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.

Wave scattering by arrays of cylinders has received special attention by many authors and analytical solutions have been derived. The investigation of optical and acoustical analogies to the problem of interaction of water waves with rigid and flexible cylinder arrays is the main focus of this thesis. In acoustics, a sound may be attenuated while it propagates through a layer of bubbly liquid. In fact, if the natural frequency of the bubbles is in the range of the wave periods, the attenuation becomes more evident. The ultimate objective of the research described herein is to determine if this phenomenon may also be found in the interaction between water waves and arrays of flexible cylinders. In a first approach, arrays of rigid cylinders are studied in shallow water. The array is treated as an effective medium, which allows for the definition of reflection and transmission coefficients for the array, and theories from Hu and Chan (2005) associated with the Fabry-Perot interferometer are compared against direct computations of wave scattering using the commercial code WAMIT. Reflection and transmission coefficients from WAMIT are evaluated by applying a Maximum Likelihood Method. The results from WAMIT were found to be in good agreement with those obtained from the effective medium theory. Due to observed inconsistencies for short wave periods and small incident angles, the effective width of the medium is defined and corrected. For the case of a flexible cylinder, generalized modes corresponding to deformations of the cylinder's surface are formulated and added to WAMIT's subroutine. Equations of motion are derived from the theory of vibration for thin shells and mass and stiffness matrices are defined. The objective is to maximize wave attenuation from the array of flexible cylinders. Therefore, the natural periods of the "breathing" mode for these cylinders is set in the range of the studied wave periods. Then, material properties, as well as mass and stiffness matrices, are chosen to achieve this effect.

Generation of electricity from ocean waves has seen increasing research and commercial interest in recent years. The development of projects of several hundred megawatts rated capacity is now being considered. There is a clear need for improved understanding of the environmental impact of large-scale wave energy extraction, particularly in nearshore regions where sediment transport and cliff erosion may be affected. This thesis investigates the change in nearshore wave conditions and sediment transport due to energy extraction by long strings of wave energy devices. The influence of wave energy converter (WEC) arrays has been studied using transmission coefficients implemented within a spectral wave model. It is shown that the breaking wave height nearshore is larger (5%) if transmission is defined as frequency dependent. This is due to the energy dissipation processes associated with different wave frequencies. Linear wave theory is employed to determine frequency dependent transmission and reflection coefficients across a line of wave energy devices based onthe amplitude of scattered and radiated waves. This approach is compared with experimental measurements of the wave field in the vicinity of an array of five heaving floats. The transmitted wave amplitude is predicted with reasonable accuracy but additional numerical damping is required to predict the measured float response amplitude. This comparison indicates that linear analysis is an acceptable approach for predicting float response and wave field in the vicinity of the array for a certain range of conditions. Linear wave analysis is subsequently applied to investigate the variation of transmission coefficients with distance inshore of a long array of heaving WECs undergoing free response and with damping specified to optimise power extraction. A method is presented for identifying representative transmission and reflection coefficients such that change in wave energy is equal to energy extraction by the devices. These coefficients are employed to quantify the change in nearshore conditions due to deployment of a long line of wave devices at a site near the East Anglian coastline. Wave conditions are modelled at 12 points along the shoreline over a 140 year period and significant wave height reductions up to 30% were obtained. Importantly, changes in nearshorewave direction are also observed. Analysis using the sediment transport model SCAPE (Soft Cliff and Platform Erosion model) indicates that the introduction of the array reduces both the sediment transport rate and cliff recession rate by an average of 50%.

