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This work is a numerical and analytical study of wave motion through dynamic materials (DM). This work focuses on showing several results that greatly extend the applicability of the checkerboard focusing effect. First, it is shown that it is possible to simultaneously focus dilatation and shear waves propagating through a linear elastic checkerboard structure. Next, it is shown that the focusing effect found for the original €œperfect€� checkerboard extends to the case of the checkerboard with smooth transitions between materials, this is termed a functionally graded (FG) checkerboard. With the additional assumption of a linear transition region, it is shown that there is a region of existence for limit cycles that takes the shape of a parallelogram in (m,n)-space. Similar to the perfect case, this is termed a €œplateau€� region. This shows that the robustness of the characteristic focusing effect is preserved even when the interfaces between materials are relaxed. Lastly, by using finite volume methods with limiting and adaptive mesh refinement, it is shown that energy accumulation is present for the functionally graded checkerboard as well as for the checkerboard with non-matching wave impedances. The main contribution of this work was to show that the characteristic focusing effect is highly robust and exists even under much more general assumptions than originally made. Furthermore, it provides a tool to assist future material engineers in constructing such structures. To this effect, exact bounds are given regarding how much the original perfect checkerboard structure can be spoiled before losing the expected characteristic focusing behavior.

Quando ocorrem solicitações dinâmicas nos solos, torna-se indispensável a determinação do módulo de cisalhamento máximo (Go) para elaboração de projetos de Engenharia Geotécnica. Este parâmetro pode ser determinado a partir da velocidade de propagação das ondas S (Vs). Em campo, os ensaios mais empregadas para determinação de Vs são o cross-hole e o down-hole. O down-hole tem sido bastante empregado com a incorporação de geofones em ponteiras de piezocone. Esse ensaio tem se mostrado uma maneira rápida, econômica e muito confiável para determinação de Go, apresentando resultados consistentes com os obtidos no ensaio cross-hole. O objetivo deste trabalho é o desenvolvimento de um sistema para realização do ensaio sísmico down-hole e sua implantação. Inúmeros ensaios foram realizados no campus da Universidade Estadual Paulista, em Bauru/SP a fim de testar os procedimentos para execução do ensaio, os equipamentos utilizados e as técnicas de interpretação, onde se observou que a manutenção do eixo de vibração dos geofones paralelo a direção de aplicação do golpe foi o fator que mais influenciou na qualidade dos sinais. Para analisar a resposta dos geofones instalados na ponteira desenvolvida, realizaram-se ensaios em laboratório, onde se verificou que os geofones apresentavam resposta idêntica ao dos acelerômetro de referência. Por fim, foram realizados ensaios em três campos experimentais no interior do Estado de São Paulo, onde estão disponíveis resultados de ensaios cross-hole e ensaios down-hole realizados com equipamentos comerciais. Os resultados obtidos com o sistema desenvolvido nestes campos permitiram validar o sistema desenvolvido. / In the design stages of geotechnical engineering of a given project, it is imperative to ascertain the maximum shear modulus (Go) of those soils experiencing dynamic loads. One common method to determine Go is to measure shear wave velocity. Most field experiments are the cross-hole and down-hole tests to determine the velocity of shear waves. The downhole test has been widely used in conjunction with geophones placed behind the tip of piezocones. The down-hole test has proven to be a fast, economic, and very reliable method to determine Go, it has produced data consistent with results obtained in cross-hole tests. The objective of this work is to present a comprehensive system for the down-hole test, which includes its implementation, execution, and the interpretation of data collected. Several tests were performed at the campus of Universidade Estadual Paulista, UNESP, in Bauru, S.P. The objective of those experiments was to test the execution procedures and method of interpretation. It was observed the quality of the results obtained was chiefly dependent on maintaining the axis of vibration of the geophones parallel to the direction of application of the original blow. The analysis of the response by the geophones installed at the tip of the cone included experiments performed at the laboratory, where it was observed that the geophones responded identically to those accelerometers used as reference. Further, downhole experiments using system proposed here were performed in three experimental research sites of the state of São Paulo. The objective was to compare results to the data available in literature, which were obtained using commercial SCPT equipment and cross-hole tests. The down-hole testswere performed within the guidelines of the system proposed here and the results of the experiment served to corroborate the suitability of the developed system.

