical simulations and experimental tests has been implemented. For it, firstly, a simple and non-expensive one-dimensional model based on the discrete crack approach for concrete and the spectral element method has been developed. The progressive formation of flexural cracks and subsequent concrete-FRP interfacial debonding is formulated by the introduction of a new element able to represent both phenomena simultaneously without perturbing the numerical procedure. Furthermore, with the proposed model, high frequency dynamic response for these kinds of structures can also be obtained in a very simple and non-expensive way, which makes this procedure very useful as a tool for diagnoses and detection of debonding in its initial stage by monitoring the change in local dynamic characteristics. One very promising active non-destructive evaluation method for local monitoring is impedance-based structural health monitoring(SHM)using piezoelectric ceramic (PZT) sensor-actuators. The electrical impedance of the PZT can be directly related to the mechanical impedance of the host structural component where the PZT transducers are attached. Since the structural mechanical impedance will be affected by the presence of structural damage, comparisons of admittance (inverse of impedance) spectra at various times during the service period of the structure can be used as damage indicator. Any change in the spectra might be an indication of a change in the structural integrity. The electrical impedance is measured at high frequencies with which this methodology appears to be very sensitive to incipient damage in structural systems as desired for our application. Abonded-PZT-FRP spectral beam element approach based on an extension of the previous discrete crack approach is implemented in the calculation of the electrical impedance of the PZT transducer bonded to the FRP plates of a RC beam. This approach in conjunction with the experimental measurements of PZT actuator-sensors mounted on the structure is used to present an updating methodology to quantitatively detect interfacial debonding between a FRP strip and the host RC structure. The updating procedure is solved by using an ensemble particle swarm optimization approach with abagging algorithm, and the results demonstrate a big improvement for the performance and accuracy of the damage detection in the proposed problem. Additionally, an adaptive strategy of spectral element mesh has been also developed to detect damage location with experimental results, which shows the robustness and effectiveness of the proposed method to identify initial and incipient damages at its early stage. Lastly, multi-objective optimization has been carried out to detect debonding damage in a real scale FRP-strengthened RC beam by using impedance signatures. A net of PZT sensors is distributed along the beam to construct impedance-based multiple objectives under gradually induced damage scenario. By combining the spectral element model presented previously and an ensemble multi-objective PSO algorithm, the implemented damage detection process yields satisfactory predictions considering the scale and uncertainties of the structure. The obtained results prove the feasibility and capability of the aforementioned methods and also their potentials in real engineering applications.

Acoustic characterization of open cavities with the image source model

El objetivo de esta tesis es investigar las resonancias acústicas de una cavidad abierta tridimensional, de paredes rectas o inclinadas, mediante un método rápido y eficiente en el dominio del tiempo. Este método modela la respuesta temporal en cualquier punto como la convolución de la forma de onda de la fuente con la respuesta impulsiva de la cavidad, la cual se obtiene como una secuencia de impulsos retardados y atenuados procedentes de la fuente real, el primero, y de las fuentes imágenes especulares, los siguientes (Modelo Fuente Imagen, ISM). Además de las componentes directa y reflejadas en las paredes, la respuesta impulsiva también incluye las contribuciones difractadas en los bordes, obtenidas mediante la generación de las componentes difractadas de cada fuente imagen. Las frecuencias de resonancia acústica de la cavidad abierta son extraídas de los picos de la Función de Respuesta en Frecuencia (FRF), obtenida como la transformada de Fourier de la respuesta temporal correspondiente entre una fuente puntual y un punto cualquiera de la cavidad. Las frecuencias de resonancia acústicas estimadas mediante este Método de Fuentes Imagen + difracción en bordes son validadas por comparación con las que proporciona un Modelo de Elementos Finitos (FEM) y con las medidas experimentalmente, con diferencias menores que el 1.6 % y el 2.7 %, respectivamente. A modo de comparación, las frecuencias de resonancia estimadas para la misma cavidad por el método ISM, cuando no se incluye la difracción en los bordes, difieren en un 5.7 % de las obtenidas experimentalmente. ABSTRACT The goal of this thesis is to investigate the acoustic resonances of a three-dimensional open cavity, with parallel and non-parallel walls, by a fast and efficient method in the time domain. This method models the time response in any point as the convolution of the source waveform with the impulse response of the cavity, which, in turn, is obtained as a sequence of attenuated and delayed impulses coming, the first from the real, and the subsequent from the mirror imaged sources (Image Source Model). Besides direct and wall-reflected components, the impulse response includes also edge-diffracted contributions by generating first order diffraction components for each image source. The acoustic resonance frequencies of the open cavity are extracted from the peaks of the Frequency Response Function (FRF), obtained as the Fourier transform of the corresponding time response between a point source and any point in the cavity. The acoustic resonance frequencies estimated by the Image Source Model + edge diffraction are validated by comparison with those provided by a Finite Element Model (FEM) and the ones measured experimentally, differing less than 1.6 % and 2.7 %, respectively. As a comparison, resonance frequencies estimated with the pure Image Source Model differ by 5.7 % from the measured ones.

