Orientador: Adalberto Bono Maurizio Sacci Bassi / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Química / Made available in DSpace on 2018-08-17T03:59:51Z (GMT). No. of bitstreams: 1 Guerrero_AndredeOliveira_M.pdf: 4353295 bytes, checksum: a8e573ea1fa805457349a7a1d9c37925 (MD5) Previous issue date: 2010 / Resumo: A equação original de van der Waals é alterada de modo a aprimorar sua aderência a dados experimentais para o Argônio, desde as baixas densidades dos estados gasosos até as altas densidades dos líquidos e dos vidros. Isto permite a obtenção de uma curva spinodal (fronteira termodinâmica entre os estados não acessíveis pela matéria e os estados possíveis, estáveis ou não) mais precisa do que a atualmente disponível, além de fornecer subsídios para estudos de líquidos e gases não estáveis. A pressão repulsiva original é substituída pela pressão de um sistema de esferas rígidas, enquanto que a pressão atrativa original é substituída pela pressão de um campo médio isotrópico descrito por três parâmetros. A realização destas alterações propicia a discussão de diversos aspectos da interpretação física da equação de van der Waals. Como os estados considerados são homogêneos, mas não necessariamente estados de equilíbrio, a temporal termodinâmica dos meios homogêneos é uma teoria adequada à descrição dos estados representados pela equação alterada. / Abstract: The original van der Waals equation is altered to improve its quantitative description of argon experimental values, including those of low density gaseous states and high density liquids and glasses. A spinodal curve is obtained (the limit between thermodynamically forbidden and permitted states of matter, either stable or unstable) that is more precise than the one actually available and reveals more information for studying unstable gases and liquids. The pressure of a rigid spheres system substitutes the original repulsive pressure, while the pressure of an isotropic mean field defined by three parameters substitutes the original attractive pressure. Implementing these substitutions provokes the discussion of several aspects, related to the physical meaning of van der Waals equation. Since only homogeneous states are considered, although they are not necessarily equilibrium states, time dependent thermodynamics of homogeneous media is an adequate theory to describe the states represented by the altered equation. / Mestrado / Físico-Química / Mestre em Química

Este trabalho propõe uma extensão do método de propagação de feixe (BPM - Beam Propagation Method) para a análise de guias de ondas ópticos e acopladores baseados em materiais não-lineares do tipo Kerr. Este método se destina à investigação de estruturas onde a utilização da equação escalar de Helmholtz (EEH) em seu limite paraxial não mais se aplica. Os métodos desenvolvidos para este fim são denominados na literatura como métodos de propagação de feixe de ângulo largo. O formalismo aqui desenvolvido é baseado na técnica das diferenças finitas e nos esquemas de Crank-Nicholson (CN) e Douglas generalizado (GD). Estes esquemas apresentam como característica o fato de apresentarem um erro de truncamento em relação ao passo de discretização transversal, &#916x, proporcional a O(&#916x2) para o primeiro e O(&#916x4). A convergência do método em ambos esquemas é otimizada pela utilização de um algoritmo interativo para a correção do campo no meio não-linear. O formalismo de ângulo largo é obtido pela expansão da EEH para os esquemas CN e GD em termos de polinômios aproximantes de Padé de ordem (1,0) e (1,1) para CN e GD, e (2,2) e (3,3) para CN. Os aproximantes de ordem superior a (1,1) apresentam sérios problemas de estabilidade. Este problema é eliminado pela rotação dos aproximantes no plano complexo. Duas condições de contorno nos extremos da janela computacional são também investigadas: 1) (TBC - Transparent Boundary Condition) e 2) condição de contorno absorvente (TAB - Transparent Absorbing Boundary). Estas condições de contorno possuem a facilidade de evitar que reflexões indesejáveis sejam transmitidas para dentro da janela computacional. Um estudo comparativo da influência destas condições de contorno na solução de guias de ondas ópticos não-lineares é também abordada neste trabalho. / This work introduces an extension of the beam propagation method (BPM) for the analysis of optical waveguides and couplers based on Kerr-type nonlinear materials. This method is intended for the investigation of structures where the paraxial scalar Helmholtz equation (EEH) no longer holds. The numerical methods developed for this situation are known in the literature as wide-angle beam propagation methods. The formulation developed in this work is based on finite differences and on the Crank-Nicholson (CN) and Generalized Douglas (GD) schemes. These schemes are characterized by a truncation error with respect to the transverse discretization step, &#916x, proporcional to O(&#916x2) for the CN and to O(&#916x4) for the GD scheme. The convergence of the method for both schemes is optimized by the application of an iterative algorithm for the correction of the field in the nonlinear medium. The wide-angle formalism is obtained by the expansion of the EEH for the CN and GD schemes in terms of Padé approximant polynomials. The expansions addressed in this work utilize Padé approximants of order (1,0) and (1,1) for the CN and GD scheme, and (2,2) and (3,3) for the CN scheme. Approximants orders higher than (1,1) show serious stability problems. This problem is circumvented by rotating the approximants in the complex plane. Two boundary conditions on the edge of the computational window are also investigated: 1) transparent boundary condition (TBC) and 2) transparent absorbing boundary (TAB). These boundary conditions are necessary in order to avoid unwanted reflections back to computational domain. A comparative study of the influence of these boundary conditions on the solution of nonlinear optical waveguides is also addressed in this work.

