The ultrasonic NDE technique to characterize the ultrasonic nonlinear response of the cyclically load 7075-T6 aluminum is described in this thesis. In order to estimate the nonlinear relation of the ultrasonic waves due to material fatigue damage or degradation, the spectral analysis techniques such as the power spectrum, bispectrum, and bicoherence spectrum are applied. The ultrasonic nonlinearity parameters by Cantrell and Jhang are introduced and presented as a function of the material fatigue growth, the number of fatigue cycles. This thesis presents the effectiveness of the bispectral analysis for evaluating the nonlinear aspects of the ultrasonic wave propagation. The results show that the nonlinearity parameters by Cantrell and Jhang are responsive to the output amplitude of the received signal and vary for the various materials, and independent of the input frequency and the ultrasonic wave propagation distance. By using the bispectral analysis tools, particularly the bicoherence spectrum, the increase of the coupling levels between the fundamental, its harmonic, and subharmonic frequency components is presented as the number of fatigue cycles is increased. This thesis suggests that the application of the bicoherence spectrum based on the nonlinear wave coupling relations be more effective for estimating the level of the material fatigue life. / Master of Science

RF front-ends are nonlinear systems that have nonlinear frequency response and, hence, can impair receiver performance by harmful adjacent channel interference in non-intuitive ways. Next generation wireless networks will see unprecedented diversity across receiver and radio technologies accessing the same band of spectrum in spatio-temporal proximity. Ensuring adjacent channel co-existence is of prime importance for successful deployment and operations of next generation wireless networks. Vulnerabilities of receiver front-end can have a severe detrimental effect on network performance and spectrum co-existence. This dissertation addresses the technological challenges in understanding and accounting for receiver sensitivities in the design of next generation wireless networks. The dissertation has four major contributions. In the first contribution, we seek to understand how receiver nonlinearity impacts performance. We propose a computationally efficient framework to evaluate the adjacent channel interference in a given radio/spectrum environment. We develop novel tractable representation of receiver front-end nonlinearity to specify the adjacent channel signals that contribute to the interference at the desired channel and the total adjacent channel interference power at a given desired channel. In the second contribution, we seek to understand how the impact of receiver nonlinearity performance can be quantified. We quantify receiver performance in the presence of adjacent channel interference using information theoretic metrics. We evaluate the limits on achievable rate accounting for RF front-end nonlinearity and provide a framework to compare disparate receivers by forming generalized metrics. In the third contribution, we seek to understand how the impact of receiver nonlinearity can be managed at the network level. We develop novel and comprehensive wireless network management frameworks that account for the RF nonlinearity, impairments, and diversity of heterogeneous wireless devices. We further develop computationally efficient algorithms to optimize the proposed framework and examine network level performance. We demonstrate through extensive network simulations that the proposed receiver-centric frameworks provide substantially high spectrum efficiency gains over receiver-agnostic spectrum access in dense and diverse next generation wireless networks. In the fourth contribution, we seek to understand how scalable interference networks are with receiver nonlinearity. We propose practical achievable schemes for interference avoidance and assess the scalability of the next generation wireless networks with interference due to receiver nonlinearity. Further, we develop an algorithmic scheme to evaluate the upper bound on scalability of nonlinear interference networks. This provides valuable insights on scalability and schemes for nonlinear adjacent channel interference avoidance in next generation shared spectrum networks. / Ph. D.

Feasible span-to-depth ratios for many modern bridge systems have been identified and documented in literature. No such parameters have been adequately identified in terms of proportioning bridge piers. This thesis includes a study of 22 existing reinforced concrete highway bridges and their respective pier systems to determine the state-of-the-art in design. The effect of different geometric and material parameters such as concrete strength, reinforcement ratio and slenderness ratio on the structural behavior of individual piers and multiple pier systems was examined. Approximate methods, which may be used for the purposes of preliminary design are discussed and reviewed. Serviceability and ultimate limit states design aids that can be used to identify appropriate preliminary cross-sectional pier dimensions and reinforcement ratios for individual piers given various slenderness ratios were developed. The structural behavior as well as an approach to the preliminary design of multiple pier bridge systems is presented.

