Wave propagation problems can be modeled by partial differential equations. In this thesis, we study wave propagation in fluids and in solids, modeled by the acoustic wave equation and the elastic wave equation, respectively. In real-world applications, waves often propagate in heterogeneous media with complex geometries, which makes it impossible to derive exact solutions to the governing equations. Alternatively, we seek approximated solutions by constructing numerical methods and implementing on modern computers. An efficient numerical method produces accurate approximations at low computational cost. There are many choices of numerical methods for solving partial differential equations. Which method is more efficient than the others depends on the particular problem we consider. In this thesis, we study two numerical methods: the finite difference method and the discontinuous Galerkin method. The finite difference method is conceptually simple and easy to implement, but has difficulties in handling complex geometries of the computational domain. We construct high order finite difference methods for wave propagation in heterogeneous media with complex geometries. In addition, we derive error estimates to a class of finite difference operators applied to the acoustic wave equation. The discontinuous Galerkin method is flexible with complex geometries. Moreover, the discontinuous nature between elements makes the method suitable for multiphysics problems. We use an energy based discontinuous Galerkin method to solve a coupled acoustic-elastic problem.

Le travail réalisé pendant cette thèse a permis d'apporter de nouvelles contraintes sur le développement et la distribution de la déformation dans le manteau supérieur et plus particulièrement au niveau des grandes limites de plaques décrochantes. Grâce à l'apport de l'expérience USArray et d'une dizaine d'années d'enregistrements sismologiques supplémentaires, nous avons pu étudier, de manière précise, les variations d'anisotropie dans le voisinage de la Faille de San Andreas. Nous avons confirmé et étendu l'observation de deux couches anisotropes sous cette limite de plaque. On y observe une première couche localisée dans la lithosphère marquant la déformation induite à la limite de plaque, et une autre, asthénosphérique, cohérente avec l'anisotropie observée loin de la faille et d'origine plus discutée. Nous avons montré que la zone de déformation associée aux failles de San Andreas, Calaveras et d'Hayward a, vraisemblablement, une largeur d'au moins 40 kilomètres en base de lithosphère, sous chacune de ces failles. Nous avons ensuite procédé à la modélisation thermomécanique (ADELI) de la migration d'une limite de plaques décrochante couplée à une modélisation du développement de fabriques cristallographiques par une approche viscoplastique auto-cohérente (VPSC). Ceci nous a permis d'y observer le développement de la déformation et les conséquences des possibles interactions entre la déformation décrochante en surface et le cisaillement en base de lithosphère dû au déplacement horizontal des plaques. Les propriétés élastiques déduites des fabriques cristallographiques modélisées montrent que de telles interactions existent et provoquent, sous la limite de plaques, une rotation des orientations cristallographiques avec la profondeur. Le signal associé à ces rotations progressives n'est toutefois pas cohérent avec la présence de deux couches d'anisotropie comme proposée sous la faille de San Andreas. Nous pensons par conséquent qu'il existe, sous la Californie, une zone de découplage entre la lithosphère et l'asthénosphère, permettant d'individualiser une déformation lithosphérique d'une déformation asthénosphérique. Nous estimons, en outre, que l'anisotropie observée dans l'asthénosphère sous la Californie ne peut être expliquée seulement par le cisaillement induit par le déplacement de la lithosphère Nord Amérique. En effet, les propriétés anisotropes obtenues par modélisation à partir d'une plaque se déplaçant dans une direction et une vitesse proche de celle de la plaque Amérique du Nord montrent qu'on ne peut espérer guère plus que quelques dixièmes de seconde de délai au bout de 10 Ma de déplacement. Les déphasages mesurés en Californie étant de l'ordre de 1,5 s, il est donc nécessaire d'invoquer la présence d'écoulements mantelliques actifs sous cette région / This work provides new constraints on the development and on the distribution of the deformation in the upper mantle and particularly beneath transform plate boundaries. USArray experiment and the remarkable increase of the dataset in California for the past ten years allowed us to scrutinize the lateral variations of the anisotropy in the vicinity of the San Andreas Fault zone. We have confirmed and increased the detection of two layers of anisotropy beneath this plate boundary. The first layer, located in the lithosphere, is related to the deformation induced at the fault, and the other one, located in the asthenosphere, is coherent with the anisotropy observed far from it, its origin is however less clear. We show that the deformation zone associated both to the San Andreas, Calaveras and Hayward Faults, is likely 40 km wide at 70 km depth. We then performed numerical thermomechanical modeling (ADELI) of the displacement of a transform plate boundary associated with the computation of the development of crystallographic fabrics using a viscoplastic self-consistent approach (VPSC). We analyzed the distribution of the deformation in the model ant looked after the possible interactions at depth between deformation caused at surface by the strike-slip dynamic of the fault and the shearing at the base of the lithosphere caused by the horizontal displacement of the plates. Elastic properties derived from the crystallographic fabrics modeled, show that such interactions exist and induce, beneath the fault zone, a progressive rotation of the crystallographic fabrics with depth. Seismological signature of these smooth rotations is however not relevant with the presence of two anisotropic layers as proposed beneath California. We thus consider that a decoupling zone exists between the lithosphere and the asthenosphere beneath the California to account for the sharp separation between a lithospheric and an asthenospheric deformation. We furthermore estimate that anisotropy observed far form the San Andreas Fault in California cannot be explained only by the drag of the asthenosphere by the North America lithosphere as proposed in our article. Indeed, we can only expect few tenths of second of splitting delay from the anisotropic properties derived from the numerical modeling of a plate moving in the same direction and in the same velocity than the North American lithosphere only for 10 Ma of displacement. As delays observed in California rather reach 1.5 s, anisotropy in this region thus requires the existence of an active asthenospheric flow to be explained.

