Using the method of matched asymptotic expansions the reflection and transmission coefficients are calculated for scattering of oblique water waves by a vertical barrier. Here an assumption is made that the barrier is small compared to the wavelength and the depth of water. A number of sloshing problems are considered. The eigenfrequencies are calculated when a body is placed in a rectangular tank. Here the bodies considered are a vertical surface-piercing or bottom-mounted barrier, and circular and elliptic cylinders. When the body is a vertical barrier, the eigenfunction expansion method is applied. When the body is either a circular or elliptic cylinder, and the motion is two-dimensional, the boundary element method is applied to calculate the eigenfrequencies. For comparison, two approximations, "a wide-spacing", and "a small-body" are used for a vertical barrier and circular cylinder. In the wide-spacing approximation, the assumption is made that the wavelength is small compared with the distance between the body and walls. The small-body approximation means that a typical dimension of the body is much larger than the cross-sectional length scale of the fluid motion. For an elliptic cylinder, the method of matched asymptotic expansions is used and compared with the result of the boundary- element method. Also a higher-order solution is obtained using the method of matched asymptotic expansions, and it is compared with the exact solution for a surface-piercing barrier. Again the assumption is made that the length scale of the motion is much larger than a typical body dimension. Finally, the drift force on multiple bodies is considered the ratio of horizontal drift force in the direction of wave advance on two cylinders to that on an isolated cylinder is calculated. The method of matched asymptotic expansions is used under the assumption that the wavelength is much greater than the cylinder spacing.

The economic and technologic development experienced by the society in the last decades has caused the demand of a new type of faster and more comfortable transport. This type of demand has been covered by the air transport, the road transport and the railway transport. This situation where the society demands an improvement in her quality of life is the best situation for the birth of the high speed trains. Different studies carried out in the transport field have demonstrated that for distances between four hundred and one thousand of kilometres, the high speed trains provide a lower travelling times than the rest of the transports. These types of high speed trains have increased the axle loads and the average speeds, thus generally a dynamic analysis is required by the ERRI in all the railway bridges when the train speed is higher than 200 Km/h. Besides, when the train speed is going to be higher than 200 Km/h, the vibrations induced in the bridge can reduce the service life of the vehicles and structure, and generally, this fact leads to become the dynamic effect in the principal factor to take into account in order to design the structure. Therefore, an important knowledge in railway bridges dynamic is required to not to oversize the structures with the consequent economic cost. The purpose of this thesis is to study the possibility of accurately predicting the dynamic response of an existing railway bridge, subjected to the high speed train Gröna Tåget, implementing a simplified 2D finite element model with the aid of the program Abaqus. The bridge chosen is the Lögdeälv Bridge, a two spans composite bridge, located along the Bothnia Line (the new Swedish high-speed line), between the localities of Nordmaling and Rundvik. The measured eigenfrequencies due to bending modes of vibration are used for updating the model and then, these frequencies and the accelerations measured are used to compare and validate the different 2D updated models. The parameters used to update the models are; the damping coefficient of the structure, the mass and the stiffness of the bridge, and the supports stiffness. Finally it is concluded that the best model is achieved when the rotational support stiffness is modified in the two extremes supporters of the bridge.

