Electromagnetic acoustic transducers (EMATs) are increasingly used in industries due to their attractive features of being non-contact, cost-effective and the fact that a variety of wave modes can be generated, etc. There are two major EMATs coupling mechanisms: the Lorentz force mechanism for conductive materials and the magnetostriction mechanism for ferromagnetic materials; EMATs operated on Lorentz force mechanism are the focus of this study. This work aims to investigate novel efficient modelling techniques for EMATs, in order to gain further knowledge and understanding of EMATs wave pattern, how design parameters affect its wave pattern and based on above propose and optimise novel sensor structures. In this study, two novel modelling methods were proposed: one is the method combining the analytical method for EM simulation and the finite-difference time-domain (FDTD) method for US simulation for studying the Rayleigh waves' properties on the vertical plane of the material; the other one is the method utilizing a wholly analytical model to explore the directivity of surface waves. Both simulations models have been validated experimentally. The wholly analytical model generates the radiation pattern of surface waves, which lays a solid foundation for the optimum design of such sensors. The beam directivity of surface waves was investigated experimentally, and results showed the length of wires has a significant effect on the beam directivity of Rayleigh waves. A novel configuration of EMATs, variable-length meander-line-coil (VLMLC), was proposed and designed. The beam directivity of surface waves generated by such novel EMATs were analytically investigated. Experiments were conducted to validate such novel EMATs models, and results indicated that such EMATs are capable of supressing side lobes, and therefore resulting in a more concentrated surface waves in the desired direction. Further, another two novel configuration of EMATs, the four-directional meander-line-coil (FDMLC) and the six-directional meander-line-coil (SDMLC), were proposed and designed; results showed these EMATs are capable of generating Rayleigh waves in multiple directions and at the same time suppressing side lobes.

The goal of the dissertation is to find new method of solving two-dimensional Schrödinger equation in such cases, when the separation of the variables is not applicable. The results are applied to the two-dimensional Schrödinger equation with the potentials of the form of the quartic polynomial, of the sextic polynomial and of the quartic Morse potential. For these cases, the analytical formulae for the ground state wave functions and the corresponding energies have been found. For the specific class of the potentials of the form of the quartic polynomial, analytical formula for one of the excited states and for the corresponding energy have been found.

No presente trabalho são apresentadas soluções analíticas das equações de difusão de nêutrons bidimensionais com dois grupos de energia, a saber, nêutrons rápidos e térmicos em uma placa com propriedades homogêneas. Alem disso, são resolvidos detalhadamente os problemas onde a placa homogênea é substituída por duas e quatro regiões, tornando-os não-homogêneos. A partir da aplicação da transformada de Laplace e da Técnica da Transformada Integral Generalizada (GITT), respectivamente, é resolvida em uma forma analítica o problema de autovalor resultante para o fluxo de nêutrons. No problema heterogêneo são usados filtros para homogenizar as condições de contorno não-homogêneas. Esta é a condição para a aplicação da GITT. Os três problemas mencionados acima são resolvidos aplicando primeiramente a GITT, o qual reduz a dimensão da equação de difusão, seguida da aplicação da transformada de Laplace, o qual reduz a ordem da equação. Deste procedimento, resulta um sistema de equações algébricas dependente das constantes de integração. 0 sistema é resolvido usando a técnica da eliminação de Gauss. Os fluxos transformados pela GITT são recuperados invertendo-se analiticamente a transformada de Laplace usando a expansão de Heaviside, os quais ainda dependem das constantes de integração. A partir da aplicação das condições de contorno e de interface (para os problemas não-homogêneos) obtém-se um sistema de equações algébricas homogêneas, de onde é determinado o fator de multiplicação efetivo Keff pelo método da bissecção. As constantes de integração são determinadas fazendo use da potencia prescrita da placa. Assim, os fluxos de nêutrons transformados pela GITT ficam determinados e os fluxos de nêutrons rápidos e térmicos são recuperados através da formula da inversa da GITT, usando a expansão do potencial. Resultados são comparados com a solução do método de diferenças finitas. / In the present work we present analytical solutions of the bi-dimensional neutron diffusion equation with two energy groups, i.e. fast and thermal neutrons in a sheet with homogeneous properties. Further we solve the detailed problem where the homogeneous sheet is substituted by two and four regions, rendering the problem a non-homogeneous one. Upon application of the Laplace transform and Generalized Integral Transform Tecnique (GITT), respectively, we solve in an analytical fashion the resulting eigenvalue problem for the neutron flux. In the heterogeneous problem, we use filter functions in order to homogenize the non-homogeneous boundary conditions. This is a condition for the application of GITT. We solve the three problems mentioned above applying first GITT, which reduces the dimension of the diffusion equation followed by the Laplace transform, which reduces the order of the equation. This procedure yields a non-homogeneous algebraic system depending on integration constants. The system is solved using the elimination technique by Gauss. The transformed fluxes by GITT are recovered upon inverting analytically the Laplace transform using Heaviside's expansion which depend still on the integration constants. Upon application of the boundary and interface conditions (for the non-homogeneous problem) one obtains a system of homogeneous algebraic equations, where we determine the effective multiplication factor keff by the bisection method. The integration constants are determined making use of the predefined power of the sheet. Thus the neutron fluxes transformed by GITT are determined and the fast and thermal neutron flux are recovered by the inverse formula of GITT, using the potential expansion. Results are compared to the solution by the finite difference method.