Orientador: José Maria Campos dos Santos / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-27T14:11:06Z (GMT). No. of bitstreams: 1 Nobrega_EdilsonDantas_M.pdf: 12912450 bytes, checksum: 790ec696a10ed45d5c22747b666dea61 (MD5) Previous issue date: 2015 / Resumo: A fim de superar as limitações atuais na análise dinâmica de estruturas em médias e altas frequências e tirando proveito da natureza periódica de muitas destas estruturas, nos últimos anos, foram desenvolvidos métodos de guia de ondas. São modelos obtidos a partir de fatias das guia de ondas e modeladas pelo Método dos Elementos Finitos (MEF) e pelo Método do Elemento Espectral (SEM), também conhecidos como Método de Propagação de Ondas por Elementos Finitos (Wave Finite Element Method - WFEM) e Método de Propagação de Ondas por Elementos Espectrais (Wave Spectral Element Method - WSEM), respectivamente. Exemplos de guia de ondas podem ser encontrados em diferentes tipos de estruturas tais como, os trilhos de trem, tubulações e até mesmo em estruturas complexas tipo a fuselagem de um avião e outras. Este trabalho apresenta uma extensão destes métodos de guias de ondas para a modelagem com elementos de barra de alta ordem. Os métodos foram implementados computacionalmente em códigos Matlab e os resultados são comparados com os do Método do Elemento Espectral (Spectral Element Method - SEM), do Método dos Elementos Finitos e com os do modelo analítico da Placa de Rayleigh-Lamb. Três elementos de barra de alta ordem são formulados: o modelo de Love (ou de Um modo), o modelo de Mindlin-Herrmann (ou de Dois modos) e o modelo de Doyle (ou de Três modos). O método é avaliado através de exemplos simulados computacionalmente e os resultados são analisados e comparados com aqueles da literatura / Abstract: In order to overcome the current limitations in the dynamic analysis of structures at middle and high frequencies and taking advantage of the periodic nature of many of these structures, in recent years, waveguide methods were developed. Models are obtained from slices of patterned waveguides, were developed by Finite Element Method (FEM) and Spectral Element Method, also known as Wave Finite Element Method - WFEM and Wave Spectral Element Method - WSEM. Examples of waveguides can be found in different types of structures such as the railroad tracks, pipelines and even complex structures like the fuselage of an airplane and others. This work presents an extension of these waveguides methods to model high order rod elements. The methods were implemented in Matlab codes and the results are compared with Spectral Element Method - SEM, Finite Element Method and the analytical Rayleigh-Lamb plate model. Three high order bar elements are formulated: the Love's model (or one mode), the Mindlin-Herrmann's model (or two modes) and the Doyle's model (or three modes). The method is evaluated through computationally simulated examples and the results are analyzed and compared with those of the literature / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

