Submitted by Erika Demachki (erikademachki@gmail.com) on 2018-03-23T22:13:05Z No. of bitstreams: 2 Tese - Thiago Rodrigues Cavalcante - 2018.pdf: 2200622 bytes, checksum: 39118adda6b7ceff14825da442b5be57 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-03-26T12:16:44Z (GMT) No. of bitstreams: 2 Tese - Thiago Rodrigues Cavalcante - 2018.pdf: 2200622 bytes, checksum: 39118adda6b7ceff14825da442b5be57 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-03-26T12:16:44Z (GMT). No. of bitstreams: 2 Tese - Thiago Rodrigues Cavalcante - 2018.pdf: 2200622 bytes, checksum: 39118adda6b7ceff14825da442b5be57 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2018-02-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In the first two chapters, we consider the following problem \begin{equation*} \left \{ \begin{array}{rcll} \alpha \Delta^{2} u + \beta \Delta u & = & f(x,u)\, & \mbox{in}\,\, \Omega \\ u = \Delta u & = & 0 \, &\mbox{on } \,\,\, \partial \Omega, \end{array} \right. \end{equation*} where $\displaystyle{\Delta^{2} u = \Delta(\Delta u)-\,\mbox{biharmonic (fourth-order operator)}}$, $\alpha > 0$ and $ \beta \in \R.$ The subset $\displaystyle{ \Omega \subset \mathbb{R}^{N}\, (N \geq 4)}$ is as somooth bounded domain and $\displaystyle{ f \in C(\overline{\Omega} \times \mathbb{R},\mathbb{R}) }.$ In each of the results obtained, we will consider different technical hypotheses and characteristics for the nonlinear function $f$ e for the value of the constant $ \beta. $ In the third chapter, we study an equation of the concave type super linear, of the form: \begin{equation} \left \{ \begin{array}{rcll} \alpha \Delta^{2} u + \beta \Delta u & = & a(x)|u|^{s-2}u + f(x,u)\, & \mbox{in}\,\, \Omega \\ u = \Delta u & = & 0 \, &\mbox{on} \,\,\, \partial \Omega, \end{array} \right. \end{equation} where $\beta \in (-\infty, \alpha \lambda_{1}).$ We consider that the function $a \in L^{\infty} (\Omega)$ and $s \in (1,2).$ Finally, in the last chapter we will consider a fourth order problem in which nonlinearity is also of the convex concave type. More precisely, we study the following class of equations: \begin{equation} \left\{ \begin{aligned} \alpha \Delta^{2} u + \beta \Delta u & = \mu a(x)|u|^{q-2}u + b(x)|u|^{p-2}u&\,\,\,\,\ &\mbox{in}\,\, \Omega \\ u = \Delta u & = 0 & \,\,\,\,&\mbox{on} \,\, \partial \Omega, \end{aligned} \right. \end{equation} where the parameter $ \mu > 0 $, the powers $ 1 <q <2 <p <2 N / (N - 4) $. In addition we assume that the functions $ \displaystyle {a, b: \Omega \rightarrow \mathbb {R}}$ are continuous that can change signal and, $ a ^{+}, b ^{+} \neq 0. $ / Nos dois primeiros Capítulos, consideramos a seguinte classe de problemas: \begin{equation*} \left \{ \begin{array}{rcll} \alpha \Delta^{2} u + \beta \Delta u & = & f(x,u)\, & \mbox{em}\,\, \Omega \\ u = \Delta u & = & 0 \, &\mbox{sobre } \,\,\, \partial \Omega, \end{array} \right. \end{equation*} onde $\displaystyle{\Delta^{2} u = \Delta(\Delta u)-\,\mbox{biharmônico},}$ $\alpha > 0$ e $ \beta \in \R.