Neste estudo, consideramos um problema transiente de fluxo unidimensional vertical de água em meio poroso insaturado, modelado pela equação Richards não-linear. As reações constitutivas de Van Genuchten são empregadas para representar a capacidade hidráulica e a condutividade. A fórmula da solução é otimizada e avaliada usando a equação governante em um critério de autoconsciente. Os resultados são apresentados para alguns tipos de solo e seus parâmetros relacionados, que são mencionados em literatura. / In this study, we consider a transiente vertical one-dimensional flow problem of water in unsaturated porus media, modelled by the non-linear Richards equation. Constitutive relations of Van Genutchten are employed to represent the hydraulic capacity and conductivity. The solution formula is optimized and evaluated using to governing equation for a self-consistency criterion. The results are presented for some oil types and its related soil parameters, that are reported in the literature.

In the context of interior noise reduction, the present work aims at proposing Finite Element (FE) solution strategies for interior structural-acoustic applications including 3D modelling of homogeneous and isotropic poroelastic materials, under timeharmonic excitations, and in the low frequency range. A model based on the Biot-Allard theory is used for the poroelastic materials, which is known to be very costly in terms of computational resources. Reduced models offer the possibility to enhance the resolution of such complex problems. However, their applicability to porous materials remained to be demonstrated.First, this thesis presents FE resolutions of poro-elasto-acoustic coupled problems using modal-based approaches both for the acoustic and porous domains. The original modal approach proposed for porous media, together with a dedicated mode selection and truncation procedure, are validated on 1D to 3D applications.In a second part, modal-reduced models are combined with a Padé approximants reconstruction scheme in order to further improve the efficiency.A concluding chapter presents a comparison and a combination of the proposed methods on a 3D academic application, showing promising performances. Conclusions are then drawn to provide indications for future research and tests to be conducted in order to further enhance the methodologies proposed in this thesis.

Neste estudo, consideramos um problema transiente de fluxo unidimensional vertical de água em meio poroso insaturado, modelado pela equação Richards não-linear. As reações constitutivas de Van Genuchten são empregadas para representar a capacidade hidráulica e a condutividade. A fórmula da solução é otimizada e avaliada usando a equação governante em um critério de autoconsciente. Os resultados são apresentados para alguns tipos de solo e seus parâmetros relacionados, que são mencionados em literatura. / In this study, we consider a transiente vertical one-dimensional flow problem of water in unsaturated porus media, modelled by the non-linear Richards equation. Constitutive relations of Van Genutchten are employed to represent the hydraulic capacity and conductivity. The solution formula is optimized and evaluated using to governing equation for a self-consistency criterion. The results are presented for some oil types and its related soil parameters, that are reported in the literature.