In recent years, the desperate need for reliable clean and relatively small power demand has emerged for edge-of-grid or off-grid regions to keep pace with development demands. A salient technology that has gained much attention for this purpose is the Small Modular Reactors, i.e., SMRs. SMRs differ from conventional Nuclear Power Plants (NPPs) in many aspects, specifically the enclosing structure of the reactor. The burial depth of the SMR structure is expected to reach great depths. For example, the substructure depth reaches 30 m in the SMR design proposed by NuScale (NuScale Power, 2020). Consequently, seismic analysis of deeply embedded structures with a relatively small footprint has been identified as one of the challenges to the safe implementation of SMR technology (DIS-16-04, 2016). Such structures are expected to be more sensitive to surface wave propagation and the seismic interaction with nearby substructures and nonstructural elements such as pipelines. This dissertation develops analytical and numerical methods to analyze the seismic earth pressure exerted on the SMR substructure by considering the effects of seismic surface waves, structure-soil-structure interaction (SSSI), and the interaction with nearby pipelines. The three-dimensional wave propagation theory is employed in the analysis. Solutions for the earth pressure induced by Rayleigh waves are obtained for substructures deeply embedded into homogeneous or multilayered soil profiles. In addition, the effect of thin soil layer (stiff or soft) soils in a soil profile is investigated in the presence of Rayleigh waves. Furthermore, additional earth pressure due to SSSI is examined, and a simplified procedure is proposed based on the three-dimensional wave propagation theory and a guided flow chart to track seismic wave interference. The SSSI analysis yields solutions for the optimal distance between substructures corresponding to the minimum SSSI in new designs. The interaction between substructures and nearby pipelines is explored numerically using the Spectral Element Method. SPECFEM2D software is adopted to perform the analysis, where the three-dimensional wave propagation is successfully implemented. Based on the analysis for pipelines with different configurations, general conclusions are drawn regarding the additional earth pressure on substructures and pipelines based on a comprehensive parametric study of various parameters. In addition, this research also provides an approach to determine the backfill configuration and the selection of backfill materials, which could minimize the seismic amplitudes transmitted to substructures. / Thesis / Doctor of Philosophy (PhD) / Small Modular Reactors (SMRs) are the cornerstone of recent developments in the nuclear industry. However, the SMRs technology faces several safety-related challenges, which includes the earthquake hazards related to the large embedment depth of the enclosing structure. In particular, the major concerns are about the risks related to seismic surface waves as well as the seismic interaction between nearby structural and non-structural elements (e.g., pipelines). The thesis addressed these major concerns by developing analytical and numerical methods to complement the analysis for the integrity of SMRs with sufficient seismic resistance. The solutions are verified and benchmarked using data in the literature. Future researches are suggested to further improve seismic analysis of SMRs.

The mechanical and structural engineering community are increasingly resorting to the use of periodic metamaterials and metastructures to mitigate high amplitude vibrations; and nonlinearities are also an active area of research because they potentially provide different methods for controlling elastic waves. While the theory of propagation of linear elastic waves seems to be fairly complete and has led to remarkable discoveries in a variety of disciplines, there is still much to investigate about nonlinear waves, both in terms of their dispersion analytical description and their numerical characterization. This thesis mainly relies on the latter aspect and focuses on the analysis of nonlinear metamaterials and metastructures for both the mitigation and control of elastic waves. In particular, the thesis covers four main topics, each associated with a different nonlinearity: i) dispersion curves and mechanical parameters identification of a weakly nonlinear cubic 1D locally resonant metamaterial; ii) manipulation of surface acoustic waves (SAWs) through a postbuckling-based switching mechanism; iii) seismic vibration mitigation of a multiple-degrees-of-freedom (MDoF) system, the so-called metafoundation, by means of hysteretic nonlinear lattices; iv) seismic vibration mitigation of a periodic coupled system pipeline-pipe rack (PPR), by means of a vibro-impact system (VIS). To identify the dispersion curves of a cubic nonlinear 1D locally resonant metamaterial, a simple experimentally-informed reference subsystem (RS) which embodies the unit cell is employed. The system identification relies on the Floquet--Bloch (FB) periodic conditions applied to the RS. Instead, the parametric identification is carried out with a revised application of the subspace identification (SSI) method involving harmonic, non-persistent excitation. It is remarkable that the proposed methodology, despite the linearization caused by the FB boundary conditions, is responsive to the amplitude of the excitation that affects the dispersion curves. The FB theorem, in fact, is often adopted to reduce the computational burden in calculating the dispersion curves of metamaterials. In contrast, the experimental dispersion reconstruction requires multiple velocity measurements by means of laser Doppler vibrometers (LDVs), as for the case of SAWs. To manipulate SAWs, a proof-of-concept experiment was performed for a postbuckling-based mechanical switching mechanism. Precompressed beams are periodically arranged on one face of an elastic plate to manipulate the dispersion of the SAWs propagating as edge waves. By compressing the columns over their Euler critical load, in fact, it is possible to manipulate the surface wave dispersion: the dispersion curve’s dispersive branches, originally caused by the beams in the undeformed configuration, are cleared, and the original path of the group velocity is restored. This concept is introduced analytically and numerically in this thesis, and a novel device is proposed for controlling the SAWs. With regard to the mitigation of seismic waves, this thesis presents the application of two nonlinear dissipative devices to periodic components and structures of industrial facilities. Firstly, a finite locally resonant metafoundation of an MDoF fuel storage tank is equipped with fully nonlinear hysteretic devices to mitigate absolute accelerations and displacements in the low-frequency regime. Secondly, for mitigating the vibrations in PPRs, spatial periodicity and internal damping are combined to obtain an enhancement in the attenuation rate of the system. At the same time, the seismic performance of the PPR is improved by means of an external nonlinear VIS. These investigations show the characterization of the structures’ responses due to the stochastic nature of the input; and for the case of the VIS, a chaotic behavior is sometimes observed and demonstrated. In conclusion, this thesis investigates the nonlinear response of different periodic structures and their potential for wave control and mitigation in various applications. The results of this research contribute to the understanding of the nonlinear behavior of these periodic structures and provide insights into the design, the optimization, and the identification of metamaterials and metastructures performance.