Modelling the Impact of Built Environment, Geographical Scales and Latent Constructs On Individual Travel Behaviour

La relación entre la estructura urbana y la movilidad ha sido estudiada desde hace más de 70 años. El entorno urbano incluye múltiples dimensiones como por ejemplo: la estructura urbana, los usos de suelo, la distribución de instalaciones diversas (comercios, escuelas y zonas de restauración, parking, etc.). Al realizar una revisión de la literatura existente en este contexto, se encuentran distintos análisis, metodologías, escalas geográficas y dimensiones, tanto de la movilidad como de la estructura urbana. En este sentido, se trata de una relación muy estudiada pero muy compleja, sobre la que no existe hasta el momento un consenso sobre qué dimensión del entorno urbano influye sobre qué dimensión de la movilidad, y cuál es la manera apropiada de representar esta relación. Con el propósito de contestar estas preguntas investigación, la presente tesis tiene los siguientes objetivos generales: (1) Contribuir al mejor entendimiento de la compleja relación estructura urbana y movilidad. y (2) Entender el rol de los atributos latentes en la relación entorno urbano y movilidad. El objetivo específico de la tesis es analizar la influencia del entorno urbano sobre dos dimensiones de la movilidad: número de viajes y tipo de tour. Vista la complejidad de la relación entorno urbano y movilidad, se pretende contribuir al mejor entendimiento de la relación a través de la utilización de 3 escalas geográficas de las variables y del análisis de la influencia de efectos inobservados en la movilidad. Para el análisis se utiliza una base de datos conformada por tres tipos de datos: (1) Una encuesta de movilidad realizada durante los años 2006 y 2007. Se obtuvo un total de 943 encuestas, en 3 barrios de Madrid: Chamberí, Pozuelo y Algete. (2) Información municipal del Instituto Nacional de Estadística: dicha información se encuentra enlazada con los orígenes y destinos de los viajes recogidos en la encuesta. Y (3) Información georeferenciada en Arc-GIS de los hogares participantes en la encuesta: la base de datos contiene información respecto a la estructura de las calles, localización de escuelas, parking, centros médicos y lugares de restauración. Se analizó la correlación entre e intra-grupos y se modelizaron 4 casos de atributos bajo la estructura ordinal logit. Posteriormente se evalúa la auto-selección a través de la estimación conjunta de las elecciones de tipo de barrio y número de viajes. La elección del tipo de barrio consta de 3 alternativas: CBD, Urban y Suburban, según la zona de residencia recogida en las encuestas. Mientras que la elección del número de viajes consta de 4 categorías ordinales: 0 viajes, 1-2 viajes, 3-4 viajes y 5 o más viajes. A partir de la mejor especificación del modelo ordinal logit. Se desarrolló un modelo joint mixed-ordinal conjunto. Los resultados indican que las variables exógenas requieren un análisis exhaustivo de correlaciones con el fin de evitar resultados sesgados. ha determinado que es importante medir los atributos del BE donde se realiza el viaje, pero también la información municipal es muy explicativa de la movilidad individual. Por tanto, la percepción de las zonas de destino a nivel municipal es considerada importante. En el contexto de la Auto-selección (self-selection) es importante modelizar conjuntamente las decisiones. La Auto-selección existe, puesto que los parámetros estimados conjuntamente son significativos. Sin embargo, sólo ciertos atributos del entorno urbano son igualmente importantes sobre la elección de la zona de residencia y frecuencia de viajes. Para analizar la Propensión al Viaje, se desarrolló un modelo híbrido, formado por: una variable latente, un indicador y un modelo de elección discreta. La variable latente se denomina “Propensión al Viaje”, cuyo indicador en ecuación de medida es el número de viajes; la elección discreta es el tipo de tour. El modelo de elección consiste en 5 alternativas, según la jerarquía de actividades establecida en la tesis: HOME, no realiza viajes durante el día de estudio, HWH tour cuya actividad principal es el trabajo o estudios, y no se realizan paradas intermedias; HWHs tour si el individuo reaiza paradas intermedias; HOH tour cuya actividad principal es distinta a trabajo y estudios, y no se realizan paradas intermedias; HOHs donde se realizan paradas intermedias. Para llegar a la mejor especificación del modelo, se realizó un trabajo importante considerando diferentes estructuras de modelos y tres tipos de estimaciones. De tal manera, se obtuvieron parámetros consistentes y eficientes. Los resultados muestran que la modelización de los tours, representa una ventaja sobre la modelización de los viajes, puesto que supera las limitaciones de espacio y tiempo, enlazando los viajes realizados por la misma persona en el día de estudio. La propensión al viaje (PT) existe y es específica para cada tipo de tour. Los parámetros estimados en el modelo híbrido resultaron significativos y distintos para cada alternativa de tipo de tour. Por último, en la tesis se verifica que los modelos híbridos representan una mejora sobre los modelos tradicionales de elección discreta, dando como resultado parámetros consistentes y más robustos. En cuanto a políticas de transporte, se ha demostrado que los atributos del entorno urbano son más importantes que los LOS (Level of Service) en la generación de tours multi-etapas. la presente tesis representa el primer análisis empírico de la relación entre los tipos de tours y la propensión al viaje. El concepto Propensity to Travel ha sido desarrollado exclusivamente para la tesis. Igualmente, el desarrollo de un modelo conjunto RC-Number of trips basado en tres escalas de medida representa innovación en cuanto a la comparación de las escalas geográficas, que no había sido hecha en la modelización de la self-selection. The relationship between built environment (BE) and travel behaviour (TB) has been studied in a number of cases, using several methods - aggregate and disaggregate approaches - and different focuses – trip frequency, automobile use, and vehicle miles travelled and so