Det här projektet har gått ut på att med hjälp av FEdatorprogram analysera hållfastheten hos ett ställdon utvecklat av företaget Cascade Drives. Ställdonet ska användas för att driva en vattenpump som utsätts för laster på upp till 30 ton. Det består av ett växelhus, en elmotor och ett kuggstång-pinionsystem. Motorn sitter direkt på växelhuset med ett motorfäste. De egenskaper som skulle studeras var dels växelhusets deformation och vilka spänningar som uppstod i detta, samt dess egenfrekvenser. Dessutom skulle motorfästes egenfrekvenser och egensvängningar undersökas speciellt för att säkerställa att ingen av de frekvenser som kunde tänkas exciteras vid drift skulle kunna få motorfästet i egensvängning. Motorfästet skulle också modelleras som både aluminium och stål, för att bestämma vilket materialval som var bäst lämpat.  Alla delarna utom kuggstången och dess bussningar erhölls som CADmodeller från Cascade Drives, och analysen gjordes i FEprogrammet Ansys Academic Teaching Mechanical and CFD, 2020 R1, med modulerna Static Structural och Modal. Då licensen begränsade antalet noder som kunde användas i meshen för lösningen till max 256 000 noder, var en del av delarnas geometri tvungna att förenklas genom att ta bort hål, avrundningar och inre ihåligheter. Motorns inre geometri visade sig vara så komplicerad att en helt ny simplifierad modell av den togs fram. Likaså utvecklades enkla modeller av kuggstången och dess bussningar. Allt CADarbete utfördes i programmet Solid Edge 2019.  För att spara noder modellerades inte rullagren eller stängerna som CADmodeller, utan ersattes av joints respektive beam connections i Ansys. Lagerkrafterna som förs över från axlarna till lagersätena modellerades som bearing forces i radiell led. Lagrens och kugghjulens massor simulerades som punktmassor. Inspänningsrandvillkoren sattes på flänsarnas undersidor för att simulera att ställdonet stod på en stålställning. Remote displacement, frictionless support och elastic support användes för detta.  Resultaten visade att växelhuset med god marginal håller för påfrestningarna, och att ingen av dess egenfrekvenser direkt överlappar med excitationsfrekvenserna. Motorfästet görs med fördel av stål, då motorfästets resonansfrekvenser hamnade relativt nära motorfrekvenserna och stålfästets resonansfrekvenser låg högre i spektrumet än frekvenserna för fästet gjort i aluminium. / The purpose of this project was to use FE computer software to analyse the durability of an actuator developed by the company Cascade Drives. The actuator will be used to drive a water pump subjected to loads of up to 30 tonnes. It consists of a gearbox, an electric motor and a rack and pinion system. The motor is directly mounted to the gear housing. The characteristics studied were the deformation of the gearbox, the generated stresses as well as its natural frequencies. Furthermore, the eigenfrequencies of the motor mount were to be investigated to ensure that none of the frequencies excited in the gear housing by the gears and motor risked inducing self-oscillation.  The mount was also to be analysed as if made from steel or aluminium, in order to decide the most appropriate material. All parts except the rack and the bushings were obtained as CAD models from Cascade Drives. The analysis was done in the FE program Ansys Academic Teaching Mechanical and CFD, 2020 R1, with the modules Static Structural and Modal. As the license only allowed a maximum of 256 000 nodes in the mesh, some of the part’s geometries had to be simplified by removing holes, fillets, and cavities. The motor’s geometry was especially complex, and a completely new, simplified model was created, as well as a simple rack and bushing models. All CAD work was done in the software Solid Edge 2019 To further decrease the number of nodes used neither the bearings nor the bars were modelled as CAD models, but rather as joints and beam connections in Ansys. The feature ‘bearing forces’ was used to model the forces from the shafts on the bearing seats. The weight of the gears and bearings were simulated as point masses. In order to simulate the actuator as being mounted on a steel frame, the boundary conditions ‘remote displacement’, ‘frictionless support’ and ‘elastic support’ were added to the bottom of the flanges.  The results showed that the gear housing can withstand the stresses with a good margin, and that none of the eigenfrequencies matched those excited. It also showed that the best material for the mount is steel, as the eigenfrequencies of the steel mount were higher than those of the aluminium mount, which is preferable since they then are further from the motor’s frequency.

With the development of high-speed railroads the dynamic behaviour of railroad bridges is increasingly important to explore. Deeper knowledge about the influence of different factors and what should be included in a model is essential if the designer shall be able to make reliable estimates of responses in existing and new structures. One factor is the soil-structure interaction (SSI), describing how the foundation of the bridge and the soil properties affect the behavior of the bridge under dynamic loading. In this thesis, the influence of including SSI in a model of a portal frame railway bridge is studied, and an analysis procedure in the frequency domain for models with frequency-dependent boundary conditions is described. A 3D finite element model of an e isting bridge has been built up, based on the theory of linear elasticity. The model has been given three different types of boundary conditions: clamped, static stiffness and frequency-dependent stiffness from SSI. Results from simulated train passages, with a train set consisting of two wagons, were compared for the different boundary conditions. The models have also been compared with measurement data from the bridge, which has given indications about which model describes reality in the best way. The results show that the model in which SSI is included by frequency dependent boundary conditions is in slightly better agreement with measurement data than the clamped model and the model with static stiffness. The model gives a slightly better damping of the free vibrations and the natural frequencies correspond better with experimental data. The difference in maximum acceleration from a train passage is very small between the different models, even if it is found that the clamped model generally has lower accelerations and hence is non-conservative. It appears that the train speed affects the maximum acceleration, the size of the free vibrations and the natural frequencies that are present in the free vibrations in the models. Further studies are suggested where it is emphasized that an analysis with longer trains, which give resonance phenomena, should be made to see how the different eigenfrequencies in the models affect the accelerations at different speeds. It is also noted that more measurements would be needed in order to draw more general conclusions about the degree of correspondence between the measurements and the models, and to calibrate the parameters of the model against measurement data.

