Sistemas de ensaios não destrutivos por ondas guiadas despertam cada vez mais a atenção tanto da indústria, como da academia. Isso deve-se, principalmente, às possibilidades que as ondas guiadas permitem, como maior área de triagem que o ultrassom convencional. Porém a técnica tem suas limitações, já que esta apenas gera uma estimativa da localização de um defeito e não a sua dimensão. Nessa limitação, algoritmos tomográficos apresentam uma possibilidade de avanço da técnica, pois permitem determinar não só a localização de corrosões e defeitos, mas também seu dimensionamento. Este trabalho apresenta tomografia de difração como uma alternativa para avaliação de integridade estrutural. Primeiramente, utilizou-se análise por métodos numéricos para mostrar a validade dos algoritmos e posteriormente foi realizado um experimento em uma chapa real com o objetivo de reconstruir a imagem do defeito. / Guided waves nondestructive testing systems are increasingly attracting industrial and academic attention. The mainly reason for this attention is the possibility of screening a large area than conventional ultrasound technique. However, Guided Waves Testing has limitations, since it gives only an estimation of the location of a defect, but not the dimensions. Tomographic algorithms come up with an improvement of the technique, because it allows discovery not only the location of corrosions and defects, but the dimensions too. This work brings Diffraction Tomography as an alternative to structural health monitoring. First, a numerical analysis was implemented to demonstrate the validity of the algorithms, after that an experiment in a real plate was made with the objective to recover the defect image.

A adoção de materiais compósitos pela indústria de petróleo e gás vem ocorrendo de forma gradual, e ainda encontra certa resistência devido à novidade de sua aplicação em projetos mecânicos do setor, e da menor confiabilidade que possuem em relação a metais. A sua implementação em maiores escalas depende também do desenvolvimento de métodos de inspeção e monitoramento de integridade estrutural. Em paralelo a isso, sistemas de varredura de tubulações baseados em ondas guiadas ultrassônicas vêm ganhando espaço devido à sua capacidade de inspecionar toda a seção de trechos extensos de uma tubulação metálica. Baseado nestas duas premissas, este trabalho tem como objetivo apresentar estudos visando o desenvolvimento de uma metodologia que seja capaz de obter as propriedades elásticas de um meio e obter as características de propagação das ondas mecânicas, cobrindo uma metodologia para obtenção das propriedades elásticas baseados em ensaios ultrassônicos, um método de otimização baseado em propriedades vibracionais e por fim, confrontando dados provenientes de modelos em elementos finitos com resultados experimentais e aproximações teóricas. Como resultados espera-se gerar informações necessárias para que possa-se compreender os mecanismo de propagação das ondas elásticas, pois é ele que permitirá a obtenção de informações a respeito dos defeitos presentes na estrutura analisada ou ainda utilizar as informações de dispersão em função da frequência e em função da direção para localização de fontes acústicas em meios ortotrópicos, sendo o conhecimento das propriedades de fase e energia das ondas em tais materiais de fundamental importância para a plena exploração do seu potencial de inspeção e monitoramento. / The adoption of new materials by the oil and gas industry has been occurring gradually and still finds some resistance due to the novelty of their application in mechanical design and their lower reliability compared to metals. The usage in large scales also depends on the development of inspection methods and structure health monitoring. In a parallel way, systems that scan pipes using mechanical guided waves have gained space because of their ability to inspect the section of large excerpts of an metallic pipe. Based on these two assumptions, this work aims to study the development of a methodology that is able to obtain the elastic properties of a medium and obtain mechanical characteristics through propagation of the stress waves in it. For this, a method to obtain elastic properties based on ultrasonic testing, a optimization method was based on vibrational properties, and comparison of to data from finite element models with experimental results and theoretical approaches were used. The results are expected to generate information needed for understand the mechanism of propagation of elastic waves, needed to obtain information about defects present in the structure or using information of angular or frequency dispersion for localizing acoustic sources in orthotropic media. As knowledge of the properties of the phase and energy waves propagation in such material are crucial for the full exploitation of inspection and monitoring.