$ O subconjunto $\displaystyle{ \Omega \subset \mathbb{R}^{N}\,(N \geq 4)}$ será um domínio limitado e a não linearidade $\displaystyle{ f \in C(\overline{\Omega} \times \mathbb{R},\mathbb{R}) }.$ Em cada um dos resultados obtidos, consideraremos hipóteses técnicas e características diferentes para a função não linear $f$ e para o valor da constante $\beta.$ No terceiro Capítulo, estudamos uma equação do tipo côncavo super linear, da forma: \begin{equation*} \left \{ \begin{array}{rcll} \alpha \Delta^{2} u + \beta \Delta u & = & a(x)|u|^{s-2}u + f(x,u)\, & \mbox{em}\,\, \Omega \\ u = \Delta u & = & 0 \, &\mbox{sobre } \,\,\, \partial \Omega, \end{array} \right. \end{equation*} onde $\alpha > 0$ e $\beta \in (-\infty, \alpha \lambda_{1})$. Consideramos que a função $a \in L^{\infty}(\Omega)$ e que $s \in (1,2).$ Por fim, no último Capítulo vamos considerar um problema de quarta ordem no qual a não linearidade é do tipo côncavo-convexa. Mais precisamente, estudamos a seguinte classe de equações: \begin{equation*} \left\{ \begin{aligned} \alpha \Delta^{2} u + \beta \Delta u & = \mu a(x)|u|^{q-2}u + b(x)|u|^{p-2}u&\,\,\,\,\ &\mbox{em}\,\, \Omega \\ u = \Delta u & = 0 & \,\,\,\,&\mbox{sobre} \,\, \partial \Omega, \end{aligned} \right. \end{equation*} onde o parâmetro $\mu > 0$ e as potências $ 1 < q < 2 < p < 2 N /(N - 4)$. Adicionalmente supomos que as funções $\displaystyle{a, b : \Omega \rightarrow \mathbb{R} }$ sejam contínuas podendo trocar de sinal em $\Omega$ e que $a^{+},b^{+} \neq 0.$

For repeated transient solutions of geometrically nonlinear structures the numerical effort often poses a major obstacle. Thus, the introduction of a reduced order model, which takes the nonlinear effects into account and accelerates the calculations considerably, is often necessary.This work yields a method that allows for rapid, accurate and parameterisable solutions by means of a reduced model of the original structure. The structure is discretised and its dynamic equilibrium described by a matrix equation. The projection on a reduced basis is introduced to obtain the reduced model. A comprehensive numerical study on several common reduced bases shows that the simple introduction of a constant basis is not sufficient to account for the nonlinear behaviour. Three requirements for an rapid, accurate and parameterisable solution are derived. The solution algorithm has to take into account the nonlinear evolution of the solution, the solution has to be independent of the nonlinear finite element terms and the basis has to be adapted to external parameters.Three approaches are provided, each responding to one requirement. These approaches are assembled to the integrated method. The approaches are the update and augmentation of the basis, the polynomial formulation of the nonlinear terms and the interpolation of the basis. A Newmark-type time-marching algorithm provides the frame of the integrated method. The application of the integrated method on test-cases with geometrically nonlinear finite elements confirms that this method leads to the initial aim of a rapid, accurate and parameterisable transient solution.

