Essa dissertação aborda o tema de propagação de ondas de tensão em hastes metálicas retangulares. Este tipo de onda pode ser utilizada como base na verificação da integridade estrutural através de um ensaio não destrutivo (END). A propagação de ondas elásticas em sólidos apresenta muito potencial quando se deseja estimar a integridade de determinada estrutura. Porém para transformar esse fenômeno físico em uma técnica aplicável na detecção de danos, alguns passos devem ser seguidos, dentre eles: a compreensão das características de propagação da estrutura em estudo, in teração das ondas elásticas com defeitos, aten uação das ondas propagadoras devido a fontes de amortecimento e dispersão. Neste contexto o presente trabalho tem o principal foco no desenvolvimento de uma metodologia eficiente para a investigação da propagação de ondas de tensão em hastes retangulares metálicas, abordando o tema por diversos aspectos. No decorrer do mesmo são calcu ladas as curvas de dispersão de uma haste retangular com seção transversal de 15 x5 [rum], para uma faixa de frequência determinada [0,100 kHz], utilizando três metodologias distintas e realizando a comparação crítica entre elas. São realizadas investigações teóricas, de forma analítica e numérica (via análise explícita empregando elementos finitos) e uma inves tigação experimental das características de propagação da geometria referida. Também os efeitos da aten uação das ondas na geometria é estudado. Os resulta dos obtidos são discutidos procurando mostrar sua coerência e enfatizando a informação sobre o comportamento mecânico das ondas de tensão nesse tipo de estrutura, observando aspectos relevantes à concepção de técnicas de END que possi bilitem a avaliação da integridade dessas estruturas. / This dissertation addresses the issue of propagation of stress waves in metallic rectangular rods. This type of wave can be used as the integrity check structural integrity through a non-destructive test (NDT). The propagation of elastic waves in solids has a lot of potential when estimating the given structure integrity. But to turn this physical phenomenon in an applicable technique for the detection of damage, some steps should be taken, including: understanding of propagating characteristics of the structure under study, interaction of elastic waves with defects, attenuation of the propagating waves due to sources of damping and dispersion. In this context, the present work is the main focus in developing an effective methodology for investigating the propagation of stress waves in rectangular metal rods, addressing the issue by several aspects. During the same are calculated dispersion curves of a rod with rectangular cross section 15 x5 [mm], for a given frequency range [0,100 kHz], using three different methodologies and performing the critical comparison between them. Are performed theoretical investigations, in analytical and numerical form (via explicit analysis using finite element) and an experimental investigation of the propagation features said geometry. Also the effects of attenuation of the waves on geometry is studied. The results are discussed trying to show their consistency and emphasizing information about the mechanical behavior of stress waves in this type of structure, observing relevant aspects to the design of NDT techniques to enable the assessment of the integrity of these structures.

In this thesis, we study the exact eigenvalue distribution of product of independent rectangular complex Gaussian matrices and also that of product of independent truncated Haar unitary matrices and inverses of truncated Haar unitary matrices. The eigenvalues of these random matrices form determinantal point processes on the complex plane. We also study the limiting expected empirical distribution of appropriately scaled eigenvalues of those matrices as the size of matrices go to infinity. We give the first example of a random matrix whose eigenvalues form a non-rotation invariant determinantal point process on the plane. The second theme of this thesis is infinite products of random matrices. We study the asymptotic behaviour of singular values and absolute values of eigenvalues of product of i .i .d matrices of fixed size, as the number of matrices in the product in-creases to infinity. In the special case of isotropic random matrices, We derive the asymptotic joint probability density of the singular values and also that of the absolute values of eigenvalues of product of right isotropic random matrices and show them to be equal. As a corollary of these results, we show probability that all the eigenvalues of product of certain i .i .d real random matrices of fixed size converges to one, as the number of matrices in the product increases to infinity.

