[pt] Este estudo apresenta um método computacional para modelar campos eletromagnéticos em guias de onda retangulares curvados com seção transversal uniforme, usando o método variacional de Rayleigh-Ritz. Potenciais aplicações desta pesquisa em engenharia incluem o projeto de alimentadores para antenas, conversores de modais na faixa de micro-ondas, filtros, entre outros. Embora vários modelos tenham sido propostos para resolver este problema, as técnicas numéricas convencionais baseadas em elementos finitos, diferenças finitas e volumes finitos requerem altos custos computacionais. Para superar esses problemas, foi desenvolvida uma formulação variacional para resolver as equações de Maxwell em um sistema de coordenadas toroidal local, por meio de um novo funcional introduzido neste trabalho. O funcional foi adaptado para domínios uniformemente curvados com seção transversal arbitrária, e investigações analíticas foram conduzidas para confirmar suas características estacionárias. O formalismo Rayleigh-Ritz foi utilizado para converter o funcional em um problema equivalente de autovalores e autovetores, usando uma expansão em harmônicas retangulares de um guia de onda reto como funções de base para modelar um guia de onda retangular curvo. Um algoritmo numérico foi desenvolvido em Matlab para validar nosso modelo, e os resultados foram comparados com soluções perturbacionais e numéricas de referência, demonstrando alta precisão e menor custo computacional. / [en] This study presents a computational method for modeling electromagnetic fields in curved rectangular waveguides with uniform cross-section, using the variational Rayleigh-Ritz method. The potential applications of this research in engineering include the design of feeders for antennas, microwave mode converter devices, filters, among others. While various models have been proposed to solve this problem, conventional numerical techniques based on finite elements, finite differences, and finite volumes require high computational costs. To overcome these issues, a variational formulation for solving Maxwell s equations in a local toroidal coordinate system was developed via a novel functional introduced in this work. The functional was adapted to handle uniformly bend domains with arbitrary cross-section, and analytical investigations were conducted to confirm its stationary characteristics. The Rayleigh-Ritz formalism was employed to convert the functional into an equivalent problem of eigenvalues and eigenvectors using an expansion in terms of rectangular harmonics of a straight waveguide as basis functions for modeling a bend rectangular waveguide. A numerical algorithm was developed in Matlab to validate our model, and the results were compared against reference perturbational and numerical solutions, demonstrating high accuracy and lower computational costs.

This thesis discusses the aero-acoustic characterisation of a perforate sample using a three-port technique. A rectangular T-junction with a flush mounted perforated sample at the intersection form the acoustical three-port. Under acoustic excitation from three different directions a direct method of impedance determination is incorporated to experimentally determine the passive acoustic properties of the perforate. The three-port scattering matrix and the normalised transfer impedance are calculated in the presence of grazing flow and for high-level excitation and the behaviour of these characteristics is studied. Validation of the determined results in the linear range is carried out by comparing it with existing models. Moreover, based on the experimental results for low grazing flow velocities the dependence of the real part of the transfer impedance on the grazing flow parameters as well as dimensionless numbers is described, and a semi-empirical model quantifying the behaviour is proposed. Furthermore, the thesis explains some experimental errors pertaining to standing wave patterns and operating conditions, and corrections are suggested to reduce the errors. / <p>QC 221007</p>

Предметом исследования является производство прямоугольной медной проволоки для электротехнических целей. Приведен патентно-литературный обзор, включающий в себя некоторые особенности производства медной проволоки, а также способы ее производства, оборудование и инструмент. Представлена общая технологическая схема производства прямоугольной медной проволоки. Также приведена информация, касающаяся схемы напряженного состояния в зоне очага деформации при волочении и конфигурация канала волоки. Помимо вышеприведенной, приведена информация, касающаяся испытаний проволоки на растяжение и анализ их результатов. / The subject of the study is production of rectangular copper wire for electrical purposes. There are patent and literature review which include several features of production of copper wire, methods of production, equipment and tools. Given the general technological scheme of production of rectangular copper wire. Given information about scheme of stress state in deformation zone when drawing and configuration of die hole. Also given information about tensile test and analysis of its results.