Orientador: Gustavo Luiz Chagas Manhães de Abreu / Resumo: O presente trabalho propõe uma nova estratégia para supressão ativa robusta do fenômeno Ground Resonance (GR) em Helicópteros. O modelo clássico de análise deste fenômeno é desenvolvido para um rotor isotrópico e a análise de estabilidade é feita no domínio de Coleman, para encontrar as fronteiras de instabilidade. Também é proposta uma nova estratégia para lidar com essas fronteiras de instabilidade e suprimir o GR usando controladores com formulação descrita por conjuntos politópicos convexos. Controladores são projetados via desigualdades lineares matriciais (LMIs, Linear Matrix Inequalities), formulados de acordo com a Teoria de Estabilidade de Lyapunov. Adicionalmente, incertezas paramétricas na frequência de lead-lag das pás e a apresentação de uma falha estrutural nos atuadores são consideradas e, assim, novos controladores robustos são projetados a fim de expandir o envelope operacional da aeronave. Ainda, são considerados diferentes tipos de não-linearidades estruturais na rigidez e amortecimento do trem de pouso do helicóptero e a caracterização da estabilidade não-linear do sistema exibe oscilações em ciclo limite (LCO, Limit Cycle Oscillation), que são determinadas a partir da construção de Diagramas de Bifurcação. Utiliza-se a modelagem Fuzzy-TS do sistema para cada caso de estudo e, com base nas fronteiras de estabilidade não-linear do GR, definidas a partir dos Diagramas de Bifurcação, têm-se o projeto de controladores para supressão das LCOs do sistema. Os res... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The present work proposes a new strategy for robust active suppression of Ground Resonance (GR) phenomenon in Helicopters. The classical model to analysis of this phenomenon is developed for an isotropic rotor and stability analysis is done in Coleman domain, to nd the boundaries of instability. It is also proposed a new strategy for dealing with these boundaries of instability and suppressing GR using controllers with polytopic convex hulls formulation. Controllers are designed via Linear Matrix Inequalities (LMIs), formulated according to the Lyapunov Stability Theory. Additionally, parametric uncertainties in the lead-lag frequency of the blades and actuators faults are considered and thus new robust controllers are designed to expand the aircraft operating envelope. Also, di erent types of structural nonlinearities in the landing gear sti ness and damping of the helicopter are considered, and the characterization of the nonlinear stability of the system exhibits Limit Cycle Oscillation (LCO), which are determined from the construction of Bifurcation Diagrams. Fuzzy-TS modeling is used for each case study and, based on the nonlinear stability boundaries of the GR, de ned from the Bifurcation Diagrams, the controllers to suppress the LCO are designed. The results of numerical simulations, discussions and conclusions are presented and show that the control strategy proposed is an attractive solution to suppress the linear and nonlinear GR problem, being able to expand the o... (Complete abstract click electronic access below) / Doutor

Les non-linéarités des ondes de surface, qui se caractérisent par leur aspect dissymétrique, sont reconnues comme l'un des principaux moteurs du transport de sédiments en zone littorale. Cependant, l'estimation du transport reste imparfaite, en partie du fait d’une description inexacte des non-linéarités de la vitesse de l'écoulement orbital. Les ondes infra-gravitaires, qui coexistent avec les ondes courtes en zone littorale, sont des ondes de longue période (20-200 s) associés aux groupes d'ondes courtes. Les mécanismes de génération, propagation et dissipation de ces ondes sont maintenant relativement bien compris, mais leur effet sur le transport sédimentaire est encore mal connu. Afin (i) d’améliorer les paramétrisations existantes des non-linéarités de vitesse et (ii) d’étudier le rôle des ondes infra-gravitaires dans le transport sédimentaire, de nouvelles expériences ont été réalisées dans deux canaux à houle, l’un avec un fond fixe et l'autre avec un fond mobile constitué de sédiments de faible densité. Les données obtenues avec ces modèles physiques ont été utilisés conjointement à des données de terrain et des simulations numériques pour étudier les deux sujets.