No presente trabalho são apresentadas soluções analíticas das equações de difusão de nêutrons bidimensionais com dois grupos de energia, a saber, nêutrons rápidos e térmicos em uma placa com propriedades homogêneas. Alem disso, são resolvidos detalhadamente os problemas onde a placa homogênea é substituída por duas e quatro regiões, tornando-os não-homogêneos. A partir da aplicação da transformada de Laplace e da Técnica da Transformada Integral Generalizada (GITT), respectivamente, é resolvida em uma forma analítica o problema de autovalor resultante para o fluxo de nêutrons. No problema heterogêneo são usados filtros para homogenizar as condições de contorno não-homogêneas. Esta é a condição para a aplicação da GITT. Os três problemas mencionados acima são resolvidos aplicando primeiramente a GITT, o qual reduz a dimensão da equação de difusão, seguida da aplicação da transformada de Laplace, o qual reduz a ordem da equação. Deste procedimento, resulta um sistema de equações algébricas dependente das constantes de integração. 0 sistema é resolvido usando a técnica da eliminação de Gauss. Os fluxos transformados pela GITT são recuperados invertendo-se analiticamente a transformada de Laplace usando a expansão de Heaviside, os quais ainda dependem das constantes de integração. A partir da aplicação das condições de contorno e de interface (para os problemas não-homogêneos) obtém-se um sistema de equações algébricas homogêneas, de onde é determinado o fator de multiplicação efetivo Keff pelo método da bissecção. As constantes de integração são determinadas fazendo use da potencia prescrita da placa. Assim, os fluxos de nêutrons transformados pela GITT ficam determinados e os fluxos de nêutrons rápidos e térmicos são recuperados através da formula da inversa da GITT, usando a expansão do potencial. Resultados são comparados com a solução do método de diferenças finitas. / In the present work we present analytical solutions of the bi-dimensional neutron diffusion equation with two energy groups, i.e. fast and thermal neutrons in a sheet with homogeneous properties. Further we solve the detailed problem where the homogeneous sheet is substituted by two and four regions, rendering the problem a non-homogeneous one. Upon application of the Laplace transform and Generalized Integral Transform Tecnique (GITT), respectively, we solve in an analytical fashion the resulting eigenvalue problem for the neutron flux. In the heterogeneous problem, we use filter functions in order to homogenize the non-homogeneous boundary conditions. This is a condition for the application of GITT. We solve the three problems mentioned above applying first GITT, which reduces the dimension of the diffusion equation followed by the Laplace transform, which reduces the order of the equation. This procedure yields a non-homogeneous algebraic system depending on integration constants. The system is solved using the elimination technique by Gauss. The transformed fluxes by GITT are recovered upon inverting analytically the Laplace transform using Heaviside's expansion which depend still on the integration constants. Upon application of the boundary and interface conditions (for the non-homogeneous problem) one obtains a system of homogeneous algebraic equations, where we determine the effective multiplication factor keff by the bisection method. The integration constants are determined making use of the predefined power of the sheet. Thus the neutron fluxes transformed by GITT are determined and the fast and thermal neutron flux are recovered by the inverse formula of GITT, using the potential expansion. Results are compared to the solution by the finite difference method.