Evaluations of stress history and the geostatic state of stress of soils are ascertained on the basis of field geophysical measurements that provide paired complementary types of shear waves. It is well-established that multiple types of shear waves occur in the ground due to their directional and polarization properties. The shear wave velocity (Vs) provides the magnitude of small strain stiffness (G0) which depends on effective stress, void ratio, stress history, and other factors (cementation, age, saturation). Herein, this study examines a hierarchy of shear wave modes with different directions of propagation and particle motion from in-situ geophysical tests (HH, VH, and HV) and laboratory bender element data. A special compiled database from well-documented worldwide sites is assembled where full profiles of stress state, stress history, and several paired modes of Vs profiles have been obtained from crosshole tests (CHT), downhole tests (DHT), and rotary crosshole (RCHT). Reference profiles of the lateral stress coefficient (K0) are available from direct in-situ measurements (self-boring pressuremeter, hydrofracture, and push-in spade cells). Stress history is documented in terms of yield stress ratio (YSR) from consolidation testing and careful engineering geology studies. A methodology is developed that relates both the YSR and K0 to stiffness ratios obtained from directional shear wave velocities. In further efforts, means to extract reliable shear wave profiles from continuous downhole testing via a new GT autosource and seismic piezocone testing are outlined and applied to results from three test sites in Windsor/VA, Norfolk/VA, and Richmond/BC. A driving impetus to this research involves the geologic conditions at the US Dept. of Energy's Savannah River Site (SRS) in South Carolina. Here, the overburden soils in the upper 60 m depths consist of very old Miocene and Eocene sediments, primarily layered deposits of sands, clayey sands, silty sands, and interbedded clays which exhibit an apparent and unusual stress history profile. Special geologic conditions include the dissolutioning of old calcareous sediments (Santee Formation) at depths of 40 to 50 m below grade, similar to karstic limestone deposits. As a consequence, caves, voids, and infilled soft soil zones occur within the soil matrix at these elevations, probably resulting in localized collapse of the overlying soil column. Based on conventional laboratory and in-situ test data conducted during geotechnical investigations at SRS, available interpretative relationships for assessing the soil stress history and geostatic stress states show scattered and inconsistent results. Complications abound in the systematic assessments of these geomaterials due to effects of very old ageing, cementation, desiccation, and diagenesis, as evidenced by unusual in-situ shear wave velocity profiles that decrease in magnitude with depth, as measured by CHT and DHT. Based on the findings of this study, it is recommended that a new set of shear wave velocity measurements be made at SRS to obtain HH waves (and complementary VH waves) needed for an independent assessment of YSR in the upper soil column.

Velocity-coupled combustion instability is a major issue facing lean combustor design in modern gas turbine applications. In this study, we analyze the complex acoustic field excited by a transverse acoustic mode in an annular combustor. This work is motivated by the need to understand the various velocity disturbance mechanisms present in the flame region during a transverse instability event. Recent simulation and experimental studies have shown that much of the flame response during these transverse instabilities may be due to the longitudinal motion induced by the fluctuating pressure field above the nozzles. This transverse to longitudinal coupling has been discussed in previous work, but in this work it is given a robust acoustic treatment via computational methods in order to verify the mechanisms by which these two motions couple. We will provide an in-depth discussion of this coupling mechanism and propose a parameter, Rz, also referred to as the Impedance Ratio, in order to compare the pressure/velocity relationship at the nozzle outlet to quasi one-dimensional theoretical acoustic approximations. A three-dimensional inviscid simulation was developed to simulate transversely propagating acoustic pressure waves, based on an earlier experiment designed to measure these effects. Modifications to this geometry have been made to account for lack of viscosity in the pure acoustic simulation and are discussed. Results from this study show that transverse acoustic pressure excites significant axial motion in and around the nozzle over a large range of frequencies. Furthermore, the development of Rz offers a defined physical parameter through which to reference this important velocity-coupled instability mechanism. Therefore, this study offers an in-depth and quantifiable understanding of the instability mechanism caused by transversely propagating acoustic waves across a combustor inlet, which can be applied to greatly improve annular combustor design in future low-emissions gas turbine engines.