abstract: Although high performance, light-weight composites are increasingly being used in applications ranging from aircraft, rotorcraft, weapon systems and ground vehicles, the assurance of structural reliability remains a critical issue. In composites, damage is absorbed through various fracture processes, including fiber failure, matrix cracking and delamination. An important element in achieving reliable composite systems is a strong capability of assessing and inspecting physical damage of critical structural components. Installation of a robust Structural Health Monitoring (SHM) system would be very valuable in detecting the onset of composite failure. A number of major issues still require serious attention in connection with the research and development aspects of sensor-integrated reliable SHM systems for composite structures. In particular, the sensitivity of currently available sensor systems does not allow detection of micro level damage; this limits the capability of data driven SHM systems. As a fundamental layer in SHM, modeling can provide in-depth information on material and structural behavior for sensing and detection, as well as data for learning algorithms. This dissertation focusses on the development of a multiscale analysis framework, which is used to detect various forms of damage in complex composite structures. A generalized method of cells based micromechanics analysis, as implemented in NASA's MAC/GMC code, is used for the micro-level analysis. First, a baseline study of MAC/GMC is performed to determine the governing failure theories that best capture the damage progression. The deficiencies associated with various layups and loading conditions are addressed. In most micromechanics analysis, a representative unit cell (RUC) with a common fiber packing arrangement is used. The effect of variation in this arrangement within the RUC has been studied and results indicate this variation influences the macro-scale effective material properties and failure stresses. The developed model has been used to simulate impact damage in a composite beam and an airfoil structure. The model data was verified through active interrogation using piezoelectric sensors. The multiscale model was further extended to develop a coupled damage and wave attenuation model, which was used to study different damage states such as fiber-matrix debonding in composite structures with surface bonded piezoelectric sensors. / Dissertation/Thesis / Ph.D. Mechanical Engineering 2012

Ce travail de recherche est dédié à la simulation de la réponse transitoire des assemblages de poutres soumis à des chocs. De tels chargements entraînent la propagation d’ondes haute fréquence dans l’ensemble de la structure. L’énergie qu’elles transportent peut être dommageable pour son fonctionnement ou celui des équipements embarqués. Dans des études précédentes, il a été observé sur des structures expérimentales qu’un régime vibratoire diffusif tend à s’installer pour des temps longs. Le but de cette étude est donc de développer un modèle robuste de la réponse transitoire des assemblages de poutres soumis à des chocs permettant de simuler, entre autres, cet état diffusif. Les champs de déplacement étant très oscillants et la densité modale élevée, la simulation numérique de la réponse transitoire à des chocs peut difficilement être menée par une méthode d’éléments finis classique. Une approche utilisant un estimateur de la densité d’énergie de chaque mode de propagation a donc été mise en œuvre. Elle permet d’accéder à des informations locales sur les états vibratoires, et de contourner certaines limitations intrinsèques aux longueurs d’onde courtes. Après avoir comparé plusieurs modèles de réduction cinématique de poutre à un modèle de Lamb de propagation dans un guide d’ondes circulaire, la cinématique de Timoshenko a été retenue afin de modéliser le comportement mécanique haute fréquence des poutres. En utilisant ce modèle dans le cadre de l’approche énergétique évoquée plus haut, deux groupes de modes de propagation de la densité d’énergie vibratoire dans une poutre ont été isolés : des modes longitudinaux regroupant un mode de compression et des modes de flexion, et des modes transversaux regroupant des modes de cisaillement et un mode de torsion. Il peut être également montré que l’´evolution en temps des densités d’énergie associées obéit à des lois de transport. Pour des assemblages de poutres, les phénomènes de réflexion/transmission aux jonctions ont du être pris en compte. Les opérateurs permettant de les décrire en termes de flux d’´energie ont été obtenus grâce