Neste estudo, consideramos um problema transiente de fluxo unidimensional vertical de água em meio poroso insaturado, modelado pela equação Richards não-linear. As reações constitutivas de Van Genuchten são empregadas para representar a capacidade hidráulica e a condutividade. A fórmula da solução é otimizada e avaliada usando a equação governante em um critério de autoconsciente. Os resultados são apresentados para alguns tipos de solo e seus parâmetros relacionados, que são mencionados em literatura. / In this study, we consider a transiente vertical one-dimensional flow problem of water in unsaturated porus media, modelled by the non-linear Richards equation. Constitutive relations of Van Genutchten are employed to represent the hydraulic capacity and conductivity. The solution formula is optimized and evaluated using to governing equation for a self-consistency criterion. The results are presented for some oil types and its related soil parameters, that are reported in the literature.

Este trabalho propõe uma extensão do método de propagação de feixe (BPM - Beam Propagation Method) para a análise de guias de ondas ópticos e acopladores baseados em materiais não-lineares do tipo Kerr. Este método se destina à investigação de estruturas onde a utilização da equação escalar de Helmholtz (EEH) em seu limite paraxial não mais se aplica. Os métodos desenvolvidos para este fim são denominados na literatura como métodos de propagação de feixe de ângulo largo. O formalismo aqui desenvolvido é baseado na técnica das diferenças finitas e nos esquemas de Crank-Nicholson (CN) e Douglas generalizado (GD). Estes esquemas apresentam como característica o fato de apresentarem um erro de truncamento em relação ao passo de discretização transversal, &#916x, proporcional a O(&#916x2) para o primeiro e O(&#916x4). A convergência do método em ambos esquemas é otimizada pela utilização de um algoritmo interativo para a correção do campo no meio não-linear. O formalismo de ângulo largo é obtido pela expansão da EEH para os esquemas CN e GD em termos de polinômios aproximantes de Padé de ordem (1,0) e (1,1) para CN e GD, e (2,2) e (3,3) para CN. Os aproximantes de ordem superior a (1,1) apresentam sérios problemas de estabilidade. Este problema é eliminado pela rotação dos aproximantes no plano complexo. Duas condições de contorno nos extremos da janela computacional são também investigadas: 1) (TBC - Transparent Boundary Condition) e 2) condição de contorno absorvente (TAB - Transparent Absorbing Boundary). Estas condições de contorno possuem a facilidade de evitar que reflexões indesejáveis sejam transmitidas para dentro da janela computacional. Um estudo comparativo da influência destas condições de contorno na solução de guias de ondas ópticos não-lineares é também abordada neste trabalho. / This work introduces an extension of the beam propagation method (BPM) for the analysis of optical waveguides and couplers based on Kerr-type nonlinear materials. This method is intended for the investigation of structures where the paraxial scalar Helmholtz equation (EEH) no longer holds. The numerical methods developed for this situation are known in the literature as wide-angle beam propagation methods. The formulation developed in this work is based on finite differences and on the Crank-Nicholson (CN) and Generalized Douglas (GD) schemes. These schemes are characterized by a truncation error with respect to the transverse discretization step, &#916x, proporcional to O(&#916x2) for the CN and to O(&#916x4) for the GD scheme. The convergence of the method for both schemes is optimized by the application of an iterative algorithm for the correction of the field in the nonlinear medium. The wide-angle formalism is obtained by the expansion of the EEH for the CN and GD schemes in terms of Padé approximant polynomials. The expansions addressed in this work utilize Padé approximants of order (1,0) and (1,1) for the CN and GD scheme, and (2,2) and (3,3) for the CN scheme. Approximants orders higher than (1,1) show serious stability problems. This problem is circumvented by rotating the approximants in the complex plane. Two boundary conditions on the edge of the computational window are also investigated: 1) transparent boundary condition (TBC) and 2) transparent absorbing boundary (TAB). These boundary conditions are necessary in order to avoid unwanted reflections back to computational domain. A comparative study of the influence of these boundary conditions on the solution of nonlinear optical waveguides is also addressed in this work.