The deployment of dedicated short-range communications (DSRC) roadside units (RSUs) allows a connected or automated vehicle to acquire information from the surrounding environment using vehicle-to-infrastructure (V2I) communication. However, wireless communication using DSRC has shown to exhibit null points, at repeatable distances. The null points are significant and there was unexpected loss in the wireless signal strength along the pathway of the V2I communication. If the wireless connection is poor or non-existent, the V2I safety application will not obtain sufficient data to perform the operation services. In other words, a poor wireless connection between a vehicle and infrastructure (e.g., RSU) could hamper the performance of a safety application. For example, a designer of a V2I safety application may require a minimum rate of data (or packet count) over 1,000 meters to effectively implement a Reduced Speed/Work Zone Warning (RSZW) application. The RSZW safety application is aimed to alert or warn drivers, in a Cooperative Adaptive Cruise Control (CACC) platoon, who are approaching a work zone. Therefore, the packet counts and/or signal strength threshold criterion must be determined by the developer of the V2I safety application. Thus, we selected an arbitrary criterion to develop an empirical method of ascertaining the null points from a DSRC RSU. The research motivation focuses on developing an empirical method of calculating the null points of a DSRC RSU for V2I communication at a highway on/off-ramp. The intent is to improve safety, mobility, and environmental applications since a map of the null points can be plotted against the distance between the DSRC RSU and a vehicle's onboard unit (OBU). The main research question asks: 'What is a more robust empirical method, compared to the horizontal and vertical laws of reflection formula, in determining the null points from a DSRC RSU on a highway on/off ramp?' The research objectives are as follows: 1. Explain where and why null points occur from a DSRC RSU (Chapter 2) 2. Apply the existing horizontal and vertical polarization model and discuss the limitations of the model in a real-world scenario for a DSRC RSU on a highway on/off ramp (Chapter 3 and Appendix A) 3. Introduce an extended horizontal and vertical polarization null point model using empirical data (Chapter 4) 4. Discuss the conclusion, limitations of work, and future research (Chapter 5). The simplest manner to understand where and why null points occur is depicted as two sinusoidal waves: direct and reflective waves (i.e., also known as a two-ray model). The null points for a DSRC RSU occurs because the direct and reflective waves produce a destructive interference (i.e., decrease in signal strength) when they collide. Moreover, the null points can be located using Pythagorean theorem for the direct and reflective waves. Two existing models were leveraged to analyze null points: 1) signal strength loss (i.e., a free space path loss model, or FSPL, in Appendix A) and 2) the existing horizontal and vertical polarization null points from a DSRC RSU. Using empirical data from two different field tests, the existing horizontal and vertical polarization null point model was shown to contain limitations in short distances from the DSRC RSU. Moreover, the existing horizontal and vertical polarization model for null points was extremely challenging to replicate with over 15 DSRC RSU data sets. After calculating the null point for several DSRC RSU heights, the paper noticed a limitation of the existing horizontal and vertical polarization null point model with over 15 DSRC RSU data sets (i.e., the model does not account for null points along the full length of the FSPL model). An extended horizontal and vertical polarization model is proposed that calculates the null point from a DSRC RSU. There are 18 model comparisons of the packet counts and signal strengths at various thresholds as perspective extended horizontal and vertical polarization models. This paper compares the predictive ability of 18 models and measures the fit. Finally, a predication graph is depicted with the neural network's probability profile for packet counts =1 when greater than or equal to 377. Likewise, a python script is provided of the extended horizontal and vertical polarization model in Appendix C. Consequently, the neural network model was applied to 10 different DSRC RSU data sets at 10 unique locations around a circular test track with packet counts ranging from 0 to 11. Neural network models were generated for 10 DSRC RSUs using three thresholds with an objective to compare the predictive ability of each model and measure the fit. Based on 30 models at 10 unique locations, the highest misclassification was 0.1248, while the lowest misclassification was 0.000. There were six RSUs mounted at 3.048 (or 10 feet) from the ground with a misclassification rate that ranged from 0.1248 to 0.0553. Out of 18 models, seven had a misclassification rate greater than 0.110, while the remaining misclassification rates were less than 0.0993. There were four RSUs mounted at 6.096 meters (or 20 feet) from the ground with a misclassification rate that ranged from 0.919 to 0.000. Out of 12 models, four had a misclassification rate greater than 0.0590, while the remaining misclassification rates were less than 0.0412. Finally, there are two major limitations in the research: 1) the most effective key parameter is packet counts, which often require expensive data acquisition equipment to obtain the information and 2) the categorical type (i.e., decision tree, logistic regression, and neural network) will vary based on the packet counts or signal strength threshold that is dictated by the threshold criterion. There are at least two future research areas that correspond to this body of work: 1) there is a need to leverage the extended horizontal and vertical polarization null point model on multiple DSRC RSUs along a highway on/off ramp, and 2) there is a need to apply and validate different electric and magnetic (or propagation) models. / Ph. D. / The