No presente trabalho são apresentadas soluções analíticas das equações de difusão de nêutrons bidimensionais com dois grupos de energia, a saber, nêutrons rápidos e térmicos em uma placa com propriedades homogêneas. Alem disso, são resolvidos detalhadamente os problemas onde a placa homogênea é substituída por duas e quatro regiões, tornando-os não-homogêneos. A partir da aplicação da transformada de Laplace e da Técnica da Transformada Integral Generalizada (GITT), respectivamente, é resolvida em uma forma analítica o problema de autovalor resultante para o fluxo de nêutrons. No problema heterogêneo são usados filtros para homogenizar as condições de contorno não-homogêneas. Esta é a condição para a aplicação da GITT. Os três problemas mencionados acima são resolvidos aplicando primeiramente a GITT, o qual reduz a dimensão da equação de difusão, seguida da aplicação da transformada de Laplace, o qual reduz a ordem da equação. Deste procedimento, resulta um sistema de equações algébricas dependente das constantes de integração. 0 sistema é resolvido usando a técnica da eliminação de Gauss. Os fluxos transformados pela GITT são recuperados invertendo-se analiticamente a transformada de Laplace usando a expansão de Heaviside, os quais ainda dependem das constantes de integração. A partir da aplicação das condições de contorno e de interface (para os problemas não-homogêneos) obtém-se um sistema de equações algébricas homogêneas, de onde é determinado o fator de multiplicação efetivo Keff pelo método da bissecção. As constantes de integração são determinadas fazendo use da potencia prescrita da placa. Assim, os fluxos de nêutrons transformados pela GITT ficam determinados e os fluxos de nêutrons rápidos e térmicos são recuperados através da formula da inversa da GITT, usando a expansão do potencial. Resultados são comparados com a solução do método de diferenças finitas. / In the present work we present analytical solutions of the bi-dimensional neutron diffusion equation with two energy groups, i.e. fast and thermal neutrons in a sheet with homogeneous properties. Further we solve the detailed problem where the homogeneous sheet is substituted by two and four regions, rendering the problem a non-homogeneous one. Upon application of the Laplace transform and Generalized Integral Transform Tecnique (GITT), respectively, we solve in an analytical fashion the resulting eigenvalue problem for the neutron flux. In the heterogeneous problem, we use filter functions in order to homogenize the non-homogeneous boundary conditions. This is a condition for the application of GITT. We solve the three problems mentioned above applying first GITT, which reduces the dimension of the diffusion equation followed by the Laplace transform, which reduces the order of the equation. This procedure yields a non-homogeneous algebraic system depending on integration constants. The system is solved using the elimination technique by Gauss. The transformed fluxes by GITT are recovered upon inverting analytically the Laplace transform using Heaviside's expansion which depend still on the integration constants. Upon application of the boundary and interface conditions (for the non-homogeneous problem) one obtains a system of homogeneous algebraic equations, where we determine the effective multiplication factor keff by the bisection method. The integration constants are determined making use of the predefined power of the sheet. Thus the neutron fluxes transformed by GITT are determined and the fast and thermal neutron flux are recovered by the inverse formula of GITT, using the potential expansion. Results are compared to the solution by the finite difference method.