In the context of interior noise reduction, the present work aims at proposing Finite Element (FE) solution strategies for interior structural-acoustic applications including 3D modelling of homogeneous and isotropic poroelastic materials, under timeharmonic excitations, and in the low frequency range. A model based on the Biot-Allard theory is used for the poroelastic materials, which is known to be very costly in terms of computational resources. Reduced models offer the possibility to enhance the resolution of such complex problems. However, their applicability to porous materials remained to be demonstrated.First, this thesis presents FE resolutions of poro-elasto-acoustic coupled problems using modal-based approaches both for the acoustic and porous domains. The original modal approach proposed for porous media, together with a dedicated mode selection and truncation procedure, are validated on 1D to 3D applications.In a second part, modal-reduced models are combined with a Padé approximants reconstruction scheme in order to further improve the efficiency.A concluding chapter presents a comparison and a combination of the proposed methods on a 3D academic application, showing promising performances. Conclusions are then drawn to provide indications for future research and tests to be conducted in order to further enhance the methodologies proposed in this thesis. / Dans le contexte de lutte contre les nuisances sonores, cette thèse porte sur le développement de méthodes de résolution efficaces par éléments finis, pour des problèmes de vibroacoustique interne avec interfaces dissipatives, dans le domaine des basses fréquences. L’étude se limite à l’utilisation de solutions passives telles que l’intégration de matériaux poreux homogènes et isotropes, modélisés par une approche fondée sur la théorie de Biot-Allard. Ces modèles étant coûteux en terme de résolution, un des objectifs de cette thèse est de proposer une approche modale pour la réduction du problème poroélastique, bien que l’adéquation d’une telle approche avec le comportement dynamique des matériaux poreux soit à démontrer.Dans un premier temps, la résolution de problèmes couplés élasto-poro-acoustiques par sous-structuration dynamique des domaines acoustiques et poreux est établie. L’approche modale originale proposée pour les milieux poroélastiques, ainsi qu’une procédure de sélection des modes significatifs, sont validées sur des exemples 1D à 3D.Une deuxième partie présente une méthode combinant l’utilisation des modèles réduits précédemment établis avec une procédure d’approximation de solution par approximants de Padé. Il est montré qu’une telle combinaison offre la possibilité d’accroître les performances de la résolution (allocation mémoire et ressources en temps de calcul).Un chapitre dédié aux applications permet d’évaluer et comparer les approches sur un problème académique 3D, mettant en valeur leurs performances encourageantes. Afin d’améliorer les méthodes établies dans cette thèse, des perspectives à ces travaux de recherche sont apportées en conclusion. / <p>QC 20120224</p> / FP6 Marie-Curie Smart Structures / FP7 Marie-Curie Mid-Frequency