In reality, dynamic response of a structure supported on a compliant soil may vary significantly from the response of same structure when supported on a rigid base. A parametric study is conducted for the analysis of the variation in the global and the local deformation demands caused by the inertial soil-structure interaction effects. For the purposes of the study, nonlinear dynamic analyses are performed on 7 steel moment-resisting frame models, which are prepared by the virtue of fixed-base and flexible-base (interacting) conditions. Foundation is modeled with the Truncated Cone Model (Wolf, 1994) with the frequency independent coefficients. Free-field earthquake acceleration records are selected to conform to NEHRP equivalent Site Classes C and D. The study is limited to the structures founded on surface rigid mat foundations subjected to vertically propagating horizontally polarized coherent shear waves. Statistical analysis based on multiple linear regression procedure is performed to represent the variation in the response. Within the scope of the study, the wave parameter and the aspect ratio are observed to be directly proportional to the variation in the response, as a general trend. Maximum beneficial contribution of the SSI is found to be 6% in both global and local deformation demands. In addition, the contribution of inertial interaction effects is found to be in a decreasing trend for the increasing levels of ductility demands. Finally, upper limits of wave parameter for H/R=0.5, 1, 2 and 3 are calculated where the variation in the demands are capped at 1.0.

Quando ocorrem solicitações dinâmicas nos solos, torna-se indispensável a determinação do módulo de cisalhamento máximo (Go) para elaboração de projetos de Engenharia Geotécnica. Este parâmetro pode ser determinado a partir da velocidade de propagação das ondas S (Vs). Em campo, os ensaios mais empregadas para determinação de Vs são o cross-hole e o down-hole. O down-hole tem sido bastante empregado com a incorporação de geofones em ponteiras de piezocone. Esse ensaio tem se mostrado uma maneira rápida, econômica e muito confiável para determinação de Go, apresentando resultados consistentes com os obtidos no ensaio cross-hole. O objetivo deste trabalho é o desenvolvimento de um sistema para realização do ensaio sísmico down-hole e sua implantação. Inúmeros ensaios foram realizados no campus da Universidade Estadual Paulista, em Bauru/SP a fim de testar os procedimentos para execução do ensaio, os equipamentos utilizados e as técnicas de interpretação, onde se observou que a manutenção do eixo de vibração dos geofones paralelo a direção de aplicação do golpe foi o fator que mais influenciou na qualidade dos sinais. Para analisar a resposta dos geofones instalados na ponteira desenvolvida, realizaram-se ensaios em laboratório, onde se verificou que os geofones apresentavam resposta idêntica ao dos acelerômetro de referência. Por fim, foram realizados ensaios em três campos experimentais no interior do Estado de São Paulo, onde estão disponíveis resultados de ensaios cross-hole e ensaios down-hole realizados com equipamentos comerciais. Os resultados obtidos com o sistema desenvolvido nestes campos permitiram validar o sistema desenvolvido. / In the design stages of geotechnical engineering of a given project, it is imperative to ascertain the maximum shear modulus (Go) of those soils experiencing dynamic loads. One common method to determine Go is to measure shear wave velocity. Most field experiments are the cross-hole and down-hole tests to determine the velocity of shear waves. The downhole test has been widely used in conjunction with geophones placed behind the tip of piezocones. The down-hole test has proven to be a fast, economic, and very reliable method to determine Go, it has produced data consistent with results obtained in cross-hole tests. The objective of this work is to present a comprehensive system for the down-hole test, which includes its implementation, execution, and the interpretation of data collected. Several tests were performed at the campus of Universidade Estadual Paulista, UNESP, in Bauru, S.P. The objective of those experiments was to test the execution procedures and method of interpretation. It was observed the quality of the results obtained was chiefly dependent on maintaining the axis of vibration of the geophones parallel to the direction of application of the original blow. The analysis of the response by the geophones installed at the tip of the cone included experiments performed at the laboratory, where it was observed that the geophones responded identically to those accelerometers used as reference. Further, downhole experiments using system proposed here were performed in three experimental research sites of the state of São Paulo. The objective was to compare results to the data available in literature, which were obtained using commercial SCPT equipment and cross-hole tests. The down-hole testswere performed within the guidelines of the system proposed here and the results of the experiment served to corroborate the suitability of the developed system.