Feasible span-to-depth ratios for many modern bridge systems have been identified and documented in literature. No such parameters have been adequately identified in terms of proportioning bridge piers. This thesis includes a study of 22 existing reinforced concrete highway bridges and their respective pier systems to determine the state-of-the-art in design. The effect of different geometric and material parameters such as concrete strength, reinforcement ratio and slenderness ratio on the structural behavior of individual piers and multiple pier systems was examined. Approximate methods, which may be used for the purposes of preliminary design are discussed and reviewed. Serviceability and ultimate limit states design aids that can be used to identify appropriate preliminary cross-sectional pier dimensions and reinforcement ratios for individual piers given various slenderness ratios were developed. The structural behavior as well as an approach to the preliminary design of multiple pier bridge systems is presented.

Analog-to-digital converter (ADC) is the main workhorse in a digital waveform recorder. Strictly speaking, an ADC is supposed to perform uniformly, irrespective of the characteristics of the signal to be acquired. However, because of certain hardware related inconsistencies, its performance declines, particularly, when acquiring non-repetitive, fast-rising, high frequency signals. The error and distortion contributed due to its declining performance, for the entire range of signals, can be comprehensively characterized by the static and dynamic nonlinearities. Actual testing of ADCs is the only way of estimating these indices. These characteristics reveal information at the microscopic level, such as bit-level aberrations, code transitions, response and settling trends, etc. These tests attain greater significance, when the digitizer is part of a reference measuring or a calibration system, because, the levels of accuracies to be achieved in such a setup may become comparable to the error introduced by the ADC. Hence, testing ADCs is a priority. International and national standards exist for testing digital waveform recorders and ADCs. For several years, the matter related to reducing static test time of high-resolution ADCs was highlighted through many publications. A critical examination of the literature indicates the major schools-of-thought pursued so far, are, (i) refinements to ramp/triangular signal based static testing, (ii) proposals for use of alternative methods and/or test signals for static test, (iii) innovative ways of achieving a relaxation in signal source requirements and, (iv) efforts to combine static and dynamic test into a single test with an appropriate test signal. As a consequence of the literature review, objectives of the thesis were formulated. They attempt to resolve- (i) Conceive a suitable test signal for simultaneous estimation of static and dynamic nonlinearity through a single test (ii) Explore possibility of employing a low-linearity ramp signal to estimate static nonlinearity (iii) Estimating static nonlinearity by exploiting linearity property of a sine signal • In the first part of the thesis, a method is proposed for the concurrent estimation of static and dynamic nonlinearity characteristics of an ADC, with the application of a single test signal. The novelty arises from the fact that the test signal proposed is new, and so is the concept of extracting the static and dynamic nonlinearity from the ADC output. This was achieved by conceiving a test signal, comprising of a high frequency sinusoid (which addresses the dynamic requirement), modulated by a low frequency ramp (which addresses the static requirement). • Static characteristics of an ADC can be determined directly from the histogram-based quasi-static approach by measuring the ADC output, when excited by an ideal ramp/triangular signal of sufficiently low frequency. This approach requires only a fraction of time compared to the conventional DC test, is straightforward, easy to implement, and, in principle is an accepted method as per the revised IEEE-1057. However, the only drawback is that ramp signal sources are not ideal. Thus, nonlinearity present in the ramp signal gets superimposed on the measured ADC characteristics, which renders them, as such, unusable. The second part of the work describes a proposal to get rid of the ramp signal nonlinearity, before it is applied to the ADC. A simple method is presented which employs a low-linearity ramp signal, but yet causes only a fraction of influence on the measured ADC static characteristics. • The third part of the thesis describes a novel method to estimate the actual static characteristics of an ADC using a low frequency sine signal, say, less than 10 Hz, by employing the histogram-based approach. It is based on the well known fact that variation of sine signal is ‘reasonably linear,’ when the angle is small. In the proposed method, the ADC under test has to be ‘fed’ with this ‘linear’ portion of the sine wave. Due to harmonics and offset in input excitation, this ‘linear’ part of the sine signal is marginally different, compared to an ideal ramp signal of equal amplitude. However, since it is a sinusoid, this difference can be accurately determined and later compensated from the measured ADC output. Thus, the corrected ADC output will correspond to the true ADC static nonlinearity. The proposed approach successfully addresses all the three concerns while estimating static linearity, i.e. it is time-efficient, excites all the ADC code-bins reasonably uniformly and tackles the source linearity issue quite nicely. These proposals are novel, simple, easy to implement, time-efficient and importantly static nonlinearity characteristics determined from them are in good agreement with that estimated by the original DC-based technique. Implementation of each method is discussed along with experimental results, for two 8-bit digital oscilloscopes and a 10-bit real time digitizer. Further details are presented in the thesis.