L'hybridation des méthodes numériques est l'une des nombreuses pistes dans la recherche de la rapidité et de l'efficacité et de la précision d'une modélisation électromagnétique des structures complexes associant des parties de formes régulières de grandes dimensions électriques et des parties de formes complexes de dimensions plus modestes. Au lieu d'une seule formulation globale, on cherche à appliquer l'hybridation de plusieurs méthodes numériques notamment la méthode variationnelle multimodale (MVM), la méthode des éléments finis (FEM) et les réseaux de neurones artificiels. Un nouveau schéma hybride original qui combine la MVM et la FEM a été proposé pour caractériser une discontinuité complexe dans un guide d'onde rectangulaire. Les résultats obtenus tout en étant conformes aux résultats fournis par les simulateurs commerciaux et les résultats expérimentaux, apportent une amélioration sensible quant au temps de calcul. Le schéma hybride a été étendu pour la caractérisation des discontinuités complexes en cascade et appliqué à la conception de filtres micro-onde présentant des discontinuités complexes permettant ainsi un gain de temps très important. L'hybridation des réseaux de neurones artificiels et les méthodes modales a amélioré le temps de calcul pour l'analyse des discontinuités simples dans les guides d'onde rectangulaires ce qui a permis d'améliorer l'optimisation des filtres à guides d'ondes nervurés. / Hybridization of numerical methods is one inventive way in the research of the rapidity, the efficiency and the precision of the electromagnetic modeling of complex structures joining straight and large elements with complex and small ones. Instead of a global and unique formulation, we hybridize many numerical methods which are the modal methods, the finite element methods and the artificial neural networks. A novel computer- ided design (CAD) tool of complex passive microwave devices in rectangular waveguide technology is suggested. The multimodal variational method is applied to the full-wave description in the rectangular waveguides while the finite element analysis characterizes waves in the arbitrarily shaped discontinuities. The suggested hybrid approach is successfully applied to the full-wave analysis of complex discontinuities with great practical interest, thus improving CPU time and memory storage against several full-wave finite element method (FEM) based CAD tools. The proposed hybrid CAD tool is successfully extended to the design of filters with cascaded complex discontinuities. The hybridization of modal methods and the artificial neural networks improved the CPU time in the analysis of simple waveguide discontinuities which enhanced the optimization of rectangular ridged waveguide filters.

The aim of this thesis is to assess the suitability of cold-formed rectangular hollow sections (RHS) for plastic design. The project involved an extensive range of tests on cold-formed Grade C350 and Grade C450 (DuraGal) RHS beams, joints and frames. A large number of finite element analyses was also carried out on models of RHS beams. The conclusion is that cold- formed RHS can be used in plastic design, but stricter element slenderness (b/t) limits and consideration of the connections, are required. Further research, particularly into the effect of axial compression on element slenderness limits, is required before changes to current design rules can be finalised. Bending tests were performed on cold-formed RHS to examine the web and flange slenderness required to maintain the plastic moment for a large enough rotation suitable for plastic design. The major conclusions of the beam tests were: (i) Some sections which are classified as Compact or Class 1 by current steel design specifications do not maintain plastic rotations considered sufficient for plastic design. (ii) The current design philosophy, in which flange and web slenderness limits are independent, is inappropriate. An interaction formula is required, and simple formulations are proposed for RHS. Connection tests were performed on various types of knee joints in RHS, suitable for the column - rafter connection in a portal frame. The connection types investigated were welded stiffened and unstiffened rigid knee connections, bolted plate knee joints, and welded and bolted internal sleeve knee joints, for use in RHS portal frames. The ability of the connections to act as plastic hinges in a portal frame was investigated. The most important finding of the joint tests was the unexpected fracture of the cold-formed welded connections under opening moment before significant plastic rotations occurred. The use of an internal sleeve moved the plastic hinge in the connection away from the connection centre- line thus eliminating the need for the weld between the RHS, or the RHS and the stiffening plate, to carry the majority of the load. The internal sleeve connections were capable of sustaining the plastic moment for large rotations considered suitable for plastic design. Tests on pinned-base portal frames were also performed. There were three separate tests, with two different ratios of vertical to horizontal point loads, simulating gravity and horizontal wind loads. Two grades of steel were used for comparison. The aims of the tests were to examine if a plastic collapse mechanism could form in a cold-formed RHS frame, and to investigate if plastic design was suitable for such frames. In each frame, two regions of highly concentrated curvature were observed before the onset of local buckling, which indicated the formation of plastic hinges and a plastic collapse mechanism. An advanced plastic zone structural analysis which accounted for second order effects, material non-linearity and member imperfections slightly overestimated the strength of the frames. The analysis slightly underestimated the deflections, and hence the magnitude of the second order effects. A second order plastic zone analysis, which did not account for the effects of structural imperfections, provided the best estimates of the strengths of the frames, but also underestimated the deflections. While cold-formed RHS did not satisfy the material ductility requirements specified for plastic design in some current steel design standards, plastic hinges and plastic collapse mechanisms formed. This suggests that the restriction on plastic design for cold-formed RHS based on insufficient material ductility is unnecessary, provided that the connections are suitable for plastic hinge formation, if required. A large number of finite element analyses were performed to simulate the bending tests summarised above, and to examine various parameters not studied in the experimental investigation. To simulate the experimental rotation capacity of the RHS beams, a sinusoidally varying longitudinal local imperfection was prescribed. The finite element analysis determined similar trends as observed experimentally, namely that the rotation capacity depended on both the web slenderness and flange slenderness, and that for a given section aspect ratio, the relationship between web slenderness and rotation capacity was non-linear. The main finding of the finite element study was that the size of the imperfections had an unexpectedly large influence on the rotation capacity. Larger imperfections were required in the more slender sections to simulate the experimental results. There should be further investigation into the effect of varying material properties on rotation capacity.