The soil strata is often subjected to various kinds of vibrations such as that caused by earthquakes, water waves, traffic loads, wind power plants, construction related equipments, pile driving and vibratory machines. The strains induced in a soil mass due to the vibrations generated by these different sources often lie in a range of 0.0001% - 0.1%. The estimation of the shear modulus (G) and damping (D) of soils in this strain range becomes an important aspect for performing the analysis and design of various geotechnical structures subjected to different kinds of vibrations. Strain amplitude, effective confining stress, void ratio/relative density, number of vibration cycles and cyclic strain history are some of the key parameters that influence the modulus and damping characteristics of sands. Although, the effects of strain amplitude, confining pressure and relative density have been studied quite extensively in literature, only limited studies seem to have been reported in literature to examine the effects of the cyclic strain history and the vibration cycles on these dynamic properties. The objective of this thesis is to study the effects of the cyclic strain history and the number of vibration cycles on the shear modulus and damping ratio of dry sands in a strain range of 0.0001% to 0.1%. A number of resonant column tests have been performed on dry sand specimens to examine the effect of the cyclic shear strain history, by including both increasing and decreasing strain paths, on the shear modulus and damping ratio for different combinations of relative densities (Dr) and confining pressures (σ3); an increasing strain path intends to simulate a situation when a vibratory machine is just started before reaching a steady state of vibration, and on the other hand, the decreasing strain path matches a condition when the machine is shut down after running continuously in a steady state for some time. The specimen has been subjected to a series of cycles of increasing and decreasing shear strain paths approximately in a shear strain range of 0.0006% - 0.1%. For chosen values of relative density and confining pressure, two different series of tests beginning with either (i) an increasing strain path or (ii) a decreasing strain path, were performed. In addition, the influence of the numbers of the vibration cycles which are used to measure the resonant frequency of the specimen, referred to as the cycle constant, on the values of shear modulus has also been analyzed. Irrespective of the strain path adopted to commence the test or the cycle constant used to perform a resonant column test, for a given strain amplitude, the shear modulus along the increasing strain path has been found to be always greater than the corresponding modulus value along the decreasing strain path. For the series of tests which were commenced with the increasing strain path, the shear modulus corresponding to the first increasing strain path becomes always the highest as compared to the subsequent strain paths. For a given strain cycle, irrespective of relative density of sand, the difference between the values of G associated with the increasing and decreasing strain paths becomes always the maximum corresponding to a certain shear strain level. The maximum reduction in the shear modulus, due to the cyclic variation of the shear strain, was noted to be approximately one fourth of the maximum shear modulus (G0). This reduction in the shear modulus, on account of the cyclic variation of the shear strain, increases generally with decrease in the values of both relative density and confining pressure. The damping ratio for a given shear strain for the increasing strain path was noted to be lower than the corresponding value for the decreasing strain path except for the first increasing strain path. For a particular strain level, the series of tests started with the decreasing strain path resulted in a lower value of shear modulus for all the cyclic strain paths as compared to the tests which were commenced with the increasing strain path. The modulus reduction curve for the first increasing strain path was noted to be more or less the same irrespective of the value of the chosen cycle constant. For the subsequent strain paths, an increment in the cycle constant value caused a reduction in the shear modulus at a particular shear strain level. In order to match a situation when the machine is running continuously in a steady state of vibration, resonant column tests were conducted in a torsional mode by inducing a large