Orientador: Leandro Palermo Junior / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-13T11:09:20Z (GMT). No. of bitstreams: 1 Millan_LeandroPrearo_M.pdf: 2561778 bytes, checksum: 002f0fe2a5fe91ab93b8b2d452b7b3b7 (MD5) Previous issue date: 2009 / Resumo: O Método dos Elementos de Contorno foi empregado no estudo do efeito transiente de temperatura em problemas de condução de calor para elementos planos. O objetivo do trabalho foi apresentar uma formulação usando elementos de contorno lineares contínuos ou descontínuos com parâmetros nodais fixados nas extremidades dos elementos. Os pontos de colocação foram situados nas extremidades dos elementos contínuos ou deslocados para o interior dos elementos no caso de elementos descontínuos. As integrações foram feitas com expressões analíticas quando o ponto de colocação pertencia ao elemento e com a quadratura de Gauss-Legendre para os outros casos. Um código computacional foi desenvolvido com a linguagem de programação C/C++ que tem uma descrição de forma simplificada apresentada no texto. Os resultados são comparados com soluções disponíveis na literatura para mostrar a precisão da formulação. / Abstract: The Boundary Elements Method was employed in the study of the transient effect of the temperature in heat conduction problems for plain elements. The purpose was to present a formulation using linear continuous or discontinuous boundary elements with nodal parameters fixed at the ends of elements. The collocations points were positioned at the ends of continuous elements or shifted to the interior of elements in case of discontinuous elements. The integrations were performed with analytical expressions for the case of collocation points belonging to the boundary element and the Gauss-Legendre quadrature for other cases. A computer code was developed with the C/C++ programming language which had a simplified explanation included in the text. The results were compared to available solutions in the literature to show the precision of the formulation. / Mestrado / Estruturas / Mestre em Engenharia Civil

Doctor of Philosophy / Department of Civil Engineering / Hayder A. Rasheed / The use of laminated composites in aerospace, automotive, and civil engineering applications is ever growing due to their distinguished properties (High stiffness-to-weight ratio, high strength-to-weight ratio, fatigue and corrosion resistance). This growth has resulted in increasing the demand for better understanding the mechanics of laminated composites. Composite columns and wide plates, like any traditional members subjected to axial compression, undergo stability issues prior to failure. Limited amount of research studies has focused on the buckling of laminated anisotropic composite members. Analytical formula for the buckling load of generally anisotropic laminated composite simply supported thin columns and wide plates is derived using the Rayleigh Ritz approximation and bifurcation approach. The effective axial, coupling and flexural stiffness coefficients of the anisotropic layup is determined from the generalized constitutive relationship using dimensional reduction by static condensation of the 6x6 composite stiffness matrix. The resulting explicit formula is expressed in terms of the generally anisotropic material properties as well as the member geometry. The developed formula may be considered an extension to Euler buckling formula using Rayleigh-Ritz approximation and the first of its kind since Euler. This formula reduces down to Euler buckling formula once the effective coupling stiffness term vanishes for isotropic and certain classes of laminated composites. The analytical results are verified against finite element Eigen value solutions for a wide range of anisotropic laminated layups yielding high accuracy. Comparisons with experiments; conducted at Kansas State University for the simply supported case, are also performed showing good correspondence. A brief parametric study is then conducted to examine the effect of ply orientations and material properties including hybrid carbon/glass fiber composites, element thickness, and element type in FE analysis. Relevance of the numerical and analytical results is discussed for all these cases.

No description available.

Beams are among the most commonly used structural members that are encountered in virtually all systems of structural design at various scales. Mathematical models used to determine the response of beams under external loads are deduced from the three-dimensional elasticity theory through a series of assumptions concerning the kinematics of deformation and constitutive behavior. The kinematic assumptions exploit the fact that such structures do not experience significant trans- verse normal and shear strains and stresses. For example, the solution of the three- dimensional elasticity problem associated with a straight beam is reformulated as a one-dimensional problem in terms of displacements whose form is presumed on the basis of an educated guess concerning the nature of the deformation. In many cases beam structures are subjected to compressive in-plane loads that may cause out-of-plane buckling of the beam. Typically, before buckling and during compression, the beam develops internal axial force that makes the beam stiffer. In the linear buckling analysis of beams, this internal force is not considered. As a result the buckling loads predicted by the linear analysis are not accurate. The present study is motivated by lack of suitable theory and analysis that considers the nonlinear effects on the buckling response of beams. This thesis contains three new developments: (1) the conventional beam theories are generalized by accounting for nonlinear terms arising from εzz and εxz that are of the same magnitude as the von K´arm´an nonlinear strains appearing in εxx. The equations of motion associated with the generalized Euler–Bernoulli and Timoshenko beam theories with the von K´arm´an type geometric nonlinear strains are derived using Hamilton’s principle. These equations form the basis of investigations to determine certain microstructural length scales on the bending, vibration and buckling response of beams used in micro- and nano-devices. (2) Analytical solutions of the conventional Timoshenko beam theory with the von K´arm´an nonlinearity are de- veloped for the case where the inplane inertia is negligible when compared to other terms in the equations of motion. Numerical results are presented to bring out the effect of transverse shear deformation on the buckling response. (3) The development of a nonlinear finite element model for post-buckling behavior of beams.