O projeto de estruturas e máquinas deve considerar as restrições impostas pelas condições de contorno. Tais condições podem ser de natureza dinâmica, limitando assim as faixas de frequência às quais a estrutura ou máquina pode operar. Dentre as diferentes ferramentas disponíveis para trabalhar com restrições dinâmicas, a otimização de forma se mostra como uma interessante alternativa para afastar as frequências naturais das faixas problemáticas. Um modelo de elementos finitos de malha de 4x5 elementos é correlacionado com os resultados de uma análise modal experimental, e a otimização é realizada utilizando-se o software Nastran. Após usinar a placa com a espessura otimizada, boa concordância é atingida entre os resultados experimentais e os previstos numericamente. Apesar dos bons resultados, obter a placa com 4x5 elementos, cada qual com sua espessura, foi difícil por conta das dimensões envolvidas. É mais apropriado fabricar uma superfície contínua na placa com uma geometria conhecida. Para isso, modelos com malhas mais finas são necessários no procedimento de otimização, e tal quantidade de variáveis nem sempre converge a uma solução. De fato, um modelo com 48x60 elementos para a placa estudada não convergiu a uma solução para as mesmas frequências desejadas. A contribuição principal deste trabalho é mostrar que uma interpolação (linear ou cúbica) dos resultados de uma otimização de forma de malha grossa leva à solução do problema de otimização de uma malha mais refinada. Em outras palavras, é possível obter uma geometria de superfície contínua que otimiza frequências naturais em placas a partir de modelos de elementos finitos de malha mais grossa, sendo assim desnecessários modelos de malhas muito refinadas e altos custos computacionais. / The design of structures and machines must consider the restrictions imposed by the boundary conditions. Such conditions can be of dynamic nature, thus limiting the frequency ranges that the structure/machine can operate. Among the different design tools available for dealing with dynamics restrictions, shape optimization is an interesting way of deviating natural frequencies from problematic ranges. In this work, one presents the shape optimization of a cantilever plate aiming at desired natural frequencies. A 4x5 elements grid finite element model is correlated to results from experimental modal analysis, and the optimization is done with help of Nastran software. After machining the plate with optimized thickness, good agreement is achieved between experimental and numerically predicted results. Despite successful results, machining the plate in 4x5 discrete elements with individual (stepped) thickness showed to be cumbersome. It is more appropriated to machine a smooth surface on the plate with known geometry. For that, finer grid element models are necessary in the optimization procedure, and such amount of design variables not always converge to a solution. In fact, a model with 48x60 elements for the plate in study did not converge to a solution for the same target frequencies. The main contribution of this work is showing that an interpolation (linear or cubic) of the coarser grid shape optimization results leads to the solution of a finer grid optimization problem. In other words, it is possible to obtain the smooth surface geometry that optimizes natural frequencies in plates from coarser grid finite element models, thus not requiring fine grid models and high computational costs.