For noiseless sampled data, we describe the close connections between Prony--like methods, namely the classical Prony method, the matrix pencil method and the ESPRIT method. Further we present a new efficient algorithm of matrix pencil factorization based on QR decomposition of a rectangular Hankel matrix. The algorithms of parameter estimation are also applied to sparse Fourier approximation and nonlinear approximation.

The aim of this thesis is to assess the suitability of cold-formed rectangular hollow sections (RHS) for plastic design. The project involved an extensive range of tests on cold-formed Grade C350 and Grade C450 (DuraGal) RHS beams, joints and frames. A large number of finite element analyses was also carried out on models of RHS beams. The conclusion is that cold- formed RHS can be used in plastic design, but stricter element slenderness (b/t) limits and consideration of the connections, are required. Further research, particularly into the effect of axial compression on element slenderness limits, is required before changes to current design rules can be finalised. Bending tests were performed on cold-formed RHS to examine the web and flange slenderness required to maintain the plastic moment for a large enough rotation suitable for plastic design. The major conclusions of the beam tests were: (i) Some sections which are classified as Compact or Class 1 by current steel design specifications do not maintain plastic rotations considered sufficient for plastic design. (ii) The current design philosophy, in which flange and web slenderness limits are independent, is inappropriate. An interaction formula is required, and simple formulations are proposed for RHS. Connection tests were performed on various types of knee joints in RHS, suitable for the column - rafter connection in a portal frame. The connection types investigated were welded stiffened and unstiffened rigid knee connections, bolted plate knee joints, and welded and bolted internal sleeve knee joints, for use in RHS portal frames. The ability of the connections to act as plastic hinges in a portal frame was investigated. The most important finding of the joint tests was the unexpected fracture of the cold-formed welded connections under opening moment before significant plastic rotations occurred. The use of an internal sleeve moved the plastic hinge in the connection away from the connection centre- line thus eliminating the need for the weld between the RHS, or the RHS and the stiffening plate, to carry the majority of the load. The internal sleeve connections were capable of sustaining the plastic moment for large rotations considered suitable for plastic design. Tests on pinned-base portal frames were also performed. There were three separate tests, with two different ratios of vertical to horizontal point loads, simulating gravity and horizontal wind loads. Two grades of steel were used for comparison. The aims of the tests were to examine if a plastic collapse mechanism could form in a cold-formed RHS frame, and to investigate if plastic design was suitable for such frames. In each frame, two regions of highly concentrated curvature were observed before the onset of local buckling, which indicated the formation of plastic hinges and a plastic collapse mechanism. An advanced plastic zone structural analysis which accounted for second order effects, material non-linearity and member imperfections slightly overestimated the strength of the frames. The analysis slightly underestimated the deflections, and hence the magnitude of the second order effects. A second order plastic zone analysis, which did not account for the effects of structural imperfections, provided the best estimates of the strengths of the frames, but also underestimated the deflections. While cold-formed RHS did not satisfy the material ductility requirements specified for plastic design in some current steel design standards, plastic hinges and plastic collapse mechanisms formed. This suggests that the restriction on plastic design for cold-formed RHS based on insufficient material ductility is unnecessary, provided that the connections are suitable for plastic hinge formation, if required. A large number of finite element analyses were performed to simulate the bending tests summarised above, and to examine various parameters not studied in the experimental investigation. To simulate the experimental rotation capacity of the RHS beams, a sinusoidally varying longitudinal local imperfection was prescribed. The finite element analysis determined similar trends as observed experimentally, namely that the rotation capacity depended on both the web slenderness and flange slenderness, and that for a given section aspect ratio, the relationship between web slenderness and rotation capacity was non-linear. The main finding of the finite element study was that the size of the imperfections had an unexpectedly large influence on the rotation capacity. Larger imperfections were required in the more slender sections to simulate the experimental results. There should be further investigation into the effect of varying material properties on rotation capacity.