number of the vibration cycles with the shear strain amplitude in a range of 0.0005%-0.05%. Corresponding to a given input voltage of the drive mechanism, the specimens were subjected to a number of vibration cycles ranging from 1,000 to 50,000. The values of shear modulus and damping ratio, before and after the application of vibration cycles, were determined for several input voltages ranging from 0.001 V (minimum) to 0.3 V (maximum). The tests were carried out for different combinations of relative densities and confining pressures. For the chosen relative densities, hardly any influence of vibration cycles on the values of G and D were noted for the strain amplitude below the threshold strain level (0.0024% - 0.0044%). Beyond the threshold strain level, an induction of the vibration cycles leads to a continuous increment in the shear strain which eventually causes (i) a decrease in the shear modulus, and (ii) an increase in the damping ratio. This effect was found to become especially more significant for lower values of relative densities as well as confining pressures. The percentage changes in the values of (i) shear strain, (ii) shear modulus, and (iii) damping ratios after the introduction of vibration cycles were noted to increase with an increment in the number of vibration cycles. However, for a given increment of the vibration cycles, the changes in the values of shear modulus and damping ratio were generally noted to subside with an increase in the number of the vibration cycles. At various strain levels, the magnitude of the shear modulus was observed to increase continuously with an increase in the values of both relative density and confining pressure. For the shear strain greater than the threshold strain (0.0024% - 0.0044%), a reduction in the damping ratio values was also noted with an increase in the magnitudes of the confining pressure. On the other hand, the influence of relative density on the damping ratio was found to be relatively negligible. The shear modulus reduction curves from the present tests' data were found to compare reasonably well with the empirical curves proposed in the literature, especially for low values of the confining pressure. A deviation of the present modulus reduction curves from the empirical curves was observed generally at large shearing strains. However, the damping values obtained from the present study were noted to be lower than the values predicted by the existing empirical correlations, particularly for low values of the confining pressure. An attempt has also been made to improve the accuracy of the measurement of the arrival times of both primary (P) waves and shear (S) waves while conducting bender/extender element tests. For this purpose, a series of laboratory tests were performed on dry sand at different frequencies, varying between 1 kHz and 10 kHz, for medium dense and very dense sands with different values of the confining pressures. While determining the times of arrival of both P and S waves, two corrections have been proposed to incorporate (i) the presence of an initial offset in the input signal, and (ii) the time lag due to an existence of peripheral electronics between the input and received signals when the source and receiver elements are kept in direct contact with each other. The absolute magnitude of the resultant of these two corrections was found to reduce with an increase in the frequency of the input signal. The determination of the P-wave arrival time does not pose much difficulty. It has been noted that it becomes equally accurate to measure the arrival times of the S-wave provided the proposed corrections are incorporated. The maximum shear modulus values measured from the resonant column tests and the bender element tests by incorporating these two corrections were found to compare reasonably well with each other. The thesis brings out the effects of the cyclic strain history and the vibration cycles on the shear modulus and damping ratio of dry sand. The results obtained are expected to be useful while doing the analysis and design of geotechnical structures subjected to different kinds of vibrations.