deployment of dedicated short-range communications (DSRC) roadside units (RSUs) allows a connected or automated vehicle to acquire information from the surrounding environment using vehicle-to-infrastructure (V2I) communication. However, wireless communication using DSRC has shown to exhibit null points, at repeatable distances. The null points are significant and there was unexpected loss in the wireless signal strength along the pathway of the V2I communication. If the wireless connection is poor or non-existent, the V2I safety application will not obtain sufficient data to perform the operation services. In other words, a poor wireless connection between a vehicle and infrastructure (e.g., RSU) could hamper the performance of a safety application. For example, a designer of a V2I safety application may require a minimum rate of data (or packet count) over 1,000 meters to effectively implement a Reduced Speed/Work Zone Warning (RSZW) application. The RSZW safety application is aimed to alert or warn drivers, in a Cooperative Adaptive Cruise Control (CACC) platoon, who are approaching a work zone. Therefore, the packet counts and/or signal strength threshold criterion must be determined by the developer of the V2I safety application. Thus, we selected an arbitrary criterion to develop an empirical method of ascertaining the null points from a DSRC RSU. The research motivation focuses on developing an empirical method of calculating the null points of a DSRC RSU for V2I communication at a highway on/off-ramp. The intent is to improve safety, mobility, and environmental applications since a map of the null points can be plotted against the distance between the DSRC RSU and a vehicle’s onboard unit (OBU). The main research question asks: “What is a more robust empirical method, compared to the horizontal and vertical laws of reflection formula, in determining the null points from a DSRC RSU on a highway on/off ramp?” The research objectives are as follows: 1. Explain where and why null points occur from a DSRC RSU (Chapter 2) 2. Apply the existing horizontal and vertical polarization model and discuss the limitations of the model in a real-world scenario for a DSRC RSU on a highway on/off ramp (Chapter 3 and Appendix A) 3. Introduce an extended horizontal and vertical polarization null point model using empirical data (Chapter 4) 4. Discuss the conclusion, limitations of work, and future research (Chapter 5). The simplest manner to understand where and why null points occur is depicted as two sinusoidal waves: direct and reflective waves (i.e., also known as a two-ray model). The null points for a DSRC RSU occurs because the direct and reflective waves produce a destructive interference (i.e., decrease in signal strength) when they collide. Moreover, the null points can be located using Pythagorean theorem for the direct and reflective waves. Two existing models were leveraged to analyze null points: 1) signal strength loss (i.e., a free space path loss model, or FSPL, in Appendix A) and 2) the existing horizontal and vertical polarization null points from a DSRC RSU. Using empirical data from two different field tests, the existing horizontal and vertical polarization null point model was shown to contain limitations in short distances from the DSRC RSU. Moreover, the existing horizontal and vertical polarization model for null points was extremely challenging to replicate with over 15 DSRC RSU data sets. After calculating the null point for several DSRC RSU heights, the paper noticed a limitation of the existing horizontal and vertical polarization null point model with over 15 DSRC RSU data sets (i.e., the model does not account for null points along the full length of the FSPL model). An extended horizontal and vertical polarization model is proposed that calculates the null point from a DSRC RSU. There are 18 model comparisons of the packet counts and signal strengths at various thresholds as perspective extended horizontal and vertical polarization models. This paper compares the predictive ability of 18 models and measures the fit. Finally, a predication graph is depicted with the neural network’s probability profile for packet counts =1 when greater than or equal to 377. Likewise, a python script is provided of the extended horizontal and vertical polarization model in Appendix C. Consequently, the neural network model was applied to 10 different DSRC RSU data sets at 10 unique locations around a circular test track with packet counts ranging from 0 to 11. Neural network models were generated for 10 DSRC RSUs using three thresholds with an objective to compare the predictive ability of each model and measure the fit. Based on 30 models at 10 unique locations, the highest misclassification was 0.1248, while the lowest misclassification was 0.000. There were six RSUs mounted at 3.048 (or 10 feet) from the ground with a misclassification rate that ranged from 0.1248 to 0.0553. Out of 18 models, seven had a misclassification rate greater than 0.110, while the remaining misclassification rates were less than 0.0993. There were four RSUs mounted at 6.096 meters (or 20 feet) from the ground with a misclassification rate that ranged from 0.919 to 0.000. Out of 12 models, four had a misclassification rate greater than 0.0590, while the remaining misclassification rates were less than 0.0412. Finally, there are two major limitations in the research: 1) the most effective key parameter is packet counts, which often require expensive data acquisition equipment to obtain the information and 2) the categorical type (i.e., decision tree, logistic regression, and neural network) will vary based on the packet counts or signal strength threshold that is dictated by the threshold criterion. There are at least two future research areas that correspond to this body of work: 1) there is a need to leverage the extended horizontal and vertical polarization null point model on multiple DSRC RSUs along a highway on/off ramp, and 2) there is a need to apply and validate different electric and magnetic (or propagation) models.