In der vorliegenden Arbeit wird eine Methode zur Charakterisierung von Mikrosystemen mit beweglichen Komponenten dargestellt. Sie erlaubt, funktionsrelevante Parameter und deren Schwankungen produktionsbegleitend auf Waferlevel zu ermitteln. Dabei wird vorausgesetzt, dass die Sollform der Struktur und die Abweichungsarten bekannt sind. Die Methode beruht auf dem Vergleich von numerisch berechneten mit experimentell ermittelten Eigenfrequenzen der untersuchten Mikrosysteme. Dazu wird die Abhängigkeit verschiedener Eigenfrequenzen von den gesuchten Parametern mittels einer Parametervariationsanalyse berechnet und durch eine geeignete Funktion angenähert. Die Messung der dynamischen Eigenschaften erfolgt mit Hilfe eines Bewegungsanalysators, der auf einem Laser-Doppler-Vibrometer basiert. Im letzen Schritt werden die gesuchten Parameter berechnet. Kernpunkt der entwickelten Methode sind Messungen auf der Basis von speziellen Teststrukturen, die im Waferlayout neben den eigentlichen Nutzstrukturen platziert sind und parallel mit den Nutzstrukturen prozessiert werden. Es werden Algorithmen zur Generierung des Designs der Teststrukturen und ihrer Platzierung im Waferlayout entwickelt. Dabei werden das Design der Nutzstruktur und deren funktionsrelevante Parameter, der technologische Ablauf und materialspezifische Kennwerte berücksichtigt. Im Ergebnis liegt eine Bibliothek von Standard-Teststrukturen vor, die für produktionsbegleitende Messungen sowie für die Übertragbarkeit der Ergebnisse geeignet sind. Außerdem werden allgemeingültige Richtlinien zur Durchführung der Messungen an den Standard-Teststrukturen abgeleitet. Das Messverfahren wurde an unterschiedlichen Mikrosystemen mit beweglichen Komponenten überprüft und zu einer allgemeinen Messmethode für diese Klasse von Mikrosystemen erweitert. / In this work a method for the characterization of microsystems with movable components is presented. The method allows to determine the relevant parameters and their variations on wafer level if the nominal shape of the structure and the type of deviations are known. The method is based on a comparison of the numerically calculated and experimentally measured Eigenfrequencies of the microsystems. For that purpose, the relationships between various Eigenfrequencies and the searched parameters are calculated by parameter variation analysis and the results of this analysis are approximated with appropriate functions. A Laser Doppler vibrometer based motion analyzer is used to determine the frequency response function of the micromechanical structure and extract Eigenfrequencies. The comparison of the measured and the calculated frequencies provides values for the searched parameters. The key element of the developed method is the measurement on special test structures that are placed in the wafer layout next to the actual microsystems and processed in the same technological process parallel to the actual microsystems. Algorithms for designing the test structures and their placement in the wafer layout are shown, taking into account the design of the actual microsystems and the function parameters of the technological process as well as material characteristics. As a result, a library of standard test structures for function relevant parameters is available. A general guideline for the measurement on the test structures is presented. The presented method is verified on various microsystems and extended to a whole class of microsystems with movable components.

O projeto de estruturas e máquinas deve considerar as restrições impostas pelas condições de contorno. Tais condições podem ser de natureza dinâmica, limitando assim as faixas de frequência às quais a estrutura ou máquina pode operar. Dentre as diferentes ferramentas disponíveis para trabalhar com restrições dinâmicas, a otimização de forma se mostra como uma interessante alternativa para afastar as frequências naturais das faixas problemáticas. Um modelo de elementos finitos de malha de 4x5 elementos é correlacionado com os resultados de uma análise modal experimental, e a otimização é realizada utilizando-se o software Nastran. Após usinar a placa com a espessura otimizada, boa concordância é atingida entre os resultados experimentais e os previstos numericamente. Apesar dos bons resultados, obter a placa com 4x5 elementos, cada qual com sua espessura, foi difícil por conta das dimensões envolvidas. É mais apropriado fabricar uma superfície contínua na placa com uma geometria conhecida. Para isso, modelos com malhas mais finas são necessários no procedimento de otimização, e tal quantidade de variáveis nem sempre converge a uma solução. De fato, um modelo com 48x60 elementos para a placa estudada não convergiu a uma solução para as mesmas frequências desejadas. A contribuição principal deste trabalho é mostrar que uma interpolação (linear ou cúbica) dos resultados de uma otimização de forma de malha grossa leva à solução do problema de otimização de uma malha mais refinada. Em outras palavras, é possível obter uma geometria de superfície contínua que otimiza frequências naturais em placas a partir de modelos de elementos finitos de malha mais grossa, sendo assim desnecessários modelos de malhas muito refinadas e altos custos computacionais. / The design of structures and machines must consider the restrictions imposed by the boundary conditions. Such conditions can be of dynamic nature, thus limiting the frequency ranges that the structure/machine can operate. Among the different design tools available for dealing with dynamics restrictions, shape optimization is an interesting way of deviating natural frequencies from problematic ranges. In this work, one presents the shape optimization of a cantilever plate aiming at desired natural frequencies. A 4x5 elements grid finite element model is correlated to results from experimental modal analysis, and the optimization is done with help of Nastran software. After machining the plate with optimized thickness, good agreement is achieved between experimental and numerically predicted results. Despite successful results, machining the plate in 4x5 discrete elements with individual (stepped) thickness showed to be cumbersome. It is more appropriated to machine a smooth surface on the plate with known geometry. For that, finer grid element models are necessary in the optimization procedure, and such amount of design variables not always converge to a solution. In fact, a model with 48x60 elements for the plate in study did not converge to a solution for the same target frequencies. The main contribution of this work is showing that an interpolation (linear or cubic) of the coarser grid shape optimization results leads to the solution of a finer grid optimization problem. In other words, it is possible to obtain the smooth surface geometry that optimizes natural frequencies in plates from coarser grid finite element models, thus not requiring fine grid models and high computational costs.