L'élastographie ultrasonore est une technique d'imagerie émergente destinée à cartographier les paramètres mécaniques des tissus biologiques, permettant ainsi d’obtenir des informations diagnostiques additionnelles pertinentes. La méthode peut ainsi être perçue comme une extension quantitative et objective de l'examen palpatoire. Diverses techniques élastographiques ont ainsi été proposées pour l'étude d'organes tels que le foie, le sein et la prostate et. L'ensemble des méthodes proposées ont en commun une succession de trois étapes bien définies: l'excitation mécanique (statique ou dynamique) de l'organe, la mesure des déplacements induits (réponse au stimulus), puis enfin, l'étape dite d'inversion, qui permet la quantification des paramètres mécaniques, via un modèle théorique préétabli. Parallèlement à la diversification des champs d'applications accessibles à l'élastographie, de nombreux efforts sont faits afin d'améliorer la précision ainsi que la robustesse des méthodes dites d'inversion. Cette thèse regroupe un ensemble de travaux théoriques et expérimentaux destinés à la validation de nouvelles méthodes d'inversion dédiées à l'étude de milieux mécaniquement inhomogènes. Ainsi, dans le contexte du diagnostic du cancer du sein, une tumeur peut être perçue comme une hétérogénéité mécanique confinée, ou inclusion, affectant la propagation d'ondes de cisaillement (stimulus dynamique). Le premier objectif de cette thèse consiste à formuler un modèle théorique capable de prédire l'interaction des ondes de cisaillement induites avec une tumeur, dont la géométrie est modélisée par une ellipse. Après validation du modèle proposé, un problème inverse est formulé permettant la quantification des paramètres viscoélastiques de l'inclusion elliptique. Dans la continuité de cet objectif, l'approche a été étendue au cas d'une hétérogénéité mécanique tridimensionnelle et sphérique avec, comme objectifs additionnels, l'applicabilité aux mesures ultrasonores par force de radiation, mais aussi à l'estimation du comportement rhéologique de l'inclusion (i.e., la variation des paramètres mécaniques avec la fréquence d'excitation). Enfin, dans le cadre de l'étude des propriétés mécaniques du sang lors de la coagulation, une approche spécifique découlant de précédents travaux réalisés au sein de notre laboratoire est proposée. Celle-ci consiste à estimer la viscoélasticité du caillot sanguin via le phénomène de résonance mécanique, ici induit par force de radiation ultrasonore. La méthode, dénommée ARFIRE (''Acoustic Radiation Force Induced Resonance Elastography'') est appliquée à l'étude de la coagulation de sang humain complet chez des sujets sains et sa reproductibilité est évaluée. / Ultrasound elastography is an emerging technology derived from the concept of manual palpation and dedicated to the mapping of biological tissue mechanical properties in a diagnostic context. Various elastographic approaches have been applied to the study of organs such as the liver, breast or prostate. All proposed techniques rely on a three-steps procedure: first, the tissue to be studied is mechanically excited, in a static or dynamic way. Induced displacements are then measured and used to estimate qualitatively or quantitatively mechanical properties of the medium. This step is called inversion. While application fields of elastography are constantly broadened, efforts are made to provide robust and accurate inversion algorithms. In this monography, theoretical and experimental works related to the development of new inversion methods dedicated to the study of mechanically inhomogeneous media in dynamic ultrasound elastography are provided. In the context of breast cancer diagnosis, a localized tumour can be assumed as a confined mechanical heterogeneity, also referred as an inclusion, which can disturb the propagation of shear waves (dynamic excitation). The first objective of this thesis is to provide a theoretical model to describe physical interactions occurring between incident shear waves and a tumour, here geometrically assumed as an ellipse. Once the theoretical model is validated, an inverse problem is formulated allowing further quantification of inclusion viscoelastic parameters. Aiming the development of realistic models, the previous work has been extended to the case of three dimensional spherical heterogeneities and adapted to the specific case of an acoustic radiation force excitation. Furthermore, the feasibility of assessing the medium rheological model (i.e., the frequency dependence of mechanical properties) is demonstrated. Finally, in the context of vascular diseases and blood coagulation, an inversion method based on the study of the mechanical resonance phenomenon induced by acoustic radiation force is proposed. The technique, termed ARFIRE (Acoustic Radiation Force Induced Resonance Elastography), is applied to human whole blood samples and the reproducibility of results is assessed.