}TEXT{}{Les paramétrisations classiques pour les non-linéarités de vitesse prennent seulement en compte l'influence de paramètres locaux (la hauteur de vague, la longueur d'onde et la profondeur d’eau), ce qui entraîne des erreurs importantes dans les estimations, en particulier les valeurs maximales de non-linéarité. Ce travail montre que les non-linéarités de vitesse ont aussi une dépendance avec des paramètres qui ne sont pas locaux: (i) la cambrure de vague et (ii) la largeur de la bande spectrale au large, ainsi que (iii) la pente de la plage. Une nouvelle paramétrisation est proposée, qui réduit d’environ 50% l'erreur sur les résultats obtenus avec les paramétrisations existantes. Les résultats expérimentaux obtenus dans le canal à houle avec un fond mobile montrent que des conditions de vagues avec la même énergie d'ondes courtes, mais avec une modulation basse fréquence différente, modèlent des profils de plage différents. L'influence des ondes infra-gravitaires sur le transport sédimentaire est mis en évidence par deux mécanismes distincts: (i) l’advection par les ondes infra-gravitaires de sédiment mis en suspension par l'action des ondes courtes, qui dépend de la hauteur des ondes infra-gravitaires et de leur phase par rapport aux groupes d'ondes courtes et (ii) les ondes infra-gravitaires modifient les non-linéarités des ondes courtes, que ce soit directement ou indirectement, par modulation de la hauteur de la colonne d'eau. Les variations morphologiques du haut de plage induites par les ondes infra-gravitaires sont associées à des changements du profil de la plage dans les zones de déferlement et de levée, en mettant en évidence le lien entre les différentes régions du profil transversal de la plage. / Wave nonlinearities have long been recognised as being among the main drivers of sediment transport in the coastal zone. However, there are still significant errors in the prediction of this transport associated, partially due to inaccurate predictions of the velocity nonlinearities. The infragravity waves, which coexist with the short waves in the coastal zone, are long-period waves (with 20-200 s) associated to the short-wave groups. Their generation, propagation and dissipation mechanisms are already reasonably well understood, but their influence on sediment transport is still very poorly characterised. In order to (i) improve current predictions of velocity nonlinearities and (ii) investigate the role of infragravity waves in sediment transport, new experiments were carried out both in a fixed-bed wave flume and in a light-weight-sediment wave flume. The physical-modelling data set is used in combination with field data and numerical simulations for studying both subjects. Existing parameterizations of velocity nonlinearities account only for the influence of local wave parameters (e.g. wave height, wave length and water depth), which leads to considerable estimation errors, especially of the maximal values of nonlinearity. This work shows that the velocity nonlinearities depend also on non-local wave parameters: (i) offshore wave steepness, (ii) offshore spectral bandwidth and (iii) beach slope. A new parameterization is proposed, which reduces by about 50% the root-mean-square error relatively to former parameterizations. The experimental results in the light-weight-sediment wave flume demonstrate that wave conditions with the same short-wave energy, but different low-frequency modulation, shape different equilibrium beach profiles. The influence of the infragravity waves on the sediment transport is confirmed and depends on two different mechanisms: (i) advection of the short-wave suspended sediment by the infragravity-waves, which is dependent on the infragravity-wave height and phasing with the short-wave groups and (ii) modulation of short-wave nonlinearities by infragravity-wave motion, both directly and indirectly, through water-depth modulation. Changes in the beachface morphology induced by infragravity waves are connected to beach-profile changes in the surf and inner-shoaling zones, highlighting the existent link between the different zones of the cross-shore beach profile.