on. Definitely, travel is generated by the need to undertake activities and obtain services, and there is a general consensus that urban components affect TB. However researches are still needed to better understand which components of the travel behaviour are affected most and by which of the urban components. In order to fill the gap in the research, the present dissertation faced two main objectives: (1) To contribute to the better understanding of the relationship between travel demand and urban environment. And (2) To develop an econometric model for estimating travel demand with urban environment attributes. With this purpose, the present thesis faced an exhaustive research and computation of land-use variables in order to find the best representation of BE for modelling trip frequency. In particular two empirical analyses are carried out: 1. Estimation of three dimensions of travel demand using dimensions of urban environment. We compare different travel dimensions and geographical scales, and we measure self-selection contribution following the joint models. 2. Develop a hybrid model, integrated latent variable and discrete choice model. The implementation of hybrid models is new in the analysis of land-use and travel behaviour. BE and TB explicitly interact and allow richness information about a specific individual decision process For all empirical analysis is used a data-base from a survey conducted in 2006 and 2007 in Madrid. Spatial attributes describing neighbourhood environment are derived from different data sources: National Institute of Statistics-INE (Administrative: municipality and district) and GIS (circular units). INE provides raw data for such spatial units as: municipality and district. The construction of census units is trivial as the census bureau provides tables that readily define districts and municipalities. The construction of circular units requires us to determine the radius and associate the spatial information to our households. The first empirical part analyzes trip frequency by applying an ordered logit model. In this part is studied the effect of socio-economic, transport and land use characteristics on two travel dimensions: trip frequency and type of tour. In particular the land use is defined in terms of type of neighbourhoods and types of dwellers. Three neighbourhood representations are explored, and described three for constructing neighbourhood attributes. In particular administrative units are examined to represent neighbourhood and circular – unit representation. Ordered logit models are applied, while ordinal logit models are well-known, an intensive work for constructing a spatial attributes was carried out. On the other hand, the second empirical analysis consists of the development of an innovative econometric model that considers a latent variable called “propensity to travel”, and choice model is the choice of type of tour. The first two specifications of ordinal models help to estimate this latent variable. The latent variable is unobserved but the manifestation is called “indicators”, then the probability of choosing an alternative of tour is conditional to the probability of latent variable and type of tour. Since latent variable is unknown we fit the integral over its distribution. Four “sets of best variables” are specified, following the specification obtained from the correlation analysis. The results evidence that the relative importance of SE variables versus BE variables depends on how BE variables are measured. We found that each of these three spatial scales has its intangible qualities and drawbacks. Spatial scales play an important role on predicting travel demand due to the variability in measures at trip origin/destinations within the same administrative unit (municipality, district and so on). Larger units will produce less variation in data; but it does not affect certain variables, such as public transport supply, that are more significant at municipality level. By contrast, land-use measures are more efficient at district level. Self-selection in this context, is weak. Thus, the influence of BE attributes is true. The results of the hybrid model show that unobserved factors affect the choice of tour complexity. The latent variable used in this model is propensity to travel that is explained by socioeconomic aspects and neighbourhood attributes. The results show that neighbourhood attributes have indeed a significant impact on the choice of the type of tours either directly and through the propensity to travel. The propensity to travel has a different impact depending on the structure of each tour and increases the probability of choosing more complex tours, such as tours with many intermediate stops. The integration of choice and latent variable model shows that omitting important perception and attitudes leads to inconsistent estimates. The results also indicate that goodness of fit improves by adding the latent variable in both sequential and simultaneous estimation. There are significant differences in the sensitivity to the latent variable across alternatives. In general, as expected, the hybrid models show a major improvement into the goodness of fit of the model, compared to a classical discrete choice model that does not incorporate latent effects. The integrated model leads to a more detailed analysis of the behavioural process. Summarizing, the effect that built environment characteristics on trip frequency studied is deeply analyzed. In particular we tried to better understand how land use characteristics can be defined and measured and which of these measures do have really an impact on trip frequency. We also tried to test the superiority of HCM on this field. We can concluded that HCM shows a major improvement into the goodness of fit of the model, compared to classical discrete choice model that does not incorporate latent effects. And consequently, the application of HCM shows the importance of LV on the decision of tour complexity. People are more elastic to built environment attributes than level of services. Thus, policy implications must take place to develop more mixed areas, work-places in combination with commercial retails.