In der vorliegenden Arbeit wird eine Methode zur Charakterisierung von Mikrosystemen mit beweglichen Komponenten dargestellt. Sie erlaubt, funktionsrelevante Parameter und deren Schwankungen produktionsbegleitend auf Waferlevel zu ermitteln. Dabei wird vorausgesetzt, dass die Sollform der Struktur und die Abweichungsarten bekannt sind. Die Methode beruht auf dem Vergleich von numerisch berechneten mit experimentell ermittelten Eigenfrequenzen der untersuchten Mikrosysteme. Dazu wird die Abhängigkeit verschiedener Eigenfrequenzen von den gesuchten Parametern mittels einer Parametervariationsanalyse berechnet und durch eine geeignete Funktion angenähert. Die Messung der dynamischen Eigenschaften erfolgt mit Hilfe eines Bewegungsanalysators, der auf einem Laser-Doppler-Vibrometer basiert. Im letzen Schritt werden die gesuchten Parameter berechnet. Kernpunkt der entwickelten Methode sind Messungen auf der Basis von speziellen Teststrukturen, die im Waferlayout neben den eigentlichen Nutzstrukturen platziert sind und parallel mit den Nutzstrukturen prozessiert werden. Es werden Algorithmen zur Generierung des Designs der Teststrukturen und ihrer Platzierung im Waferlayout entwickelt. Dabei werden das Design der Nutzstruktur und deren funktionsrelevante Parameter, der technologische Ablauf und materialspezifische Kennwerte berücksichtigt. Im Ergebnis liegt eine Bibliothek von Standard-Teststrukturen vor, die für produktionsbegleitende Messungen sowie für die Übertragbarkeit der Ergebnisse geeignet sind. Außerdem werden allgemeingültige Richtlinien zur Durchführung der Messungen an den Standard-Teststrukturen abgeleitet. Das Messverfahren wurde an unterschiedlichen Mikrosystemen mit beweglichen Komponenten überprüft und zu einer allgemeinen Messmethode für diese Klasse von Mikrosystemen erweitert. / In this work a method for the characterization of microsystems with movable components is presented. The method allows to determine the relevant parameters and their variations on wafer level if the nominal shape of the structure and the type of deviations are known. The method is based on a comparison of the numerically calculated and experimentally measured Eigenfrequencies of the microsystems. For that purpose, the relationships between various Eigenfrequencies and the searched parameters are calculated by parameter variation analysis and the results of this analysis are approximated with appropriate functions. A Laser Doppler vibrometer based motion analyzer is used to determine the frequency response function of the micromechanical structure and extract Eigenfrequencies. The comparison of the measured and the calculated frequencies provides values for the searched parameters. The key element of the developed method is the measurement on special test structures that are placed in the wafer layout next to the actual microsystems and processed in the same technological process parallel to the actual microsystems. Algorithms for designing the test structures and their placement in the wafer layout are shown, taking into account the design of the actual microsystems and the function parameters of the technological process as well as material characteristics. As a result, a library of standard test structures for function relevant parameters is available. A general guideline for the measurement on the test structures is presented. The presented method is verified on various microsystems and extended to a whole class of microsystems with movable components.