This bachelor's thesis aims to implement a wave propagation experiment on Field-Programmable Gate Array to detect the signal strength at pre-defined frequencies for use in sounding rocket experiments. This includes the choice of suitable components such as analog to digital converters, filters, voltage regulators, and amplifiers. The board prototype was designed by keeping in mind the need for a miniaturized solution that would still provide the wanted results, by following design guidelines. The second part of the project involves the design of the software in a hardware description language. An analysis in MATLAB® was done to determine the parameters needed to successfully reconstruct the transmitted signal on the receiver, while still being able to fit on the given FPGA. To make sure of that, a simulation was performed on ModelSim a tool for simulation and debugging for VHDL. From the simulations, it can be concluded that this design is feasible and that this project gives the basis for further development, to create a viable solution for a wave propagation experiment with a miniaturized payload. / Denna kandidatuppsats syftar till att implementera ett vågutbredningsexperiment på Field-Programmable Gate Array för att detektera signalstyrkan vid fördefinierade frekvenser för användning i sonderingsraketexperiment. Detta inkluderar val av lämpliga komponenter som analog till digital omvandlare, filter, spänningsregulatorer och förstärkare. Kortprototypen designades genom att ha i åtanke behovet av en miniatyriserad lösning som fortfarande skulle ge önskat resultat, genom att följa designriktlinjerna. Den andra delen av projektet involverar design av programvaran i ett hårdvarubeskrivningsspråk. En analys i MATLAB® gjordes för att bestämma parametrarna som behövs för att framgångsrikt rekonstruera den sända signalen på mottagaren, samtidigt som den fortfarande kan passa på den givna FPGA. För att säkerställa det gjordes en simulering på ModelSim ett verktyg för simulering och felsökning för VHDL. Från simuleringarna kan man dra slutsatsen att denna design är genomförbar och att detta projekt ger grunden för vidareutveckling, för att skapa en hållbar lösning för ett vågutbredningsexperiment med en miniatyriserad nyttolast. / Kandidatexjobb i elektroteknik 2022, KTH, Stockholm

No description available.

A combination of theoretical, numerical, and experimental methods were utilized to determine that shock waves can form in brain tissue from smooth boundary conditions. The conditions that lead to the formation of shock waves were determined. The implication of this finding was that the high gradients of stress and strain that could occur at the shock wave front could contribute to mechanism of brain injury in blast loading conditions. The approach consisted of three major steps. In the first step, a viscoelastic constitutive model of bovine brain tissue under finite step-and-hold uniaxial compression with 10 1/s ramp rate and 20 s hold time has been developed. The assumption of quasi-linear viscoelasticity (QLV) was validated for strain levels of up to 35%. A generalized Rivlin model was used for the isochoric part of the deformation and it was shown that at least three terms (C_10, C_01 and C_11) are needed to accurately capture the material behavior. Furthermore, for the volumetric deformation, a linear bulk modulus model was used and the extent of material incompressibility was studied. The hyperelastic material parameters were determined through extracting and fitting to two isochronous curves (0.06 s and 14 s) approximating the instantaneous and steady-state elastic responses. Viscoelastic relaxation was characterized at five decay rates (100, 10, 1, 0.1, 0 1/s) and the results in compression and their extrapolation to tension were compared against previous models. In the next step, a framework for understanding the propagation of stress waves in brain tissue under blast loading was developed. It was shown that tissue nonlinearity and rate dependence are key parameters in predicting the mechanical behavior under such loadings, as they determine whether traveling waves could become steeper and eventually evolve into shock discontinuities. To investigate this phenomenon, the QLV material model developed based on finite compression results mentioned above was extended to blast loading rates, by utilizing the stress data published on finite torsion of brain tissue at high rates (up to 700 1/s). It was shown that development of shock waves is possible inside the head in response to compressive pressure waves from blast explosions. Furthermore, it was argued that injury to the nervous tissue at the microstructural level could be attributed to the high stress and strain gradients with high temporal rates generated at the shock front and this was proposed as a mechanism of injury in brain tissue. In the final step, the phenomenon of shock wave formation and propagation in brain tissue was further studied by developing a one-dimensional model of brain tissue using the Discontinuous Galerkin finite element method. This model is capable of capturing high-gradient waves with higher accuracy than commercial finite element software. The deformation of brain tissue was investigated under displacement input and pressure input boundary conditions relevant to blast over-pressure reported in the literature. It was shown that a continuous wave can become a shock wave as it propagates in the tissue when the initial changes in acceleration are beyond a certain limit. The high spatial gradients of stress and strain at the shock front cause large relative motions at the cellular scale at high temporal rates even when the maximum strains and stresses are relatively low. This gradient-induced local deformation occurs away from the boundary and can therefore contribute to the diffuse nature of blast-induced injuries.   / Mechanical Engineering