aux équations de continuité des déplacements et des efforts aux jonctions. Quelques caractéristiques typiques d’un régime haute fréquence ont été mises en évidence, tel que le découplage entre les modes de rotation et les modes de translation. En revanche, les champs de densité d’énergie sont quant à eux discontinus aux jonctions. Une méthode d’éléments finis discontinus a donc été développée afin de les simuler numériquement comme solutions d’´equations de transport. Si l’on souhaite atteindre le régime diffusif aux temps longs, le schéma numérique doit être peu dissipatif et peu dispersif. La discrétisation spatiale a été faite avec des fonctions d’approximation de type spectrales, et l’intégration temporelle avec des schémas de Runge-Kutta d’ordre élevé du type ”strong stability preserving”. Les simulations numériques ont donné des résultats concluants car elles permettent d’exhiber le régime de diffusion. Il a été remarqué qu’il existait en fait deux limites diffusives différentes : (i) la diffusion spatiale de l’´energie sur l’ensemble de la structure, et (ii) l’équirépartition des densités d’énergie entre les différents modes de propagation. Enfin, une technique de renversement temporel a été développée. Elle pourra être utile dans de futurs travaux sur le contrôle non destructif des assemblages complexes et de grandes tailles. / This research is dedicated to the simulation of the transient response of beam trusses under impulse loads. The latter lead to the propagation of high-frequency waves in such built up structures. In the aerospace industry, that phenomenon may penalize the functioning of the structures or the equipments attached to them on account of the vibrational energy carried by the waves. It is also observed experimentally that high-frequency wave propagation evolves into a diffusive vibrational state at late times. The goal of this study is then to develop a robust model of high-frequency wave propagation within three-dimensional beam trusses in order to be able to recover, for example, this diffusion regime. On account of the small wavelengths and the high modal density, the modelling of high-frequency wave propagation is hardly feasible by classical finite elements or other methods describing the displacement fields directly. Thus, an approach dealing with the evolution of an estimator of the energy density of each propagating mode in a Timoshenko beam has been used. It provides information on the local behavior of the structures while avoiding some limitations related to the small wavelengths of high-frequency waves. After a comparison between some reduced-order beam kinematics and the Lamb model of wave propagation in a circular waveguide, the Timoshenko kinematics has been selected for the mechanical modelling of the beams. It may be shown that the energy densities of the propagating modes in a Timoshenko beam obey transport equations. Two groups of energy modes have been isolated: the longitudinal group that gathers the compressional and the bending energetic modes, and the transverse group that gathers the shear and torsional energetic modes. The reflection/transmission phenomena taking place at the junctions between beams have also been investigated. For this purpose, the power flow reflection/transmission operators have been derived from the continuity of the displacements and efforts at the junctions. Some characteristic features of a high-frequency behavior at beam junctions have been highlighted such as the decoupling between the rotational and translational motions. It is also observed that the energy densities are discontinuous at the junctions on account of the power flow reflection/transmission phenomena. Thus a discontinuous finite element method has been implemented, in order to solve the transport equations they satisfy. The numerical scheme has to be weakly dissipative and dispersive in order to exhibit the aforementioned diffusive regime arising at late times. That is the reason why spectral-like approximation functions for spatial discretization, and strong-stability preserving Runge-Kutta schemes for time integration have been used. Numerical simulations give satisfactory results because they indeed highlight the outbreak of such a diffusion state. The latter is characterized by the following: (i) the spatial spread of the energy over the truss, and (ii) the equipartition of the energy between the different modes. The last part of the thesis has been devoted to the development of a time reversal processing, that could be useful for future works on structural health monitoring of complex, multi-bay trusses.