Dans le cadre de la discrétion acoustique des navires militaires, cette thèse contribue à la modélisation de structures amorties par des matériaux viscoélastiques, sous forme de couches contraintes. Afin de pouvoir optimiser et dimensionner la structure et le matériau amortissant, il est souhaitable de disposer d'un outil numérique prédictif et efficace. Dans un premier temps, une stratégie de caractérisation et de modélisation du comportement de matériaux viscoélastiques est proposée. Elle inclue une méthode de recalage de résultats de mesures par DMA basée sur le respect des relations de Kramers-Kronig, permettant ainsi de construire des courbes maîtresses du matériau en accord avec le principe de causalité. Dans un deuxième temps, un code de calcul par éléments finis est développé, puis des essais de vibration sur structures sandwich sont réalisés afin de valider la modélisation par éléments finis de structures munies de matériaux viscoélastiques. Dans le cas d'une fine couche viscoélastique insérée dans une structure maillée par des éléments volumiques, deux éléments d'interface sont développés : ils permettent de tester simplement plusieurs configurations. Enfin, dans un troisième temps, deux catégories de méthodes de réduction adaptées au calcul de la réponse fréquentielle de structures fortement amorties par des matériaux viscoélastiques sont étudiées : les méthodes de projection sur bases modales et la méthode de reconstruction par approximants de Padé. Dans le cadre d'études paramétriques pour l'optimisation des performances acoustiques des traitements viscoélastiques contraints, les avantages des méthodes développées sont mis avant à travers deux cas d'application. / In the context of acoustic discretion of naval ships, this thesis contributes to the modelling of viscoelastically damped structures by means of thin constrained layers. In order to optimize and design the structure and the damping material, a predictive and efficient numerical tool is desirable. Firstly, a characterization and modelling strategy of the behaviour of viscoelastic materials is proposed. A shifting procedure of DMA measurements based on the fulfillment of the Kramers-Kronig relations is developed in order to build master curves of the material which are consistent with the causality principle. Secondly, a finite element code is developed, and vibration experiments are realized in order to validate the finite element modelling of structures with viscoelastic materials. In the case of thin constrained viscoelastic layers applied to a structure meshed using brick elements, two interface finite elements are developed, which facilitate parametric studies. Finally, two families of reduction methods adapted to the calculation of the frequency response of structures highly damped by viscoelastic materials are studied: modal projection methods and Padé approximants reconstruction method. The advantages of the proposed methods, in the frame of parametric studies for the optimization of the acoustic performances of constrained viscoelastic layers, are highlighted through two applications.

Dans le contexte de lutte contre les nuisances sonores, cette thèse porte sur le développement de méthodes de résolution efficaces par éléments finis, pour des problèmes de vibroacoustique interne avec interfaces dissipatives, dans le domaine des basses fréquences. L’étude se limite à l’utilisation de solutions passives telles que l’intégration de matériaux poreux homogènes et isotropes, modélisés par une approche fondée sur la théorie de Biot-Allard. Ces modèles étant coûteux en terme de résolution, un des objectifs de cette thèse est de proposer une approche modale pour la réduction du problème poroélastique, bien que l’adéquation d’une telle approche avec le comportement dynamique des matériaux poreux soit à démontrer. Dans un premier temps, la résolution de problèmes couplés élasto-poro-acoustiques par sous-structuration dynamique des domaines acoustiques et poreux est établie. L’approche modale originale proposée pour les milieux poroélastiques, ainsi qu’une procédure de sélection des modes significatifs, sont validées sur des exemples 1D à 3D. Une deuxième partie présente une méthode combinant l’utilisation des modèles réduits précédemment établis avec une procédure d’approximation de solution par approximants de Padé. Il est montré qu’une telle combinaison offre la possibilité d’accroître les performances de la résolution (allocation mémoire et ressources en temps de calcul). Un chapitre dédié aux applications permet d’évaluer et comparer les approches sur un problème académique 3D, mettant en valeur leurs performances encourageantes. Afin d’améliorer les méthodes établies dans cette thèse, des perspectives à ces travaux de recherche sont apportées en conclusion. / In the context of interior noise reduction, the present work aims at proposing Finite Element (FE) solution strategies for interior structural-acoustic applications including 3D modelling of homogeneous and isotropic poroelastic materials, under timeharmonic excitations, and in the low frequency range. A model based on the Biot-Allard theory is used for the poroelastic materials, which is known to be very costly in terms of computational resources. Reduced models offer the possibility to enhance the resolution of such complex problems. However, their applicability to porous materials remained to be demonstrated.First, this thesis presents FE resolutions of poro-elasto-acoustic coupled problems using modal-based approaches both for the acoustic and porous domains. The original modal approach proposed for porous media, together with a dedicated mode selection and truncation procedure, are validated on 1D to 3D applications.In a second part, modal-reduced models are combined with a Padé approximants reconstruction scheme in order to further improve the efficiency.A concluding chapter presents a comparison and a combination of the proposed methods on a 3D academic application, showing promising performances. Conclusions are then drawn to provide indications for future research and tests to be conducted in order to further enhance the methodologies proposed in this thesis.