A aeroelasticidade estuda a interação mútua entre os efeitos aerodinâmicos e estruturais. É sabido que essa relação muitas vezes se comporta de maneira não linear, causando diversos problemas, tais como flutter, oscilações em ciclo limite, bifurcações e caos. Tais fenômenos são difíceis de serem diagnosticados, podendo causar problemas graves à estrutura das aeronaves e também inviabilizar as suas operações. Dentre as principais fontes de não linearidades em sistemas aeroelásticos, pode-se citar as de origem aerodinâmica e estrutural. As de origem estrutural, por sua vez, podem ter caráter distribuído ou concentrado. Sabe-se que os efeitos estruturais concentrados denominados enrijecimento e folga são os de maior impacto na aeroelasticidade não linear. Desse modo, o objetivo desse trabalho é estudar a interação não linear entre duas não linearidades estruturais, ou seja, o enrijecimento associado à rigidez em torção e a folga presente nas articulações das superfícies de controle de seções típicas aeroelásticas. Experimentos em túnel de vento são realizados utilizando um dispositivo que permite variar a intensidade do efeito de enrijecimento e do tamanho da folga na articulação da superfície de comando. O modelo numérico de seção típica aeroelástica também é utilizado e validado com dados experimentais. Análises por meio de diagramas de bifurcação de Hopf e técnicas baseadas em espectros de potência são utilizadas. Todas as respostas aeroelásticas foram caracterizadas através de ferramentas de análise nos domínios do tempo e da frequência, como técnica de reconstrução de espaço de estados e os espectros de alta ordem (HOS), os quais são importantes na identificação dos tipos de acoplamentos não lineares. Resultados indicam que a combinação dos efeitos de enrijecimento e folga são responsáveis pelo comportamento subcrítico das bifurcações de Hopf e que a intensidade do enrijecimento tem influência direta nas amplitudes de ciclo limite. / Aeroelasticity is the field of engineering that deals with the mutual interaction between the aerodynamic and structural dynamics effects. It is known that this relationship often shows nonlinear behavior, causing various problems such as flutter, limit cycle oscillations, bifurcations and chaos. Such phenomena are difficult to predict and can cause serious problems to the aircraft structure and also they can jeopardize their operations. The unsteady aerodynamic and structural dynamics provide the main sources of nonlinearities in aeroelastic systems. Structural nonlinearities can be treated as distributed or concentrated effects. It is know that the nonlinear concentrated structural effects referred as hardening and freeplay have a significant impact on nonlinear aeroelasticity. The objective of this work is to analyze an aeroelastic system under the influence of combined structural nonlinearities, i.e., the hardening nonlinearity in the pitch airfoil motion and the freeplay nonlinearity in the control surface hinge. Wind tunnel experiments are carried out using one device that allows to vary the intensity of the hardening effect and the size of the freeplay gap in the control surface hinge. The numerical model of the typical aeroelastic section is also used and validated with experimental data. All aeroelastic responses are characterized by analytical tools in time and frequency domains. It was used the state space reconstruction technique and the higher order spectral analysis (HOS) to identify types of nonlinear couplings. The results indicate that the combination of hardening and freeplay effects are responsible for inducing the subcritical behavior on the Hopf bifurcations and that the intensity of the stiffness has a direct influence on the limit cycle amplitudes.

O problemas do impacto em corpos elásticos está massivamente presente na indústria e no funcionamento de grande parte dos equipamentos domésticos. Entender e dominar este fenômeno é fundamental não somente a indústria mecânica mas a todas as outras que nela se apóiam. Neste trabalho são apresentados estudos básicos sobre impacto longitudinal, transversal e propagação de ondas de tensão elástica. São introduzidos conceitos de análise modal, amortecimento, não linearidade e transformada discreta de Fourier, empregada em análise de sinais. O método dos elementos finitos foi a principal ferramenta matemática empregada. Com ele foi possível a construção das superfícies de tensão equivalente máxima, capazes de representar diversas situações de impacto que podem ocorrer a uma determinada geometria. A compilação deste trabalho, em suma, visa a compreensão geral do fenômeno do impacto e da posição nele ocupada pelas grandezas físicas massa, velocidade e tensão. O conhecimento de como estas grandezas estão relacionadas permite projetar um sistema dinâmico com mais inteligência. / The impact problem in elastic bodies is present in industry and working of most domestic equipaments. The knowledge and understanding of this phenomenon is of fundamental importance to the mechanical industry and their dependents. This work presents basic studies about longitudinal and transversal impact and elastic stress propagation. The concepts of modal analysis, damping, nonlinearities and discrete fourier transform, employed in signal analysis, are introduced. The finite element method was the main mathematical tool used here. It allowed the construction of the surface of maximum equivalent stress, which represents many crashes situations that can occur in certain model. In summary, this work intends the general comprehension of the impact phenomenon and the existing relation among mass, velocity and generated stresses. This comprehension allows to project dynamic systems with more intelligence.