Le présent travail porte sur la résolution numérique de l’équation des ondes acoustiques ou élastiques dans un milieu homogène par morceaux comportant des interfaces. On s’intéresse à un problème haute fréquence, introduit par des conditions initiales fortement oscillantes, pour lequel on détermine la répartition de la densité d’énergie dans le milieu par une approche dite cinétique (fondée sur l’utilisation d’une transformation de Wigner). Le problème considéré est alors réduit à une équation de transport en milieu homogène du type Liouville, complétée par des lois de réflexion et transmission aux interfaces. Différentes méthodes de résolution et d’autres cas d’application sont par ailleurs évoquées. La résolution numérique de l’équation de transport décrivant l’évolution de la densité d’énergie dans l’espace des phases positions vecteurs d’onde est effectuée par différences finies. Cette technique soulève plusieurs difficultés relatives à la conservation de l’énergie totale dans le milieu et aux interfaces. Elles peuvent être corrigées par des schémas numériques adaptés permettant de limiter la dissipation numérique par une approche globale ou locale. Les développements réalisés concernent l’interpolation des densités d’énergie obtenues par transmission sur la grille des vecteurs d’onde discrets, ainsi que la correction de la différence d’échelle de variation de la vitesse des ondes de part et d’autre des interfaces. L’intérêt de ces adaptations est d’obtenir des schémas conservatifs qui satisfont les critères de convergence usuels des méthodes aux différences finies. Leur construction ainsi que leur mise en œuvre effective constituent le principal apport de cette thèse. La pertinence des méthodes utilisées est illustrée par des exemples de simulation, qui montrent également leur efficacité pour des maillages relativement grossiers. / The present work focuses on the numerical resolution of the acoustic or elastic wave equation in a piece-wise homogeneous medium, splitted by interfaces. We are interested in a high-frequency setting, introduced by strongly oscillating initial conditions, for which one computes the distribution of the energy density by a so-called kinetic approach (based on the use of a Wigner transform). This problem then reduces to a Liouville-type transport equation in a piece-wise homogeneous medium, supplemented by reflection and transmission laws at the interfaces. Several numerical techniques and ranges of application are also reviewed. The transport equation which describes the evolution of the energy density in the phase space positions _ wave vectors is numerically solved by finite differences. This technique raises several difficulties related to the conservation of the total energy in the medium and at the interfaces. They may be alleviated by dedicated numerical schemes allowing to reduce the numerical dissipation by either a global or a local approach. The improvements presented in this thesis concern the interpolation of the energy densities obtained by transmission on the grid of discrete wave vectors, and the correction of the difference of variation scales of the wave celerity on each side of the interfaces. The interest of the foregoing developments is to obtain conservative schemes that also satisfy the usual convergence properties of finite difference methods. The construction of such schemes and their effective implementation constitute the main achievement of the thesis. The relevance of the proposed methods is illustrated by several numerical simulations, that also emphasize their efficiency for rather coarse meshes.

Les phénomènes de diffraction et de diffusion des ondes jouent un rôle important dans l'interprétation de la coda des sismogrammes. Par conséquent, une compréhension approfondie des mécanismes de diffraction et de leurs influences sur la propagation des ondes est une étape fondamentale vers l'identification des propriétés statistiques d'un milieu aléatoire. Cette thèse porte sur la diffraction des ondes élastiques dans des milieux aléatoirement hétérogènes avec un comportement local isotrope. On s'intéresse au régime où: La longueur d'onde est du même ordre de grandeur que la longueur de corrélation, la longueur d'onde est petite comparé à la distance de propagation (haute-fréquence) et l'amplitude des fluctuations est petite. Une approche cinétique basée sur les équations de transfert radiatif des ondes élastiques est adoptée. La première partie de cette thèse décrit une analyse détaillée de l'influence de la structure de corrélation sur les paramètres de diffraction et sur l'établissement d'un régime de diffusion. La seconde partie présente les simulations éléments spectraux à grande échelle des ondes élastiques afin d'observer numériquement l'apparition d'un régime d'équipartition. Des analyses théoriques ainsi que des simulations montrent également une nouvelle approche pour l'identification des propriétés statistiques du milieu. / Scattering and diffusion phenomena play a crucial role in the interpretation of the coda part ofseismograms. Consequently, a profound understanding of scattering mechanisms and their effectson wave propagation is a fundamental step towards the identification of the statistical propertiesof random media. The focus of this work is on the scattering of elastic waves in a randomly heterogeneousmedia with locally isotropic material behavior. The weakly heterogeneous regime isconsidered, in which the wave length is similar to the correlation length, the wave length is smallcompared to the propagation length (high frequency) and the amplitude of the heterogeneities issmall. A kinetic framework based on the transport equations of elastic waves is adopted. Thefirst part of the thesis describes a detailed analysis of the influence of the correlation structure onthe scattering parameters and on the arising of the diffusion regime. The second part presentslarge scale spectral element simulations of elastic waves to observe numerically the onset of theequipartitioning regime. The theoretical analyses and simulations also reveal a novel approach toidentify local properties of the heterogeneous medium.