Dans ce travail de thèse, nous nous sommes intéressés à la modélisation et la simulation de la propagation d'ondes ultrasonores dans l'os cortical. Plus précisément, nous avons étudié et analysé la technique dite des ultrasons quantitatifs (Quantitative Ultrasound, QUS) pour l'évaluation de la qualité du tissu osseux. Il s'agit d'une technique émergente dont l'application aux tissus osseux suscite un intérêt particulier dans la communauté scientifique. Le tissu osseux étant un tissu vivant, il est sujet au vieillissement et à divers pathologies parmi lesquelles on peut citer ostéoporose, ostéomalacie, ostéoporomalacie, ou encore, la maladie dite de Paget. Pour accompagner les soins à prodiguer au tissu osseux, une surveillance de sa qualité s'avère indispensable. Dans ce contexte, les méthodes ultrasonores sont réputées être intéressantes, de par leurs caractères non-invasif, peu coûteux, portable et non-ionisant. Cependant, utiliser des ultrasons dans le cadre de la caractérisation du tissu osseux, suppose une compréhension profonde des différents phénomènes physiques mis en jeu lors de leur propagation. Dans cette optique, notre travail est développé dans la thématique de la modélisation dédiée à la propagation des ondes ultrasonores dans des guides d'ondes multidimensionnels, hétérogènes, anisotropes, et composés de matériaux dont l'hétérogénéité peut être qualifiée d'aléatoire. Une des originalités de cette thèse concerne l'étude des coefficients de réflexion et de transmission et des courbes de dispersion en présence d'incertitudes dues aux propriétés matérielles. Dans une première partie, nous étudions les phénomènes de réflexion/transmission via un modèle tri-couches bidimensionnels prenant en compte les tissus mous et l'hétérogénéité aléatoire du tissu osseux. Nous avons pu analyser l'impact de ces caractéristiques sur les coefficients de réflexion et de transmission. Un gradient de propriétés matérielles de l'os est introduit, et son impact sur les coefficients d'intérêt est examiné. L'aspect modal des ondes est exploré, en étudiant la dispersion des ondes de Lamb. Les résultats obtenus dans une configuration géométrique bidimensionnelle ont permis de discuter l'influence des divers paramètres, en terme de propriétés mécaniques et/ou géométriques, sur la propagation des ondes ultrasonores dans le tissu cortical. Dans une deuxième partie, le modèle est étendu pour une configuration géométrique cylindrique. La discussion est menée afin d'analyser l'influence de la géométrie tridimensionnelle de l'os sur les phénomènes de propagation / In this thesis, we are interested in the modeling and simulation of the propagation of ultrasonic waves in the cortical bone. Precisely, we have studied and analyzed the Quantitative Ultrasound (QUS) technique for the evaluation of the quality of bone tissue. It is an emerging technique those the application to bone tissue arouses particular interest in the scientific community. Since bone tissue is a living tissue, it is subject to aging and various pathologies, such osteoporosis, osteomalacia, osteoporomalacia, or the so-called Paget disease. To assist in therapeutic follow-up of the bone, monitoring of quality of bone tissue is essential. In this context, methods based on QUS technique are deemed to be interesting, due of their non-invasive, inexpensive, portable and non-ionizing characteristics. However, use the ultrasound in the context of characterization of bone tissue, requires a deep understanding of the different physical phenomena involved in their propagation. In this perspective, our work is developed in the modeling theme dedicated to the propagation of ultrasonic waves in multidimensional, heterogeneous, anisotropic waveguides, constituted of materials whose heterogeneity can be qualified as random. One of the originalities of this thesis concerns the study of the reflection and transmission coefficients and the dispersion curves in the presence of uncertainties in the material properties. In a first part, we study the reflection/transmission phenomena via a two-dimensional tri-layer model taking into account the soft tissues and the random heterogeneity of the bone tissue. We analyzed the impact of these characteristics on the reflection and transmission coefficients. A gradient of material properties is introduced, and its effect on the coefficients of interest is examined. The modal aspect of the waves is explored, by studying the dispersion of Lamb waves. The results obtained in a two-dimensional geometrical configuration made it possible to discuss the influence of the various parameters, in terms of mechanical and/or geometric properties, on the propagation of the ultrasonic waves in the cortical tissue. In a second part, the proposed model is extended for a cylindrical geometric configuration. The discussion is carried out in order to analyze the influence of the three-dimensional geometry of the bone on the phenomena of propagation

