A three-dimensional, incompressible, Rayleigh damped magnetic resonance elastography (MRE) material property reconstruction algorithm capable of reconstructing the spatial distribution of both the real and imaginary parts of the shear modulus, density and bulk modulus from full-field MR-detected harmonic motion data was developed. The algorithm uses a subzone-based implementation of motion error minimization techniques, using 27 hexahedral finite elements, and is written in FORTRAN to run on high performance distributed computing systems. The theory behind the methods used is presented in a form that is directly applicable to the code's structure, to serve as a reference for future research building on this algorithm. Globally defined Rayleigh damping parameter reconstructions using simulated data showed that it is possible to reconstruct the correct combination of Rayleigh parameters under noise levels comparable to MR measurements. The elastic wave equation is used to demonstrate that use of a one parameter damping model to fit a Rayleigh damped material can lead to artefacts in the reconstructed damping parameter images, a prediction that is verified using simulated reconstructions. Initial results using MR-detected motion data from both gelatine phantoms and in-vivo cases produced good reconstructions of real shear modulus, as well as showing promise for successful imaging of damping properties. An initial investigation into an alternative elemental basis function approach to supporting the material property distribution produced some promising results, as well as highlighting some significant issues with large variations across the elements.

In a recent study, an environment-friendly material, corrugated cardboard, was used as a building block for the vibration isolator with a preliminary study. The present thesis was motivated to advance technology for improving the design of such a corrugated cardboard vibration isolator with a focus on the modeling of its stiffness and damping. In particular, this study has performed the following works: (1) improving the FE (finite element) model of the stiffness of the corrugated cardboards by more accurately identifying the material parameters in the cardboard material constitutive equation; (2) analyzing the effect of the error in geometry of the corrugated cardboards in the FE model; (3) developing the Rayleigh damping model of the corrugated cardboards and evaluating its accuracy. Several conclusions were drawn from this study: (1) the parameter identification procedure based on the inverse analysis is feasible for improving the accuracy of the model of the stiffness of the cardboard. (2) The FE model of the cardboards with a greater in-plane geometrical deflection has less vertical compressive stiffness. The geometrical deflections of the corrugated cardboards also change the condition of the contact friction stress and the compressive deformation. (3) Rayleigh damping model is accurate enough for calculating the damping of the corrugated cardboards. The contributions of the thesis include: (1) provision of a more accurate model for the compressive stiffness the corrugated cardboards, (2) finding that the friction between the cardboard and the vibrator and the geometrical error of the cardboards have a significant influence over the accuracy of the FE model, (3) finding that in practice the foregoing influence can significantly degraded the performance of the cardboards as a vibrator isolator, and (4) provision of a model for the compressive damping of the corrugated cardboards.

Magnetic Resonance Elastography (MRE) is an emerging medical imaging modality that allows quantification of the mechanical properties of biological tissues in vivo. MRE typically involves time-harmonic tissue excitation followed by the displacement measurements within the tissue obtained by phase-contrast Magnetic Resonance Imaging (MRI) techniques. MRE is believed to have great potential in the detection of wide variety of pathologies, diseases and cancer formations, especially tumors. This thesis concentrates on a thorough assessment and full rheological evaluation of the Rayleigh damping (RD) material model applied to MRE. The feasibility of the RD model to accurately reconstruct viscoelastic and damping properties was assessed. The goal is to obtain accurate quantitative estimates of the mechanical properties for the in vivo healthy brain via the subzone optimization based nonlinear image reconstruction algorithm. The RD model allows reconstruction of not only stiffness distribution of the tissue, but also energy attenuation mechanisms proportionally related to both elastic and inertial effects. The latter allows calculation of the concomitant damping properties of the material. The initial hypothesis behind this research is that accurate reconstruction of the Rayleigh damping parameters may bring additional diagnostic potential with regards to differentiation of various tissue types and more accurate characterisation of certain pathological diseases based on different energy absorbing mechanisms. Therefore, the RD model offers reconstruction of three additional material properties that might be of clinical diagnostic merit and can enhance characterisation of cancer tumors within the brain. A pneumatic-based actuator was specifically developed for in vivo human brain MRE experiments. Performance of the actuator was investigated and the results showed that the actuator produces average displacement in the range of 300 µmicrons and is well suited for generation of shear waves if applied to the human head. Unique features of the the actuator are patient comfort and safety, MRI compatibility, flexible design and good displacement characteristics. In this research, a 3D finite element (FE) subzone-based non-linear reconstruction algorithm using the RD material model has