Slot-rectangular spouted beds, with rectangular cross-section and slotted gas inlets, have been proposed as a solution to overcoming scale-up difficulties with conventional axisymmetric spouted beds. They can be utilized in gas/particle processes such as drying of coarse particles and coating of tablets. However, application of this spouted bed was limited because of instability and insufficient hydrodynamic studies. The present work is therefore aimed at the study of hydrodynamics, stability and scale-up of slot-rectangular spouted beds. The hydrodynamic study was carried out in four slot-rectangular columns of various width-to-thickness ratios combined with various slot configurations, particles of different properties and a range of operating conditions. Hydrodynamics of slot-rectangular spouted beds showed major similarity with conventional spouted beds. However, equations and mechanistic models adopted from conventional axisymmetric spouted beds generally failed to provide good predictions for the three-dimensional slot-rectangular geometry. New empirical correlations were derived for the minimum spouting velocity and maximum pressure drop for different slot configurations. Slot-rectangular spouted beds also showed more flow regimes than conventional spouted beds. Nine flow regimes, as well as unstable conditions, were identified based on frequency and statistical analysis of pressure fluctuations. Slot geometrical configuration was found to be the main factor affecting the stability of slot-rectangular spouted beds. A comprehensive hydrodynamic study on the effect of slot configuration was therefore carried out. Slots of smaller length-to-width ratio, smaller length and greater depth were found to provide greater stability. Stable criteria for the slot configuration were found consistent with the conventional axisymmetric spouted beds with extra limitation on slot length-to-width ratio and slot depth. Local distributions of pressure, particle velocity and voidage, as well as spout shape and particle circulating flux, were compared for different slot configurations. Higher slot length-to-width ratios lead to slightly higher particle circulation rates. A previously proposed scale-up method involving multiple chambers was tested in the present work using multiple slots. Instability caused by the merging of multiple spouts and asymmetric flow was successfully prevented by suspending vertical partitions between the fountains. Some criteria and guidelines were also proposed for scale-up using multiple chambers. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

Recent tsunami disasters caused devastating damages to well-engineered coastal infrastructures. In fact, the current design guidelines are not able to provide realistic estimations of tsunami loads in order to design structures to withstand tsunamis. Tsunami hydrodynamic forces are estimated using the drag coefficient. This coefficient is traditionally calculated based on a steady flow analogy. However, tsunami bores behave like unsteady flows. The present work aims at investigating the tsunami forces for different structure geometries to provide realistic guidelines to estimate drag coefficients considering unsteady flows. In the present paper, the dam-break approach is used to investigate the tsunami-like bore interaction with structures. A three-dimensional multiphase numerical model is implemented to study the tsunami induced forces on rectangular shape structures with various aspect ratios (width/depth) and orientations. The numerical model results are validated using measured forces and bore surface elevations of the physical experiments. A scaled-up domain is modeled in order to eliminate the effects of domain sidewalls in the simulation results. The drag coefficient relations with structure geometries and bore depths are provided. The obtained hydrodynamic forces and drag coefficients are compared with existing data in the literature and design codes. For the second topic, a multi-phase three-dimensional numerical reproduction of a large scale laboratory experiment of tsunami-like bores interaction with a surface-piercing circular column is presented. The numerical simulation is conducted in OpenFOAM. The dam-break mechanism is implemented in order to generate tsunami-like bores. The numerical model is validated using the experimental results performed at Canadian Hydraulics Center of the National Research Council (NRC-CHC) in Ottawa. The unsteady Reynolds Averaged Navier-Stokes equations (RANS) are used in order to treat the turbulence effects. The Shear Stress Transport (SST) k-ω turbulence model showed high level of accuracy in replication of the bore-structure interaction. Further, a scaled-up domain is used to investigate the influence of the bed condition in terms of various downstream depths and roughness. Finally, a broad investigation on the bore propagation characteristics is performed. The resulting stream-wise forces exerted on the structural column as well as the bore velocity are compared and analyzed for smooth, rough, dry and wet beds with varying depths.

When compared to traditional concrete, steel fibre reinforced concrete (SFRC) shows several enhancements in performance, including improved tensile resistance, toughness and ductility. One potential application for SFRC is in columns where the provision of steel fibres can improve performance under axial and lateral loads. The use of SFRC can also allow for partial replacement of transverse reinforcement required by modern seismic codes. To improve workability, self-consolidating concrete (SCC) can be combined with steel fibres, leading to highly workable SFRC suitable for structural applications. Recent advances in material science have also led to the development of ultra-high performance fibre reinforced concretes (UHPFRC), a material which exhibits very high compressive strength, enhanced post-cracking resistance and high damage tolerance. In heavily loaded ground-story columns, the use of UHPFRC can allow for reduced column sections. This thesis presents the results from a comprehensive research program conducted to study the axial behaviour of columns constructed with highly workable SFRC and UHPFRC. As part of the experimental program, twenty-three full-scale columns were tested under pure axial compressive loading. In the case of the SFRC columns, columns having rectangular section and constructed with SCC and steel fibres were tested, with variables including fibre content and spacing of transverse reinforcement. The results confirm that use of fibres results in improved column behaviour due to enhancements in core confinement and cover behaviour. Furthermore, the results demonstrate that the provision of steel fibres in columns can allow for partial replacement of transverse reinforcement required by modern codes. The analytical investigation indicates that confinement models proposed by other researchers for traditional RC and SFRC can predict the response of columns constructed with SCC and highly workable SFRC. In the case of the UHPFRC columns, variables included configuration and spacing of transverse reinforcement. The results demonstrate that the use of appropriate detailing in UHPFRC columns can result in suitable ductility. Furthermore, the results demonstrate the improved damage tolerance of UHPFRC when compared to traditional high-strength concrete. The analytical investigation demonstrates the need for development of confinement models specific for UHPFRC.