Modelización por métodos numéricos de la degradación térmica de un elemento estructural de madera en situación de incendio

La cuantificación de la reducción de las propiedades resistentes y de la sección de un elemento estructural en situación de incendio es fundamental de cara a garantizar la estabilidad estructural en situación de incendio. Existen investigaciones que tratan de determinar la variación de las propiedades térmicas y mecánicas de la madera sometida a cargas térmicas, y la reducción de sección transversal de un elemento estructural de madera. La normativa europea en materia de construcción con madera, el Eurocódigo 5, propone unas simplificaciones para determinar la sección residual de un elemento estructural de madera en situación de incendio. Los objetivos de este trabajo comprenden una revisión de algunos trabajos realizados en el campo de la variación en función de la temperatura de las propiedades térmicas de la madera (calor específico, densidad y conductividad térmica), y la construcción con los distintos valores propuestos de varios modelos de elementos finitos que se someterán a cargas térmicas definidas por la curva ISO 834-1. Los resultados se compararán con un modelo construido con los valores que el Eurocódigo propone y con un ensayo experimental. Como resultado final, se propone finalmente un modelo de elementos finitos que emule el comportamiento del ensayo experimental. The quantification of the decrease of strength properties and section of a structural element in a fire situation is critical in order to guarantee the structural stability in such a fire event. There are some researches in literature trying to find the variation of thermal and mechanical properties of wood subjected to thermal loads, and the decrease of cross section of a wooden structural element. The European legislation on timber construction, Eurocode 5, proposes a simplification to determine the residual section of a wooden structural element in a fire situation. This paper objectives consist in a review of some researches in the field of variations, depending on the temperature, of the thermal properties of wood (specific heat, density and thermal conductivity); and in the construction of a few finite element models of timber structural elements affected by thermal loads according to ISO 834-1. The results were compared with a model based in Eurocode 5 and with an experimental test. As final result, at last, we propose a finite element model that simulates the behavior of the experimental tested element.