Composite structures provide opportunities for weight reduction, material tailoring and integrating control surfaces with embedded transducers, which are not possible in conventional metallic structures. As a result there is a substantial increase in the use of composite materials in aerospace and other major industries, which has necessitated the need for structural health monitoring(SHM) of aerospace structures. In the context of SHM of aircraft structures, there are many areas, which are still not explored and need deep investigation. Among these, one of the major areas is the development of efficient damage models for complex composite structures, like stiffened structures, box-type structures, which are the building blocks of an aircraft wing structure. Quantification of the defect due to porosity and especially the methods for identifying the porous regions in a composite structure is another such area, which demands extensive research. In aircraft structures, it is not advisable for the structures, to have high porosity content, since it can initiate common defects in composites such as, delamination, matrix cracks etc.. In fact, there is need for a high frequency analysis to detect defects in such complex structures and also to detect damages, where the change in the stiffness due to the damage is very small. Lamb wave propagation based method is one of the efficient high frequency wave based method for damage detection and are extensively used for detecting small damages, which is essentially needed in aircraft industry. However, in order, to develop an efficient Lamb wave based SHM system, we also need an efficient computational wave propagation model. Developing an efficient computational wave propagation model for complex structures is still a challenging area. One of the major difficulty is its computational expense, when the analysis is performed using conventional FEM. However, for 1D And 2D composite structures, frequency domain spectral finite element method (SFEM), which are very effective in sensing small stiffness changes due to a defect in a structure, is one of the efficient tool for developing computationally efficient and accurate wave based damage models. In this work, we extend the efficiency of SFEM in developing damage models, for detecting damages in built-up composite structures and porous composite structure. Finally, in reality, the nature of variability of the material properties in a composite structure, created a variety of structural problems, in which the uncertainties in different parameters play a major part. Uncertainties can be due to the lack of good knowledge of material properties or due to the change in the load and support condition with the change in environmental variables such as temperature, humidity and pressure. The modeling technique is also one of the major sources of uncertainty, in the analysis of composites. In fact, when the variations are large, we can find in the literatures available that the probabilistic models are advantageous than the deterministic ones. Further, without performing a proper uncertain wave propagation analysis, to characterize the effect of uncertainty in different parameters, it is difficult to maintain the reliability of the results predicted by SFEM based damage models. Hence, in this work, we also study the effect of uncertainty in different structural parameters on the performance of the damage models, based on the models developed in the present work. First, two SFEM based models, one based on the method of assembling 2D spectral elements and the other based on the concept of coupling 2D and 1D spectral elements, are developed to perform high frequency wave propagation analysis of some of the commonly used built-up composite structures. The SFEM model developed using the plate-beam coupling approach is then used to model wave propagation in a multiple stiffened structure and also to model the stiffened structures with different cross sections such as T-section, I-section and hat section. Next, the wave propagation in a porous laminated composite beam is modeled using SFEM, based on the modified rule of mixture approach. Here, the material properties of the composite is obtained from the modified rule of mixture model, which are then used in SFEM to develop a new model for solving wave propagation problems in porous laminated composite beam. The influence of the porosity content on the parameters such as wave number, group speed and also the effect of variation in theses parameters on the time responses are studied first. Next, the effect of the length of the porous region (in the propagation direction) and the frequency of loading, on the time responses, is studied. The change in the time responses with the change in the porosity of the structure is used as a parameter to find the porosity content in a composite beam. The SFEM models developed in this study is then used in the context of wave based damage detection, in the next study. First ,the actual measured response from a structure and the numerically obtained response from a SFEM model for porous laminated composite beam are used for the estimation of porosity, by solving a nonlinear optimization problem. The damage force indicator (DFI) technique is used to locate the porous region in a beam and also to find its length, using the measured wave propagation responses. DFI is derived from the dynamic stiffness matrix of the healthy