been applied and rigorously assessed to investigate the performance of elastographic based reconstruction to accurately recover mechanical properties and a concomitant damping behaviour of the material. A number of experiments were performed on a variety of homogenous and heterogeneous tissue-simulating damping phantoms comprising a set of materials that mimic range of mechanical properties expected in the brain. The result showed consistent effect of a poor reconstruction accuracy of the RD parameters which suggested the nonidentifiable nature of the RD model. A structural model identifiability analysis further supported the nonidentifiabilty of the RD parameters at a single frequency. Therefore, two approaches were developed to overcome the fundamental identifiability issue. The first one involved application of multiple frequencies over a broad range. The second one was based on parametrisation techniques, where one of the damping parameters was globally defined throughout the reconstruction domain allowing reconstruction of the two remaining parameters. Based on the findings of this research, multi-frequency (MF) elastography was performed on the tissue-simulating phantoms to investigate improvement of the elastographic reconstruction accuracy. Dispersion characteristics of the materials as well as RD changes across different frequencies in various materials were also studied. Simultaneous multi-frequency inversion was undertaken where two models were evaluated: a zero-order model and a power-law model. Furthermore, parametric-based RD reconstruction was carried out to evaluate enhancement of accurate identification of the reconstructed parameters. The results showed that parametric-based RD reconstruction, compared to MF-based RD results, allowed better material characterisation on the reconstructed shear modulus image. Also, significant improvement in material differentiation on the remaining damping parameter image was also observed if the fixed damping parameter was adjusted appropriately. In application to in vivo brain imaging, six repetitive MRE examinations of the in vivo healthy brain demonstrated promising ability of the RD MRE to resolve local variations in mechanical properties of different brain tissue types. Preliminary results to date show that reconstructed real shear modulus and overall damping levels correlate well with the brain anatomical features. Quantified shear stiffness estimates for white and gray matter were found to be 3 kPa and 2.1 kPa, respectively. Due to the non-identifiability of the model at a single frequency, reconstructed RD based parameters limit any physical meaning. Therefore, MF-based and parametric-based cerebral RD elastography was also performed.

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As many of the world’s nuclear power plants are near the end of their supposed life span a need arise to assess the components crucial to the safety of these plants. One of these crucial components is the concrete reactor confinement; to assess its condition, non-destructive testing (NDT) is an attractive method. Traditional testing of concrete structures has comprised of drilling out a sample and performing stress tests on it, but because of the radioactive environment inside the containment this method is far from ideal. NDT is of course possible to use at any structure but at reactor containments the benefits from not creating holes in the structure are prominent; NDT is also an attractive option from an esthetical point of view because it leaves the structure intact. The NDT method pertaining to this study is the impact echo method which comprise of applying a force on the structure, usually a hammer blow, and measuring the response with a receiver. The impact will excite waves propagating in the structure which gives rise to Lamb modes. Lamb modes are structural oscillations of the wall and it is the frequency of these modes that are used to determine the thickness of the wall. The elastic properties of the structure can in turn be obtained by measuring the velocities of the waves propagation. It is also possible to use the impact echo method to detect irregularities in the structure such as cracks or delamination. To simulate the dynamics of a system using NDT numerical methods such as finite element modeling (FEM) is often used. The purpose of this study is to assess the possibility to utilize absorbing layers using increasing damping (ALID) in models to reduce the computational time of FEM analyses. ALIDs are used at the edges to simulate an infinite system and are thus supposed to cancel out incoming waves to prevent unwanted reflection from the edges. The models in this study have all pertained to two dimensional plates utilizing infinitesimal strain theory; the decrease in computational time is significant when using ALIDs and for three dimensional models it would be even more so. The ALIDs are specified by length and maximum mass proportional Rayleigh damping (CMmax), in this study three different lengths are tested, 0.5, 1.5 and 4.5 m for CMmax ranging from 103 to 2*105 Ns/m. The damping is increased with increasing distance into the ALID with specified maximum value at the back edge. However, it should be noted that the increase in damping causes difference in impedance between elements and if this difference is too large it will cause reflections of waves at the boundary between the elements. The ALID must thus be defined so that it sufficiently cancels out the wave without causing unwanted reflections due to impedance differences. The conclusion is that the 0.5 m long ALID does not provide good results for any choice of maximum mass proportional Rayleigh damping. Both the 1.5 and 4.5 m long ALIDs are, however, concluded to be applicable; the 1.5 m ALID having 2*104 < CMmax <5*104 Ns/m and the 4.5 m ALID having 5*103 < CMmax < 104 Ns/m