Dynamic analysis using finite elements to calculate the critical wear section of the contact wire in suburban railway overhead conductor rails

The purpose of this study is to determine the critical wear levels of the contact wire of the catenary on metropolitan lines. The study has focussed on the zones of contact wire where localised wear is produced, normally associated with the appearance of electric arcs. To this end, a finite element model has been developed to study the dynamics of pantograph-catenary interaction. The model includes a zone of localised wear and a singularity in the contact wire in order to simulate the worst case scenario from the point of view of stresses. In order to consider the different stages in the wire wear process, different depths and widths of the localised wear zone were defined. The results of the dynamic simulations performed for each stage of wear let the area of the minimum resistant section of the contact wire be determined for which stresses are greater than the allowable stress. The maximum tensile stress reached in the contact wire shows a clear sensitivity to the size of the local wear zone, defined by its width and depth. In this way, if the wear measurements taken with an overhead line recording vehicle are analysed, it will be possible to calculate the potential breakage risk of the wire. A strong dependence of the tensile forces of the contact wire has also been observed. These results will allow priorities to be set for replacing the most critical sections of wire, thereby making maintenance much more efficient. The results obtained show that the wire replacement criteria currently borne in mind have turned out to be appropriate, although in some wear scenarios these criteria could be adjusted even more, and so prolong the life cycle of the contact wire.

Improved design of an overhead rail current conductor for application in underground lines

Overhead rail current collector systems for railway traction offer certain features, such as low installation height and reduced maintenance, which make them predominantly suitable for use in underground train infrastructures. Due to the increased demands of modern catenary systems and higher running speeds of new vehicles, a more capable design of the conductor rail is needed. A new overhead conductor rail has been developed and its design has been patented [13]. Modern simulation and modelling techniques were used in the development approach. The new conductor rail profile has a dynamic behaviour superior to that of the system currently in use. Its innovative design permits either an increase of catenary support spacing or a higher vehicle running speed. Both options ensure savings in installation or operating costs. The simulation model used to optimise the existing conductor rail profile included both a finite element model of the catenary and a three-dimensional multi-body system model of the pantograph. The contact force that appears between pantograph and catenary was obtained in simulation. A sensitivity analysis of the key parameters that influence in catenary dynamics was carried out, finally leading to the improved design.

Dynamic Effects On Culverts for High Speed Trains

Culverts are very common in recent railway lines. Wild life corridors and drainage conducts often fall in this category of partially buried structures. Their dynamic behavior has received far less attention than other structures such as bridges but its large number makes that study an interesting challenge from the point of view of safety and savings. In this paper a complete study of a culvert, including on-site measurements as well as numerical modelling, will be presented. The structure belongs to the high speed railway line linking Segovia and Valladolid, in Spain. The line was opened to traffic in 2004. Its dimensions (3x3m) are the most frequent along the line. Other factors such as reduced overburden (0.6m) and an almost right angle with the track axis make it an interesting example to extract generalized conclusions. On site measurements have been performed in the structure recording the dynamic response at selected points of the structure during the passage of high speed trains at speeds ranging between 200 and 300km/h. The measurements by themselves provide a good insight into the main features of the dynamic behaviour of the structure. A 3D finite element model of the structure, representing its key features was also studied as it allows further understanding of the dynamic response to the train loads . In the paper the discrepancies between predicted and measured vibration levels will be analyzed and some advices on numerical modelling will be proposed

Operational Modal Analysis on laminated glass beams

Laminated glass is a sandwich element consisting of two or more glass sheets, with one or more interlayers of polyvinyl butyral (PVB). The dynamic response of laminated glass beams and plates can be predicted using analytical or numerical models in which the glass and the PVB are usually modelled as linear-elastic and linear viscoelastic materials, respectively. In this work the dynamic behavior of laminated glass beams are predicted using a finite element model and the analytical model of Ross-Kerwin-Ungar. The numerical and analytical results are compared with those obtained by operational modal analysis performed at different temperatures.