This research focuses on radio wave propagation at millimeter-wave frequencies. A measurement based channel characterization approach is taken in the investigation. First, measurement techniques are analyzed. Three types of measurement systems are designed, and implemented in measurement campaigns: a narrowband measurement system, a wideband measurement system based on Vector Network Analyzer, and sliding correlator systems at 5.8+AH4AXA-mbox{GHz}, 38+AH4AXA-mbox{GHz} and 60+AH4AXA-mbox{GHz}. The performances of these measurement systems are carefully compared both analytically and experimentally. Next, radio wave propagation research is performed at 38+AH4AXA-mbox{GHz} for Local Multipoint Distribution Services (LMDS). Wideband measurements are taken on three cross-campus links at Virginia Tech. The goal is to determine weather effects on the wideband channel properties. The measurement results include multipath dispersion, short-term variation and signal attenuation under different weather conditions. A design technique is developed to estimate multipath characteristics based on antenna patterns and site-specific information. Finally, indoor propagation channels at 60+AH4AXA-mbox{GHz} are studied for Next Generation Internet (NGI) applications. The research mainly focuses on the characterization of space-time channel structure. Multipath components are resolved both in time of arrival (TOA) and angle of arrival (AOA). Results show an excellent correlation between the propagation environments and the channel multipath structure. The measurement results and models provide not only guidelines for wireless system design and installation, but also great insights in millimeter-wave propagation. / Ph. D.

Theoretical and computational methods have been used to study nonlinear effects in the mechanical response of materials at the nano and macro scales. These methods include, acoustoelastic theory, molecular dynamics and finite element models. The nonlinear indentation response of Ni thin films of thicknesses in the nano scale was studied using molecular dynamics simulations with embedded atom method (EAM) interatomic potentials. The study included both single crystal films and films containing low angle grain boundaries perpendicular to the film surface. The simulation results for single crystal films show that as film thickness decreases, larger forces are required for similar indentation depths but the contact stress necessary to emit the first dislocation under the indenter is nearly independent of film thickness. The presence of grain boundaries in the films leads to the emission of dislocations at a lower applied stress. For a single crystal Ni thin film of a thickness of 20 nm a direct comparison of simulation and experimental results is presented, showing excellent agreement in hardness values. The effects of using different interatomic potentials and indentation rates for the simulations are also discussed. Dynamic indentation of the Ni thin film was also carried out for different frequencies. It has been found that there is a 12% increase in dislocations compared to quasi static indentation and the results are consistent with experiments. Acoustoelastic theory was used to study how nonlinear elastic properties of unidirectional graphite/epoxy (gr/ep) effect the energy flux deviation due to an applied shear stress. It was found that the quasi-transverse wave (QT) exhibits more flux deviation compared to the quasi-longitudinal (QL) or the pure transverse (PT) due to an applied shear stress. The flux shift in QT wave due to an applied shear stress is higher than that for an applied normal stress along laminate stacking direction for the same magnitude. The QT wave has energy flux deviation due to shear stress at 0o and 90o fiber orientations as compared to normal stress case where the flux deviation is zero. It was found that the energy flux shift of QT wave in gr/ep varies linearly with applied shear stress. The Finite element model of the equations of motion combined with the Newmark method in time was used to confirm the flux shift predicted by theory. / Ph. D.