Cette thèse porte sur la modélisation des ondes élastodynamiques dans deux situations particulières qui pénalisent les méthodes numériques utilisées pour simuler ces phénomènes. Dans la première partie, on se place dans le cas où les ondes de pression (ondes P) se propagent à une vitesse beaucoup plus grande que celle des ondes de cisaillement (ondes S). Les modèles numériques utilisés habituellement pour traiter cette configuration sont pénalisés par la plus petite vitesse qui dicte le choix du pas du schéma. Nous proposons ici un schéma qui découple numériquement, dans le volume, les ondes P et les ondes S, pour deux types de conditions de bord en utilisant la décomposition du déplacement en potentiels de Lamé, en deux dimensions. Les conditions aux limites de Dirichlet homogènes, qui sont des conditions essentielles pour la formulation classique en déplacement, deviennent des conditions naturelles, mais non standard, pour la formulation en potentiels qui se présente comme un système de deux équations d’ondes couplées par les conditions aux limites. Cette formulation préserve une énergie équivalente à l'énergie élastodynamique. Nous construisons un schéma éléments finis en espace et utilisons un thêta-schéma en temps sur les termes de bord afin de ne pas pénaliser la CFL et mener à une condition sur le pas de temps indépendante des termes de couplage au bord. Ce schéma préserve une énergie discrète. Le cas des conditions de surface libre mène à des instabilités. Nous les avons traitées comme des perturbations des conditions de Dirichlet, ce qui permet d'obtenir de bons résultats dans le domaine fréquentiel mais donne naissance à de sévères instabilités après discrétisation en temps. La seconde partie de la thèse est consacrée à la construction, l'analyse et la validation de conditions de transmission effectives (CTE) à travers une couche mince de matériau homogène et isotrope d'épaisseur constante h. Ici, la finesse de la couche affecte les schémas explicites usuels car le maillage de la couche avec des éléments suffisamment petits entraîne une diminution analogue du pas de temps critique via la condition CFL, tandis que l'on espère avec les CTE obtenir un pas de temps indépendant de l'épaisseur de la couche. Une analyse complète du cas de la bande mince rectiligne est donnée en deux et trois dimensions. Les conditions obtenues sont stables via la conservation d'une énergie et l'ordre de l'erreur d'approximation par rapport à l'épaisseur de la couche pour les conditions d'ordre 2 est de O(h^3). Des résultats numériques sont présentés pour les configurations bi et tridimensionnelles, ils valident les résultats de stabilité, d'estimation d'erreur et de conditions de stabilité de schémas en temps proposés, qui sont des modifications du schéma explicite utilisé en l'absence de couche mince. Enfin, le traitement d'une couche curviligne est effectué dans le cas bidimensionnel. Sa stabilité est à nouveau vérifiée par conservation d'énergie et des résultats numériques sont également présentés. / This work is dedicated to the modelling of elastodynamic waves in two particular situations for which standard numerical methods experience difficulties. In the first part, the case where the velocity of the pressure waves (P waves) is much greater than the velocity of the shear waves (S waves) is studied. When applied to this situation, standard explicit time-stepping methods are hampered by the fact that the mesh size is dictated by the smallest velocity. We develop a numerical scheme that uncouples the body S-waves and P-waves by exploiting the well-known representation of elastodynamic states in terms of Lamé potentials. Formulations are derived and analysed for the 2-D case, where both potentials are scalar functions. Homogeneous essential Dirichlet boundary conditions lead to non-standard natural conditions for our potential-based formulation. A system of two wave equations, coupled by two boundary conditions, is obtained. This formulation is energy-preserving. A discretization approach involving finite elements in space and a theta-scheme in time applied to the boundary unknowns inside the domain is proposed, so that the « natural » time step for each wave speed can be used. This scheme is shown to be also energy-preserving. The case of Neumann boundary conditions is also addressed. These conditions are treated as perturbations of the Dirichlet case, an approach which yields good results in the time-harmonic case while giving rise to severe instabilities in the time-discrete transient case. The second part of this thesis is concerned with the design, analysis, numerical approximation and implementation of effective transmission conditions (ETCs) for the propagation of elastic waves through a thin elastic layer with small uniform thickness h which is embedded in a reference elastic medium, under transient conditions, with both materials assumed to have isotropic properties. Here, the thinness of the layer has an adverse effect on usual explicit schemes, since meshing the layer with small elements will induce a corresponding reduction of the critical time step through a CFL condition, whereas it is expected that the layer-less CFL condition will remain valid if the layer is modelled using ETCs. First, a complete analysis is given in the case of a planar elastic layer, applicable to two- and three-dimensional situations. The stability of the proposed second-order ETC is established as the result of energy preservation, while the approximation error on the transmission solution is shown to be of order O(h^3) in energy norm. Numerical experiments, performed for two- and three-dimensional configurations, validate the theoretical findings on stability, approximation error and stability conditions of time-stepping schemes that are natural modifications of the explicit scheme used in the absence of a thin layer. Then, ETCs are also derived for the case of a curvilinear layer embedded in a two-dimensional elastic medium. Their stability is again proven as resulting from energy preservation and the theoretical results are illustrated with numerical experiments.