El análisis y el control de las vibraciones cobra especial importancia en muchas ramas de la ingeniería, en especial la ingeniería mecánica, civil, aeronáutica y automovilística. Tal es así que prácticamente se identi¿ca como un área independiente dentro del análisis dinámico de estructuras. Desde los comienzos de esta teoría, las fuerzas disipativas o de amortiguamiento han sido uno de los fenómenos más difíciles de modelizar. El modelo viscoso, por su sencillez y versatilidad ha sido y sigue siendo el gran paradigma de los modelos de amortiguamiento. Sin embargo, como consecuencia de la aparición de materiales con memoria se introdujo el fenómeno de la viscoelasticidad; Esta, si bien está también 'íntimamente ligada ' a la velocidad de la respuesta, necesito de la introducción de las denominadas funciones hereditarias, que permiten poner a las fuerzas disipativas como función no solo de la velocidad instantánea sino de la historia de velocidades desde el comienzo del movimiento, de ahí el termino memoria. De forma natural, el avance teórico introducido en el modelo supone también una complicación computacional, pues donde antes teníamos un sistema lineal de ecuaciones diferenciales ahora tenemos un sistema de ecuaciones integro-diferenciales. El análisis de las vibraciones libres de los sistemas con amortiguamiento viscoelástico conduce a un problema nolineal de autovalores donde la característica principal es una matriz de amortiguamiento que depende de la frecuencia de excitación. El estudio de la solución de autovalores y autovectores de este problema es importante si se desean conocer los modos de vibración de la estructura o si se pretende obtener la respuesta en el dominio de la frecuencia del sistema. El objetivo fundamental de esta Tesis Doctoral es doble: Por un lado, profundizar en el conocimiento del problema de autovalores de sistemas viscoelásticos proponiendo para ello nuevos métodos numéricos de resolución. Por otro, desarrollar un nuevo modelo viscoso que, bajo ciertas condiciones, reproduzca la respuesta del modelo viscoelástico con su¿ciente aproximación. La Tesis se divide en ocho capítulos, de ellos el cuerpo principal se encuentra en los seis centrales (Capítulos 2 a 7. Todos ellos son artículos de investigación que, o bien han sido publicados, o bien están en proceso de revisión en revistas contenidas en el Journal Citation Reports (JCR). Por esta razón, todos los capítulos conservan la estructura intrínseca de un artículo, incluidas una introducción y una bibliografía en cada uno. Los cuatro primeros capítulos (Capítulos 2 a 5) se centran en el estudio del problema no lineal de autovalores. Se proponen dos metodologías de resolución: la primera es un procedimiento iterativo basado en el esquema del punto-¿jo y desarrollado para sistemas proporcionales o ligeramente no-proporcionales (aquellos en los que los modos se presentan desacoplados o casi desacoplados). La segunda metodología (presentada en dos capítulos diferentes), denominada paramétrica, permite obtener soluciones casi-analíticas de los autovalores, tanto para sistemas de un grado de libertad como para sistemas de múltiples grados de libertad y dentro de 'estos, para sistemas proporcionales y no proporcionales. El estudio del problema de autovalores se completa con un capítulo dedicado a los autovalores reales, también denominados autovalores no viscosos. En 'él se demuestra una nueva caracterización maten ática que deben cumplir dichos autovalores y que permite proponer un nuevo concepto: el conjunto no-viscoso. Los dos 'últimos capítulos (Capítulos 6 y 7) analizan el Modelo Viscoso Equivalente como propuesta para la modelización de la respuesta de sistemas viscoelásticos. El análisis se realiza desde el dominio de la frecuencia estudiando la función de transferencia. En una primera etapa (pen último capítulo), de naturaleza más maten ática, se demuestra que la función de transferencia exacta de un modelo viscoelástico se puede expresar como suma de una función de transferencia propia de un modelo viscoso más un término denominado residual, directamente dependiente del nivel de amortiguamiento inducido y del acoplamiento modal (noproporcionalidad de la matriz de amortiguamiento). En una segunda etapa ('ultimo capítulo), se desarrolla una aplicación para estructuras reales formadas por entramados planos de elementos 1D amortiguados con capas de material visco elástico. Este tipo de estructuras ha permitido usar una variante mejorada del método paramétrico para la obtención de los autovalores, de forma que en este 'ultimo capítulo ha servido como nexo de unión de las metodologías más importantes desarrolladas en la Tesis. / Lázaro Navarro, M. (2013). The Eigenvalue Problem in Linear Viscoelastic Structures: New Numerical Approaches and the Equivalent Viscous Model [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/30062