The results of mathematics level 3 have always been a problem at TVET colleges as this hampers the certification rate and the progress of the students to level 4. Students who did not do well in the current subject are not allowed to register that subject in the following level. Even though the students are allowed to progress to level 4 they won’t be certificated for both levels until they pass the remaining subject. The above challenges made the researcher to check during the marking and moderation of November / December examination the course of poor results for mathematics level 3. In the process of checking the researcher discovered that rectangular hyperbola is one of the topics that the students of mathematics level 3 are struggling with. This study therefore focuses on exploring the challenges faced by TVET Level 3 NCV students in understanding the hyperbolic function in mathematics. In addition to the literature review, an empirical investigation based on a qualitative approach and involving semi-structured interviews with the students of a TVET college in North West was conducted to collect data. The analysis of documents relevant to the study was also used as the other method. The study used participatory action research, where the researcher, collaborators and students work alongside each other to collect data and to improve practice and follow the spiral pattern of reflection, analysing the results and adapting the action. The research design and methodology was qualitative. This helped the researcher to understand the challenges students faced in the learning of rectangular hyperbola and also came up with ways to minimise those challenges. The data collection methods used was interviewing using semi-structured questions, pre-test and post-tests. During data collection different interventions (IN1 –IN3) was used depending on the understanding of the students. For ethical consideration, ethical clearance was obtained from UNISA. DHET, the principal of the college, collaborators, parents and students will also give written consent on forms which will be sent out explaining what we envisage. Since research was voluntary, an explanation was given that this was not compulsory and that participation was completely voluntary and that they could withdraw at any time. In this study, various methods to empower students were recommended. Recommendations are also made on what was found in this study, as are recommendations for further study. / Mathematics Education / M. Ed. (Mathematics Education)

For noiseless sampled data, we describe the close connections between Prony--like methods, namely the classical Prony method, the matrix pencil method and the ESPRIT method. Further we present a new efficient algorithm of matrix pencil factorization based on QR decomposition of a rectangular Hankel matrix. The algorithms of parameter estimation are also applied to sparse Fourier approximation and nonlinear approximation.

The word endogenic means growing or proceeding from within, it is commonly used to describe the process of tectonic movement and earth crust formation caused by the extrusion of magmatic material. My project is a metaphorical exploration of the geological term “endogenic process” as well as an exploration of a design approach based on the term.The work explores soft form-bearing structures and textile bodies that contrast in relation to the hard framework of the rectangular room. It touches on material hierarchies in the living environment and the field of spatial design. The research explores the relationship between interior bodies and spatial frameworks. It aims to highlight the importance of the subject within the framework of the rectangular space that divides the interior of most buildings. My work involves exploring the endogenic process as a way of relating to the creative process and through the use of soft structures and drapery creating furniture that engages people with the spatial framework of the rectangular room. It is an exploration of spatial furniture that constitutes a connection and physical involvement between bodies and space, a kind of furniture providing a multiplicity of possibilities.