Amplificador de señal analógico basado en conceptos biomiméticos. Desarrollo de modelos computacionales y validación experimental

La presente tesis doctoral estudia las características de un transductor acústico bioinspirado en la estructura del maxilar inferior de un Zifio de Couvier (Ziphius cavirostris). El mecanismo de funcionamiento del sensor se basa en las características de un sistema acoplado formado por los distintos componentes acústicos identificados en el maxilar. Para analizar las características del sensor se propone un modelo simplificado 2D que consta de una cavidad cerrada con forma de bocina acoplada a una lengüeta. Una parte de la lengüeta se encuentra dentro de la cavidad y otra en el exterior. Dicha lengüeta detecta los cambios de presión acústica y las vibraciones generadas por el sonido y las transmite con ondas de flexión al interior de la cavidad. La excitación prolongada sobre la placa puede provocar la activación de los modos propios del sistema acoplado. Dichos modos se caracterizan porque presentan un máximo de presión en el cono de la bocina la cual a su vez actúa como un amplificador acústico. Mediante el Método de los elementos Finitos se analizan las características acústicas del sensor y se construye un prototipo experimental para validar los resultados evaluados en el modelo numérico. Se propone una metodología numérica que permite desarrollar y validar un elemento tetraédrico para caracterizar el comportamiento isotrópico de los medios porosos. La metodología permite construir elementos de línea y bidimensionales. A partir de esta metodología se desarrolla un elemento plano ortotrópico. Se realiza un modelo de la cavidad en el que una de las paredes de la bocina está constituida por material poroso y se une la parte exterior de la lengüeta a dicho material para que constituya una viga sobre un apoyo elástico. Se calcula la respuesta modal y se discuten los efectos del material poroso en la eficiencia del transductor y las posibles mejoras a introducir en el mismo. SUMMARY This Thesis studies the characteristics of an acoustic transducer bioinspired by the structure of the lower maxilla of an odontoceto. In this case a Cuvier’s beaked whale (Ziphius cavirostris). The transducer working mechanism is based in a coupled system, with components identified in the maxilla. To analyze the transducer a simplified 2D model composed by a horn shaped closed cavity is modeled. The cavity is coupled with a flat belt. The belt has one part inside the cavity and the other part outside of it. The belt traverses the cavity wall and it is in charge to pick the vibrations from outside and introduce it inside the cavity. The transmission is obtained through the belt bending. A sustained external load with the right frequency contents will allow the system to reach a stationary pressure intensity distribution inside the cavity. Frequencies with modal shapes that show an important intensity increase at the horn tip are of special interest because of the signal amplification. A finite element model is constructed to study the transducer coupled modes and a prototype is constructed to validate the numerical results. A numerical methodology to construct and validate a tetrahedral finite element for isotropic porous materials is presented. The methodology allows constructing linear and 2D elements. It is extended to model orthotropic porous materials behavior. At the end, one of the horn walls is made of an orthotropic material and the external belt is glued to it in order to configure a belt over an elastic foundation. Modal response is evaluated and the porous material effects in the transducer efficiency and further improvements are discussed.

Improving the analysis of road pricing acceptability surveys by using hybrid models

Several international studies have analyzed the acceptability of road pricing schemes by means of an attitude survey in combination with the results of a stated choice experiment using both a descriptive analysis and a discrete-choice model with binary choice (?accept? or ?not accept? the toll). However, the use of hybrid discrete choice models constitutes an innovative alternative for integrating subjective attitudes and perceptions deriving from the survey of attitudes with the more objective variables from the stated choice experiment. This paper analyzes the results of applying these models to measure the acceptability of interurban road pricing among different groups of stakeholders (road freight and passenger operators, highway concessionaires, and associations of private car users) with qualitatively significant opinions on road pricing measures. Our results show that hybrid models are better suited to explaining the acceptability of a road pricing scheme by different groups of stakeholders than a separate analysis of the survey of attitudes and a discrete-choice model applied on a stated choice experiment. A particular finding was that the strong psycho-social latent variable of the perception of fairness explains the rejection or acceptance of a toll scheme by road stakeholders.