structure along with the nodal displacements of the damaged structure. Next, a wave propagation based method is developed for modeling damage in stiffened composite structures, using SFEM, to locate and quantify the damage due to a crack and skin-stiffener debonding. The method of wave scattering and DFI technique are used to quantify the damage in the stiffened structure. In the uncertain wave propagation analysis, a study on the uncertainty in material parameters on the wave propagation responses in a healthy metallic beam structure is performed first. Both modulus of elasticity and density are considered uncertain and the analysis is performed using Monte-Carlo simulation (MCS) under the environment of SFEM. The randomness in the material properties are characterized by three different distributions namely normal, Weibul and extreme value distribution and their effect on wave propagation, in beam is investigated. Even a study is performed on the usage of different beam theories and their uncertain responses due to dynamic impulse load. A study is also conducted to analyze the wave propagation response In a composite structure in an uncertain environment using Neumann expansion blended with Monte-Carlo simulation (NE-MCS) under the environment of SFEM. Neumann expansion method accelerates the MCS, which is required for composites as there are many number of uncertain variables. The effect of the parameters like, fiber orientation, lay-up sequence, number of layers and the layer thickness on the uncertain responses due to dynamic impulse load, is thoroughly analyzed. Finally, a probabilistic sensitivity analysis is performed to estimate the sensitivity of uncertain material and fabrication parameters, on the SFEM based damage models for a porous laminated composite beam. MCS is coupled with SFEM, for the uncertain wave propagation analysis and the Kullback-Leibler relative entropy is used as the measure of sensitivity. The sensitivity of different input variables on the wave number, group speed and the values of DFI, are mainly considered in this study. The thesis, written in nine chapters, presents a unified document on wave propagation in healthy and defective composite structure subjected to both deterministic and highly uncertain environment.

A adoção de materiais compósitos pela indústria de petróleo e gás vem ocorrendo de forma gradual, e ainda encontra certa resistência devido à novidade de sua aplicação em projetos mecânicos do setor, e da menor confiabilidade que possuem em relação a metais. A sua implementação em maiores escalas depende também do desenvolvimento de métodos de inspeção e monitoramento de integridade estrutural. Em paralelo a isso, sistemas de varredura de tubulações baseados em ondas guiadas ultrassônicas vêm ganhando espaço devido à sua capacidade de inspecionar toda a seção de trechos extensos de uma tubulação metálica. Baseado nestas duas premissas, este trabalho tem como objetivo apresentar estudos visando o desenvolvimento de uma metodologia que seja capaz de obter as propriedades elásticas de um meio e obter as características de propagação das ondas mecânicas, cobrindo uma metodologia para obtenção das propriedades elásticas baseados em ensaios ultrassônicos, um método de otimização baseado em propriedades vibracionais e por fim, confrontando dados provenientes de modelos em elementos finitos com resultados experimentais e aproximações teóricas. Como resultados espera-se gerar informações necessárias para que possa-se compreender os mecanismo de propagação das ondas elásticas, pois é ele que permitirá a obtenção de informações a respeito dos defeitos presentes na estrutura analisada ou ainda utilizar as informações de dispersão em função da frequência e em função da direção para localização de fontes acústicas em meios ortotrópicos, sendo o conhecimento das propriedades de fase e energia das ondas em tais materiais de fundamental importância para a plena exploração do seu potencial de inspeção e monitoramento. / The adoption of new materials by the oil and gas industry has been occurring gradually and still finds some resistance due to the novelty of their application in mechanical design and their lower reliability compared to metals. The usage in large scales also depends on the development of inspection methods and structure health monitoring. In a parallel way, systems that scan pipes using mechanical guided waves have gained space because of their ability to inspect the section of large excerpts of an metallic pipe. Based on these two assumptions, this work aims to study the development of a methodology that is able to obtain the elastic properties of a medium and obtain mechanical characteristics through propagation of the stress waves in it. For this, a method to obtain elastic properties based on ultrasonic testing, a optimization method was based on vibrational properties, and comparison of to data from finite element models with experimental results and theoretical approaches were used. The results are expected to generate information needed for understand the mechanism of propagation of elastic waves, needed to obtain information about defects present in the structure or using information of angular or frequency dispersion for localizing acoustic sources in orthotropic media. As knowledge of the properties of the phase and energy waves propagation in such material are crucial for the full exploitation of inspection and monitoring.