A turbulence model was developed for computing surface velocity coefficients and discharge under steady, uniform flow conditions for rectangular and compound open-channel cross sections. Reynolds-Average Navier-Stokes (RANS) equations, Reynolds stress equations, and kinetic energy and dissipation equations were applied in the model using the finite-volume method with the SIMPLER algorithm. The models show graphical results of the velocity distributions in the longitudinal bed slope direction, secondary velocities, pressure, turbulence kinetic energy, and kinetic energy dissipation rate across the cross section. Also, the surface velocity coefficients were computed at increments of one-eighth of the base width from the vertical walls to the center of the cross section, and the submergence depth of the floating object from zero to 30 cm, with a 5-cm depth increment. Four different sets of Reynolds stress equations (one set by Boussinesq hypothesis and three sets of algebraic stress model) were used to calculate the results. Only one version of the algebraic stress model was successful in predicting the depression of the maximum streamwise velocity below the water surface. The model was calibrated and verified using laboratory data collected at Utah State University. Calculated discharges from the turbulence model had very good agreement with the laboratory data. The surface velocity coefficients from model results were generally lower than the results from the laboratory data, but higher than the values published by the United States Bureau of Reclamation. Standard cross sections of rectangular and compound cross sections were defined to simulate the model results and model sensitivity to parameter changes. The model results were summarized to show the relationship between surface velocity coefficient and channel characteristics compared with the published values by the USBR. For rectangular cross sections, the coefficients from the model are higher than the published USBR values. But the coefficients from the model and USBR are in very close agreement for the tested compound cross sections. The published coefficients by the USBR are a function of only average water depth. However, the model results show that the coefficients are also related to channel size, surface roughness height, float submergence depth, and lateral location of the float object. These factors should be included in the determination of the surface velocity coefficient to improve the discharge estimations from the application of the float method.

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For the past four decades, Moore's law has been the most important benchmark in microelectronic circuits. Continuous improvement in lithographic technology has key enabler for growth in transistor density. In recent times, the wavelength of the light source has not kept its pace in scaling. Consequently, modern devices have feature sizes that are smaller than the wavelength of light source used currently in lithography. Printability in sub-wavelength lithography is one of the contemporary research issues. Some of the printability issues arise from optical defocus, lens aberration, wafer tilting, isotropic etching and resist thickness variation. Many of such sources lead to line width variation in today's layouts. In this work we propose to simulate such lithographic variation and estimate their impact on current devices and interconnects. We also propose to model such effects and aim to provide measures at the design level to mitigate these problems. Variations arising out of lithography process also impact yield and performance. We plan to study the impact of sub-wavelength lithography on yield and provide solutions for its measure, and directed pattern developement and testing.

The objective of this research is to determine the three-dimensional stiffness matrix of a rectangular cross-section helical coil compression spring. The stiffnesses of the spring are derived using strain energy methods and Castigliano's second theorem. A theoretical model is developed and presented in order to describe the various steps undertaken to calculate the spring's stiffnesses. The resulting stiffnesses take into account the bending moments, the twisting moments, and the transverse shear forces. In addition, the spring's geometric form which includes the effects of pitch, curvature of wire and distortion due to normal and transverse forces are taken into consideration. Similar methods utilizing Castigliano's second theorem and strain energy expressions were also used to derive equations for a circular cross-section spring. Their results are compared to the existing solutions and used to validate the equations derived for the rectangular cross-section helical coil compression spring. A finite element model was generated using IDEAS (Integrated Design Engineering Analysis Software) and the stiffness matrix evaluated by applying a unit load along the spring's axis, then calculating the corresponding changes in deformation. The linear stiffness matrix is then obtained by solving the linear system of equations in changes of load and deformation. This stiffness matrix is a six by six matrix relating the load (three forces and three moments) to the deformations (three translations and three rotations). The natural frequencies and mode shapes of a mechanical system consisting of an Additional mass and the spring are also determined. Finally, a comparison of the stiffnesses derived using the analytical methods and those obtained from the finite element analysis was made and the results presented. / Master of Science