are choices that have shown promise in the performed simulations. The hope is that the results obtained in this study will aid in the development of numerical analysis techniques for NDT methods that can be used in the construction of new reactor confinements and/or maintenance of existing reactor confinements and other thick concrete structures. / Många av världens kärnkraftverk närmar sig slutet på sin beräknade livslängd och ett behov uppstår då att kunna utvärdera de komponenter som är väsentliga för säkerheten på dessa verk. Reaktoromslutningen i betong är en av dessa komponenter och oförstörande provning (NDT) är en attraktiv metod för att bedöma dess tillstånd. Traditionellt har utvärdering av betongkonstruktioner bestått av stresstester på borrprover men p.g.a. den radioaktiva miljön på insidan av omslutningen är denna metod ej att föredra. NDT är självklart möjligt att använda på allsköns betongkonstruktioner då det ger både konstruktionsmässiga och estetiska fördelar. NDT metoden som rör denna studie kallas impact echo och går ut på att man med en hammare slår till en punkt på väggen och mäter responsen en bit därifrån. Lasten ger upphov till vågor i form av deformation som propagerar i väggen och dessa ger i sin tur upphov till Lamb moder. Lamb moderna är strukturella oscillationer av väggen och genom att studera dess frekvenser kan väggens tjocklek bestämmas. Elastiska egenskaper i väggen erhålls utifrån de olika vågornas propageringshastigheter. Impact echo metoden kan även användas för att finna strukturella oegentligheter inuti väggen så som sprickor och delaminering. För att utföra numeriska simuleringar av dynamiska system med NDT-metoder är finita elementmetoden (FEM) användbar. Syftet med denna studie är att bedöma vilka möjligheter som finns för att implementera absorberande ränder med ökande dämpning (ALID) i datamodeller för att minska beräkningstiden av FEM-analyser. ALID används vid kanterna för att simulera ett oändligt system, dess uppgift är att dämpa bort inkommande vågor så att dessa ej reflekteras tillbaka och stör mätningarna. Samtliga modeller i denna studie är två-dimensionella med antagen oändligt liten spänning i normalriktningen. Vinsten i beräkningstid av att använda ALID är stor och ökar ytterligare om modellen utökas till tre dimensioner. Ett ALID definieras genom dess längd och maximala massproportionerlig Rayleigh-dämpning (CMmax). I denna rapport har längderna 0.5, 1.5 and 4.5 m använts med CMmax i intervallet från 103 till 2*105 Ns/m. Dämpningen ökar med ökat avstånd in i ALID med det specificerade maxvärdet vid den bakre kanten. Det bör noteras att skillnad i dämpning mellan element leder till skillnad i impedans; reflektioner av vågorna uppstår vid övergång från ett element med lägre impedans till ett med högre impedans. Ett ALID måste således vara definierat så att det dämpar bort tillräckligt av de inkommande vågorna utan att oönskade reflektioner i ALID uppstår. Studien pekar på att ett 0.5 m långt ALID inte åstadkommer önskvärda resultat för något av valen för CMmax som använts i denna rapport. Både det 1.5 och 4.5 m långa ALID har däremot get bra resultat; ett 1.5 m långt ALID bör ha 2*104 < CMmax <5*104 Ns/m och ett 4.5 m långt ALID 5*103 < CMmax < 104 Ns/m. Förhoppningen med studien är att resultaten skall underlätta utvecklingen av NDT-metoder som kan användas vid konstruktion och underhåll av reaktoromslutningar och andra tjocka betongkonstruktioner.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work researches on free and forced vibrations of a double beam coupled system. The system is regarded as two Euler-Bernoulli beams which are parallel, have the same length, are simply supported and are connected through a viscoelastic layer. Natural frequencies and their mode shapes, also called eigenfunctions, of the coupled system are obtained through a uniform beam methodology which uses the free dynamical basis to represent the solution of the the modal equation. This study uses modal analysis and block matrix formulation, while the dynamical basis used to represent the modal solution is obtained from the dynamical solution of a fourth order differential equation whose coefficients are just those of the original problem. The natural frequencies and mode shapes of the undamped system are determined for several values of beam parameters. For the damped case, damping ratios of each beam and also of the viscoelastic layer (which characterizes the coupling the system) are considered. The forced response is represented using matrix impulse response, which is the solution of an initial value problem with impulsive initial conditions. / Neste trabalho é realizado um estudo sobre vibrações livres e forçadas de um sistema de dupla viga acoplado. O sistema é composto por duas vigas do tipo Euler-Bernoulli, paralelas, de mesmo comprimento, simplesmente apoiadas e conectadas por uma camada viscoelástica. São obtidas as frequências naturais e os modos de vibração ou autofunções do sistema acoplado utilizando uma metodologia para vigas uniformes, que usa a base dinâmica para escrever a solução da equação modal. O estudo é realizado através da análise modal e de uma formulação matricial em blocos, e a base dinâmica usada para escrever a solução da equação modal é gerada pela solução dinâmica de uma equação diferencial de quarta ordem cujos coeficientes são os mesmos do problema considerado. As frequências naturais e os modos de vibração para o sistema não amortecido são determinados para vários valores dos parâmetros da viga. Para o caso amortecido, consideramos o amortecimento individual em cada viga e o amortecimento que compõe a camada viscoelástica o qual caracteriza o acoplamento no sistema. A resposta forçada do sistema é escrita em função da resposta impulso matricial que é solução de um problema de valor inicial com condições iniciais impulsivas.