Cette thèse propose un formalisme général pour modéliser la propagation des ondes acoustiques dans une multicouche composée de toute combinaison de couches liquides, solides élastiques isotropes et poro-élastiques isotropes, la méthode ayant la flexibilité d'être développée pour inclure d'autres natures de couches. Dans un premier lieu, un algorithme stable est développé, basé sur l'approche récursive de la matrice de rigidité, pour modéliser la propagation d'une onde plane incidente sur la multicouche en fonction de son angle d'incidence et de sa fréquence. Cet algorithme fusionne de manière récursive les matrices de rigidité des couches individuelles de la structure en une matrice de rigidité totale et permet ensuite le calcul des coefficients de réflexion et de transmission, ainsi que les composantes de déplacement et de contrainte à l'intérieur de la multicouche pour chaque direction d'incidence des ondes planes. Deuxièmement, pour modéliser la propagation d'un faisceau délimité d'ondes incidentes, la technique du spectre angulaire est utilisée, basée sur la décomposition de ce faisceau en un spectre d'ondes planes se propageant dans des directions différentes. Par la suite, le faisceau d'onde réfléchi dans le milieu d'incidence et le faisceau d'onde transmis dans le milieu de transmission, ainsi que la distribution des champs (composantes de déplacement et de contrainte) à l'intérieur de la multicouche sont obtenus en superposant la contribution de toutes les ondes planes se propageant dans les différentes directions. Comme application numérique, une tri-couche solide-poreuse-solide immergée dans l'eau est simulée. La réflexion et la transmission qui en résultent, ainsi que les composantes de déplacement et de contrainte dans la multicouche, correspondants à l’onde plane incidente et au faisceau limité incident, révèlent la stabilité du procédé et la continuité des déplacements et des contraintes aux interfaces. / This thesis proposes a general formalism to model the acoustic wave propagation in a multilayer consisting of any combination of fluid, isotropic elastic solid, and isotropic poroelastic layers, the method having the flexibility to be extended to include other layer-natures. At a first stage, a stable algorithm is developed, based on the recursive stiffness matrix approach, to model the propagation of a plane wave incident on the multilayer as a function of its incidence angle and frequency. This algorithm merges recursively the structureindividual layers stiffness matrices into one total stiffness matrix and allows then the calculation of the reflection and transmission coefficients, as well as the displacement and stress components inside the multilayer for every incident plane wave direction. Secondly, to model the propagation of a bounded incident wave beam, the angular spectrum technique is used which is based on the decomposition of this beam into a spectrum of plane waves traveling in different directions. The corresponding reflected wave beam in the incidence medium, and the transmitted wave beam in the transmission medium, as well as the fields distributions (displacement and stress components) inside the multilayer are obtained by summing the contribution of all the plane waves traveling in different directions. As a numerical application, a three-layered solid-porous-solid structure immersed in water is simulated. The resulting reflection and transmission as well as the displacement and stress components in the multilayer corresponding to both, the incident plane wave in different directions and the incident bounded beam reveal the stability of the method and the continuity of the displacements and stresses at the interfaces.