A aeroelasticidade estuda a interação mútua entre os efeitos aerodinâmicos e estruturais. É sabido que essa relação muitas vezes se comporta de maneira não linear, causando diversos problemas, tais como flutter, oscilações em ciclo limite, bifurcações e caos. Tais fenômenos são difíceis de serem diagnosticados, podendo causar problemas graves à estrutura das aeronaves e também inviabilizar as suas operações. Dentre as principais fontes de não linearidades em sistemas aeroelásticos, pode-se citar as de origem aerodinâmica e estrutural. As de origem estrutural, por sua vez, podem ter caráter distribuído ou concentrado. Sabe-se que os efeitos estruturais concentrados denominados enrijecimento e folga são os de maior impacto na aeroelasticidade não linear. Desse modo, o objetivo desse trabalho é estudar a interação não linear entre duas não linearidades estruturais, ou seja, o enrijecimento associado à rigidez em torção e a folga presente nas articulações das superfícies de controle de seções típicas aeroelásticas. Experimentos em túnel de vento são realizados utilizando um dispositivo que permite variar a intensidade do efeito de enrijecimento e do tamanho da folga na articulação da superfície de comando. O modelo numérico de seção típica aeroelástica também é utilizado e validado com dados experimentais. Análises por meio de diagramas de bifurcação de Hopf e técnicas baseadas em espectros de potência são utilizadas. Todas as respostas aeroelásticas foram caracterizadas através de ferramentas de análise nos domínios do tempo e da frequência, como técnica de reconstrução de espaço de estados e os espectros de alta ordem (HOS), os quais são importantes na identificação dos tipos de acoplamentos não lineares. Resultados indicam que a combinação dos efeitos de enrijecimento e folga são responsáveis pelo comportamento subcrítico das bifurcações de Hopf e que a intensidade do enrijecimento tem influência direta nas amplitudes de ciclo limite. / Aeroelasticity is the field of engineering that deals with the mutual interaction between the aerodynamic and structural dynamics effects. It is known that this relationship often shows nonlinear behavior, causing various problems such as flutter, limit cycle oscillations, bifurcations and chaos. Such phenomena are difficult to predict and can cause serious problems to the aircraft structure and also they can jeopardize their operations. The unsteady aerodynamic and structural dynamics provide the main sources of nonlinearities in aeroelastic systems. Structural nonlinearities can be treated as distributed or concentrated effects. It is know that the nonlinear concentrated structural effects referred as hardening and freeplay have a significant impact on nonlinear aeroelasticity. The objective of this work is to analyze an aeroelastic system under the influence of combined structural nonlinearities, i.e., the hardening nonlinearity in the pitch airfoil motion and the freeplay nonlinearity in the control surface hinge. Wind tunnel experiments are carried out using one device that allows to vary the intensity of the hardening effect and the size of the freeplay gap in the control surface hinge. The numerical model of the typical aeroelastic section is also used and validated with experimental data. All aeroelastic responses are characterized by analytical tools in time and frequency domains. It was used the state space reconstruction technique and the higher order spectral analysis (HOS) to identify types of nonlinear couplings. The results indicate that the combination of hardening and freeplay effects are responsible for inducing the subcritical behavior on the Hopf bifurcations and that the intensity of the stiffness has a direct influence on the limit cycle amplitudes.

The subject of this Thesis is to examine nontrivial solutions of boundary value problems for second order ODEs with unilateral jumping nonlinearities. Considered problems can be interpreted as models of a simple beam supported by three types of elastic obstacles. Couples of eigenvalues and eigenfunctions are found and discussed with respect to parameter which represents the strength of the obstacle.