Orientador: José Roberto de França Arruda / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-16T06:24:37Z (GMT). No. of bitstreams: 1 Fabro_AdrianoTodorovic_M.pdf: 6602156 bytes, checksum: 3a18dd67bde7f65ae2e4dd268670356d (MD5) Previous issue date: 2010 / Resumo: Esta dissertação tem como objetivo geral levar 'a realidade industrial subsídios para a modelagem e análise de sistemas mecânicos lineares com variabilidade, assim como metodologias computacionais para quantificação de incertezas, para fins de aplicação em projeto. Neste sentido, foram realizados estudos sobre técnicas de modelagem e análise estocástica de sistemas mecânicos lineares aplicadas, inicialmente, a algumas estruturas simples, de baixo custo computacional, por meio de simulações em MatLabR. Propõe-se uma abordagem probabilística para a modelagem de incertezas baseada no Princípio da Máxima Entropia para a flexibilidade relativa a uma trinca aberta e não propagante em uma barra modelada através do Método do Elemento Espectral (SEM). Também é apresentada uma abordagem para o tratamento de problemas de campo aleatório utilizando o SEM, onde são utilizadas soluções analíticas da decomposição de Karhunen-Lo'eve. Uma formulação para elementos de viga do tipo Euler-Bernoulli é apresentada e um exemplo em que a rigidez à flexão é modelada como um campo aleatório Gaussiano é tratado. Uma abordagem para análise estocástica do comportamento dinâmico de uma tampa de compressor hermético é proposta. Uma aproximação por elementos finitos obtida com o software Ansys R foi utilizada para representar o comportamento determinístico de uma tampa de compressor, e duas abordagens de modelagem estocástica são comparadas. Um ensaio experimental foi realizado com tampas nominalmente idênticas, sendo medidas apenas frequências naturais com excitação por impacto, de modo a se poder compará-las com os valores obtidos teoricamente / Abstract: This dissertation has as a general objective to bring to the industrial reality subsidies for modeling and analysis of linear mechanical systems with variability, as well as computational methodologies to the uncertainty quantification, aiming industrial design applications. In that sense, theoretical studies about stochastic modeling and analysis for mechanical linear systems were performed. They were applied, firstly, to simple and computationally low cost structures using MatlabR. In that sense, a probabilistic modeling approach based on the Maximum Entropy Principle was proposed to treat the flexibility related to an open and nonpropagating crack in a rod modeled using the Spectral Element Method (SEM). An approach for the treatment of random field problems using SEM, which uses analytical solutions of the Karhunen-Lo'eve Decomposition, is also addressed. An Euler-Bernoulli beam formulation was used, and an example where the flexural stiffness is modeled as a Gaussian random field is presented. A finite element approximation obtained with the software Ansys R was used to represent the deterministic dynamic behavior of a compressor cap shell, and two stochastic modeling approaches were compared. Experiments were performed using nominally identical cap samples. Natural frequencies were measured using impact excitation in order to compare with the theoretical results / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

Made available in DSpace on 2014-10-09T12:53:40Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T13:58:44Z (GMT). No. of bitstreams: 0 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Neste trabalho, desenvolveu-se um modelo matemático e um aparato de medidas, que têm como objetivo auxiliar no projeto e na caracterização de estruturas de ondas lentas para válvulas de ondas progressivas. O objetivo é obter as características de velocidade de fase e de impedância de interação de uma dada estrutura de ondas lentas. Modelou-se matematicamente uma estrutura de ondas lentas do tipo ringbar como uma hélice dupla contraposta, de forma que se obteve uma série de resultados teóricos já publicados e outros inéditos. Desenvolveu-se um aparato de medida em microondas para a caracterização experimental da estrutura de ondas lentas sob análise. Apresentam-se os procedimentos de medida e os resultados experimentais obtidos, comparando-os com as predições do modelo matemático. Os resultados experimentais apresentaram boa reprodutibilidade e distaram dos teóricos de acordo com o esperado. Considerou-se que o modelo matemático e o aparato de medida, bem como as técnicas experimentais, já constituem uma importante ferramenta que será de fundamental importância no projeto e fabricação de válvulas de ondas progressivas. / Dissertação (Mestrado) / IPEN/D / Instituto de Pesquisas Energéticas e Nucleares - IPEN-CNEN/SP / FAPESP:05/03612-0