Ce travail de thèse qui a pour objet la génération et l'étude des couches absorbantes dans les problèmes impliquant la dynamique des sols, est divisé en trois parties essentielles. La première consiste à proposer une méthode de dimensionnement des couches absorbantes par l'amortissement de Rayleigh afin de simuler des problèmes de propagation d'ondes dans les milieux infinis. Cette méthode repose sur une analyse mathématique du problème de propagation d'ondes dans un milieu caractérisé par la matrice de Rayleigh, qui nous permet, d'une part, d'établir des conditions de minimisation des réflexions parasites aux interfaces, et d'autre part, de proposer une simple relation de dimensionnement du domaine absorbant basée sur la notion de décrément logarithmique. On se propose dans la deuxième partie d'appliquer une stratégie de couplage des schémas temporels pour des problèmes de propagation d'ondes dans les milieux infinis 1D et 2D. L'approche proposée est d'intégrer le domaine d'étude par un schéma explicite et le domaine absorbant par un schéma implicite, et d'évaluer le potentiel de cette méthode en faisant varier les rapports de pas de temps entre les sous domaines. Une attention particulière est accordée au cas 1D pour lequel l'effet de la finesse du maillage définie par le nombre d'éléments finis par longueur d'onde est également analysé. Par ailleurs, l'évolution du temps de calcul en fonction du rapport entre les pas de temps est étudiée afin d'estimer les gains réalisés par rapport à un calcul de référence où le problème global est intégré uniquement avec un schéma explicite. La dernière partie est dédiée à l'étude des couches amortissantes de type PML ("Perfectly Matched Layer") dans le cadre des couplages hybrides multi-pas de temps. Cette partie est introduite par une étude de stabilité des schémas temporels dans le cas d'une PML en 1D. La couche absorbante PML est intégrée selon un schéma implicite en adoptant des pas de temps plus importants que le domaine d'intérêt intégré selon un schéma explicite. Bien que cette méthodologie de couplage s'avère très efficace pour la reproduction des milieux infinis, les études paramétriques montrent une sensibilité à la taille du pas de temps plus forte que celle exhibée par les couches amortissantes de Rayleigh. / This thesis which deals with the study of absorbing layers for soil dynamics problems, is divided into three essential parts. The first part aims to propose a design method of absorbing layers by the Rayleigh damping to simulate wave propagation problems in infinite media. This method is based on a mathematical analysis of the wave propagation problem in a media characterized by a Rayleigh damping matrix, which allows us, firstly, to establish conditions for minimizing spurious waves at the interfaces, and another hand, to provide a simple design relationship for the absorbing domain based on the notion of the logarithmic decrement. The second part aims to apply the multi-time step strategy for wave propagation problems in 1D and 2D infinite media. The proposed approach is to integrate the physical domain by an explicit scheme and the absorbing domain by an implicit scheme and to evaluate the potential of this method by varying the time step ratio between subdomains. Special attention is given to the 1D case for which the effect of the mesh fineness, defined by the number of finite elements per wavelength, is also analyzed. Furthermore, the evolution of computing time depending on the time ratio is studied in order to estimate the gains made with respect to a reference computation achieved by a full explicit integration. The last part is dedicated to the study of the Perfectly Matched Layer (PML) as part of hybrid couplings multi-time step. This section is introduced by a stability study of temporal scheme for 1D cases. The absorbing layer PML is integrated by an implicit scheme with a time step larger than that of the domain of interest. Although this coupling methodology is very effective for the reproduction of infinite media, parametric studies show a sensitivity to the time ratio greater than that exhibited by the Rayleigh damping layers.

The aim of this thesis is the design and analysis of pedestrian bridge across the lagoon. Three variants were designed. The variant of structure, which combines stress ribbon with steel arches, was chosen for analysis. There is a chapter in this thesis which deals with an ideal shape of arches for different types of loads. The calculation of load effects was made in software Ansys 17.0, considering scnstruction stages. Ultimate limit state and state limit state are evaluated. For evaluation of concrete cross sections was used MS Excel. Steel cross sections were evaluated in software Ansys 17.0. d Dynamic behaviour of construction was assessed. The mode shapes and natural frequencies were calculated. The harmonic excitation response was studied. The loss of stability was checked. The design and assessment are according to the european standards.

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