Ce travail de thèse est une contribution au développement des méthodes d’acoustique non linéaire pour le contrôle non destructif et l’imagerie de défauts de type contact dans les solides.Dans ce travail, des modifications sont proposées pour deux méthodes récentes de contrôle non destructif par acoustique non linéaire : l’interférométrie de coda couplée au retournement temporel, et l’imagerie non linéaire par ultrasons aériens. Le principal avantage de la première méthode est sa sensibilité extrême liée à l’accumulation des effets induits par des changements, même faibles, des propriétés de l’échantillon durant la formation de la coda. La deuxième méthode apporte une approche complémentaire en permettant de réaliser un contrôle sans contact. Les techniques développées ont été testées sur des échantillons présentant des défauts artificiels à des emplacements connus. Les performances de chacune des méthodes ont été étudiées.La deuxième partie de ce travail porte sur la description théorique des non-linéarités acoustiques de contact et leur utilisation pour le développement d’une boite à outils numériques permettant la simulation d’ondes acoustiques dans des structures complexes contenant des contacts internes. Un model physique décrivant le décalage tangentiel de deux corps en contact en présence de friction est proposé. Il aboutit à une solution analytique pour la relation présentant une hystérésis entre les déplacements de contact normal et tangentiel et les chargements. Ce modèle est utilisé comme condition aux frontières pour les surfaces de contact internes (défauts) dans un modèle de propagation d’ondes acoustiques utilisant un logiciel d’éléments finis commercial / This PhD thesis work contributes to the development of nonlinear elastic methods for non-destructive testing and imaging of contact-type defects in solids.In this work, two modifications of recent nonlinear nondestructive testing methods are suggested: the coda wave interferometry combined with the nonlinear time reversal principle and air-coupled nonlinear ultrasonic imaging. The principal advantage of former technique is in its extremely high sensitivity owing to the fact that weak changes in sample's parameters are accumulated and finally greatly amplified during the formation of the coda wave. The other technique has a complimentary strength and offers a possibility of a remote detection. The developed techniques are tested on samples with artificially fabricated defects at known locations. The performance of each method is accessed and the potential for obtaining robust nonlinear images is demonstrated.The second part of the work is concerned with a theoretical description of contact acoustical nonlinearity and its use for creating of a numerical toolbox capable of simulating wave propagation in complex structures containing internal contacts. A physical model describing the tangential shift of two contacting bodies in the presence of friction has been proposed. Its result is an analytical computer-assisted solution for hysteretic relationships between normal and tangential contact displacements and loads. The contact model and derived load-displacement relationships are used as boundary conditions posed at the internal boundaries (contact surfaces) in a finite element wave propagation model programmed via commercial software

We correlated experimental results with theoretical estimations of the dielectric function ε(ω) in two contexts: the effect of an electric field in quantum wells and that of the spin polarization of an interacting electron-hole plasma in bulk semiconductors. In the first part, we recorded photoreflectance spectra from Ge/GeSi quantum wells of different widths but having comparable builtin electric fields caused by doping. The reason why the spectra differed in overall shape was difficult to understand by conventional methods, for example, by calculating the allowed transition energies or by fitting the data with lineshape functions at each transition energy. Instead, we computed the photoreflectance spectra from first-principles by using the confined electron and hole wavefunctions. This method showed that the spectra differ in overall shape because of the experimentally hitherto unobserved trend in quantum well electro-optical properties, from the quantum confined Franz-Keldysh effect to the bulk Franz-Keldysh effect, as the well width is increased. The second part develops a threeband microscopic theory for the optical properties due to spin-polarized carriers in quasiequilibrium. We show that calculations based on this theory reproduce all the trends observed in a recent circularly polarized pump-probe experiment reported in the literature. To make the computation less intensive, we proposed a simplified, two-band version of this theory which captured the main experimental features. Besides, we constructed a cw diode laser-based pump-probe setup for our own optical studies of spin-polarized carriers by Kerr rotation. We achieved a sensitivity of detection of Kerr rotation of 3 x 10¯ 8 rad, corresponding to an order of magnitude improvement over the best reports in the literature. The efficacy of our setup allowed for the demonstration of a pumpinduced spin polarization in bulk GaAs, under the unfavorable conditions of steady-state and room temperature.