O presente trabalho apresenta um estudo de caso de contaminação de solo e água subterrânea por derivados do petróleo em uma refinaria da região Sudeste do país, para o qual foram aplicados todos os níveis ou tiers da metodologia RBCA de avaliação de risco à saúde humana. Diferentes vias de exposição foram consideradas ao longo de toda a metodologia, a qual foi dividida em determinística, compreendendo os dois primeiros níveis, e estocástica, no caso do terceiro nível. Sobre a abordagem determinística, o modelo de Domenico (1987) para transporte de contaminantes em água subterrânea foi substituído por um conjunto de soluções analíticas que considera diferentes geometrias de fonte de contaminação para casos instantâneos e contínuos de liberação de contaminantes, permitindo que a metodologia RBCA também possa ser empregada mesmo quando o modelo de Domenico (1987) não se aplica. A comparação deste conjunto de soluções com outro utilizado apenas para comparar e confirmar a validade dos modelos escolhidos demonstrou grande estabilidade nas soluções, enquanto os modelos de comparação apresentaram instabilidade nas soluções para altos valores da variável tempo. Tal fato comprovou a viabilidade do emprego do conjunto de soluções analíticas proposto para avaliação de risco à saúde humana. No contexto da abordagem estocástica da estimativa do risco, o método de Monte Carlo foi empregado para propagação das incertezas sobre uma das soluções analíticas citadas anteriormente, da qual, por sua vez, foram extraídos os resultados para a simulação estocástica do risco para a via de contato dermal com água superficial contaminada por Benzeno. Os resultados da simulação estocástica demonstraram uma correlação muito grande do risco com a variável C (concentração do contaminante), a qual, por sua vez, foi modelada pela simulação estocástica da condutividade hidráulica. Logo, pode-se concluir que a condutividade hidráulica afeta a estimativa do risco, para o qual observou-se uma diferença de seis ordens de magnitude entre o valor mínimo e o máximo simulados e duas ordens de magnitude para o valor real do risco. / This dissertation presents a case study on soil and ground water contamination by components derived from petroleum in a refinery located in the Southeast region of Brazil. All of the RBCA health risk assessment methodology tiers were applied in this study. Different exposure pathways were considered throughout the methodology. Firstly, the deterministic approach which encompasses the first two tiers and secondly, the stochastic approach which addressed the third tier. Regarding the deterministic approach, the Domenico (1987) ground water contaminant transport model was replaced by a new set of analytical solutions that consider different geometries of contamination sources used in cases of instantaneous and continuous release of contaminants. This replacement allowed for the utilization of the RBCA methodology whenever the Domenico (1987) analytical model does not apply. A comparison between this set of analytical solutions with another set used to validate and testify the chosen set only, showed great solution stability response; whereas, the models of comparison have demonstrated instability for high values of the time variable. Such a fact proved the validity of the use of the proposed set of analytical solutions inserted in a health risk assessment context. In the context of the stochastic approach of risk estimation, the Monte Carlo method was employed to propagate uncertainties over one of the analytical solutions mentioned above, from which results were obtained to simulate dermal contact with contaminated surface water while swimming exposure pathway. The results of the stochastic simulation demonstrated a high correlation between the risk and the variable C (contaminant concentration), which was modeled by the hydraulic conductivity stochastic simulation. Hence, it may be concluded that the hydraulic conductivity affects the risk estimation, for which a difference of six orders of magnitude between the minimum and maximum simulated values and two orders of magnitude for the real risk value was observed.