Estudio numérico y experimental del efecto de tamaño en modo mixto de los paneles de yeso laminado y lana de roca

Los paneles sándwich de yeso laminado y lana de roca presentan una abundante patología de fisuración debida a flechas excesivas de forjados. Existe, por tanto, la necesidad de avanzar en la simulación y predicción de comportamiento bajo solicitaciones de tracción y cortante de ese tipo de paneles, a pesar de que en las aplicaciones habituales no tienen responsabilidad estructural. El comportamiento de este material puede ser considerado cuasi-frágil, y en base a ello en este trabajo ha sido estudiado haciendo uso de modelos de fisura cohesiva, cuya aplicación a otros materiales cuasifrágiles, como el hormigón, ha aportado resultados muy satisfactorios. En esta comunicación se presenta el trabajo realizado para estudiar el efecto del tamaño del elemento de yeso laminado y lana de roca en su comportamiento mecánico-resistente. Para ello se diseñó una campaña de ensayos en modo mixto sobre probetas de diferente tamaño. Se han realizado ensayos de flexión en tres puntos en modo mixto de unas probetas entalladas, geométricamente similares y de diferente tamaño, obteniéndose las curvas carga-desplazamiento y cargaabertura de la boca de la entalla. Para simular numéricamente el comportamiento en fractura del panel en modo mixto se ha utilizado un modelo de elementos finitos con fisura embebida basado en la fisura cohesiva en el que se introducen como entrada los parámetros obtenidos a partir de la experimentación de trabajos anteriores, obteniéndose un buen ajuste. En función de estos resultados se analiza el efecto del tamaño en los paneles. Sandwich panels of laminated gypsum and rockwool have an abundant pathology of cracking due to excessive slabs deflection. Therefore, it is necessary to progress in the simulation and prediction of behaviour under tensile and shear load of such panels, although in typical applications have no structural responsability. The behaviour of this material may be considered quasi-brittle and, based on this idea, in this work has been studied using a cohesive crack model that has been applied to other quasi-brittle materials, such as concrete, and has provided very satisfactory results. This communication presents the work carried out to study the size effect of the specimen of plasterboard and rockwool in its mechanical and resistant behaviour. The authors designed an experimental campaign under mixed mode composed by testing specimens of different sizes. Assymetrical three-point bending tests have been performed on notched specimens, geometrically similar and of different size, to obtain load-displacement and load-crack moutn opening displacement curves. To numerically simulate the mixed-mode fracture behaviour of the panels we have used a finite element model with embedded crack, based on the cohesive crack model, using as input the experimental parameters obtained in previous work, obtaining a good adjustment. Based on these results we analyze the size effect of the panels

Computational Methods for Identification of Vibrating Structures

System identification deals with the problem of building mathematical models of dynamical systems based on observed data from the system" [1]. In the context of civil engineering, the system refers to a large scale structure such as a building, bridge, or an offshore structure, and identification mostly involves the determination of modal parameters (the natural frequencies, damping ratios, and mode shapes). This paper presents some modal identification results obtained using a state-of-the-art time domain system identification method (data-driven stochastic subspace algorithms [2]) applied to the output-only data measured in a steel arch bridge. First, a three dimensional finite element model was developed for the numerical analysis of the structure using ANSYS. Modal analysis was carried out and modal parameters were extracted in the frequency range of interest, 0-10 Hz. The results obtained from the finite element modal analysis were used to determine the location of the sensors. After that, ambient vibration tests were conducted during April 23-24, 2009. The response of the structure was measured using eight accelerometers. Two stations of three sensors were formed (triaxial stations). These sensors were held stationary for reference during the test. The two remaining sensors were placed at the different measurement points along the bridge deck, in which only vertical and transversal measurements were conducted (biaxial stations). Point estimate and interval estimate have been carried out in the state space model using these ambient vibration measurements. In the case of parametric models (like state space), the dynamic behaviour of a system is described using mathematical models. Then, mathematical relationships can be established between modal parameters and estimated point parameters (thus, it is common to use experimental modal analysis as a synonym for system identification). Stable modal parameters are found using a stabilization diagram. Furthermore, this paper proposes a method for assessing the precision of estimates of the parameters of state-space models (confidence interval). This approach employs the nonparametric bootstrap procedure [3] and is applied to subspace parameter estimation algorithm. Using bootstrap results, a plot similar to a stabilization diagram is developed. These graphics differentiate system modes from spurious noise modes for a given order system. Additionally, using the modal assurance criterion, the experimental modes obtained have been compared with those evaluated from a finite element analysis. A quite good agreement between numerical and experimental results is observed.

Estudio numérico y experimental del efecto de tamaño en modo mixto de los paneles de yeso laminado y lana de roca

Los paneles sándwich de yeso laminado y lana de roca presentan una abundante patología de fisuración debida a flechas excesivas de forjados. Existe, por tanto, la necesidad de avanzar en la simulación y predicción de comportamiento bajo solicitaciones de tracción y cortante de ese tipo de paneles, a pesar de que en las aplicaciones habituales no tienen responsabilidad estructural. El comportamiento de este material puede ser considerado cuasi-frágil, y en base a ello en este trabajo ha sido estudiado haciendo uso de modelos de fisura cohesiva, cuya aplicación a otros materiales cuasifrágiles, como el hormigón, ha aportado resultados muy satisfactorios. En esta comunicación se presenta el trabajo realizado para estudiar el efecto del tamaño del elemento de yeso laminado y lana de roca en su comportamiento mecánico-resistente. Para ello se diseñó una campaña de ensayos en modo mixto sobre probetas de diferente tamaño. Se han realizado ensayos de flexión en tres puntos en modo mixto de unas probetas entalladas, geométricamente similares y de diferente tamaño, obteniéndose las curvas carga-desplazamiento y cargaabertura de la boca de la entalla. Para simular numéricamente el comportamiento en fractura del panel en modo mixto se ha utilizado un modelo de elementos finitos con fisura embebida basado en la fisura cohesiva en el que se introducen como entrada los parámetros obtenidos a partir de la experimentación de trabajos anteriores, obteniéndose un buen ajuste. En función de estos resultados se analiza el efecto del tamaño en los paneles. Sandwich panels of laminated gypsum and rockwool have an abundant pathology of cracking due to excessive slabs deflection. Therefore, it is necessary to progress in the simulation and prediction of behaviour under tensile and shear load of such panels, although in typical applications have no structural responsability. The behaviour of this material may be considered quasi-brittle and, based on this idea, in this work has been studied using a cohesive crack model that has been applied to other quasi-brittle materials, such as concrete, and has provided very satisfactory results. This communication presents the work carried out to study the size effect of the specimen of plasterboard and rockwool in its mechanical and resistant behaviour. The authors designed an experimental campaign under mixed mode composed by testing specimens of different sizes. Assymetrical three-point bending tests have been performed on notched specimens, geometrically similar and of different size, to obtain load-displacement and load-crack moutn opening displacement curves. To numerically simulate the mixed-mode fracture behaviour of the panels we have used a finite element model with embedded crack, based on the cohesive crack model, using as input the experimental parameters obtained in previous work, obtaining a good adjustment. Based on these results we analyze the size effect of the panels.

Study of the Edge and Surface Cracks Influence in the Mechanical Strength of Silicon Wafers

The objective of the present study is the estimation of the depth to which the wire sawing process causes damage to the wafer surfaces. Previous analyses were carried out by means of the four line bending test. The characteristic of this test implied that the failure could be due to surface cracks located in the central zone of the wafer or near the edges. In order to evaluate the influence of the edge or surface cracks a new study has been carried out using the ball/ring on ring test. Description and results of the tests are presented. The preliminary analysis of the failure stress using analytical methods confirms the expected results. A Finite Element model developed to get more information of the test results is also presented.