This research investigates the modeling of randomly distributed surface-breaking microcracks and their effects on higher harmonic generation in Rayleigh surface waves. The modeling is based on micromechanical considerations of rough surface contact. The nonlinear behavior of a single microcrack is described by a hyperelastic effective stress-strain relationship. Finite element simulations of nonlinear wave propagation in a solid with distributed microcracks are performed. The evolution of fundamental and second harmonic amplitudes along the propagation distance is studied and the acoustic nonlinearity parameter is calculated. The results show that the nonlinearity parameter increases with crack density and root mean square roughness of the crack faces. While, for a dilute concentration of microcracks, the increase in acoustic nonlinearity is proportional to the crack density, this is not valid for higher crack densities, as the microcracks start to interact. Finally, it is shown that odd higher harmonic generation in Rayleigh surface waves due to sliding crack faces introduces a friction nonlinearity.

O trabalho trata da formulação e implementação numérica de modelos matemáticos do comportamento de estruturas considerando-se as não-linearidades física e geométrica. O equilíbrio na posição deslocada é formulado via Princípio dos Trabalhos Virtuais, empregando-se o método dos elementos finitos para a discretização espacial das estruturas e busca de soluções aproximadas. Inicialmente destaca-se com base no caso de treliças planas o emprego de medidas de deformação e tensão conjugadas energeticamente. Particularizando-se a formulação geral do equilíbrio para os pórticos planos apresenta-se uma análise crítica das formulações lagrangiana total e atualizada. Em seguida, tendo-se em vista aplicações às estruturas em concreto armado, aborda-se o comportamento não-linear físico pela mecânica do dano em meios contínuos, empregando-se os modelos de dano para o concreto propostos por Mazars e La Borderie. Estendem-se os estudos do comportamento estrutural não-linear físico (dano) e geométrico incorporando-se a análise dinâmica. Utiliza-se para integração no domínio do tempo o método implícito de Newmark combinado com o procedimento incremental e iterativo de Newton-Raphson. O amortecimento é levado em conta por meio da regra de Rayleigh. Exemplos consistindo de análises não lineares estática e dinâmica de estruturas reticulares planas compõem numéricas. Os resultados obtidos ilustram o desempenho e as potencialidades das formulações empregadas. / The formulation and numerical implementation of mathematical models of the structural behavior of plane frames considering material and geometrical nonlinearities are treated in this work. The Principle of Virtual Work is presented in order to characterize the equilibrium in the displaced position. The structure is discretized by the finite element method. Plane trusses analysis is performed in order to show how important it is to take into account the strain and stress tensors energetically conjugated. Being particularized, the general equilibrium formulation for the plane frames a critical analysis of the total and updated lagrangian formulations is presented. The material nonlinear behavior is modeled by continuum damage mechanics by using both Mazars and La Boderie\'s damage models. The nonlinear analysis is extended including the dynamic response of the reinforced concrete plane frames. The usual iterative Newton-Raphson technique is used combined with implicit Newmark method in order to carry out the integration at time. The damping is introduced by means of the Rayleigh\'s rule. Numerical analysis by a suitable computer program show the theoretical results considering static and dynamic response of plane frames.

Neste trabalho são abordados os aspectos inerentes à análise não linear física e geométrica de núcleos rígidos pertencentes a estruturas de contraventamento de edifícios altos em concreto armado. O trabalho foca a análise estrutural dos núcleos através do uso de uma ferramenta computacional capaz de realizar uma análise não linear rigorosa, estudando modelos usuais com o emprego do método dos elementos finitos. São avaliadas as reduções de inércia que ocorrem nas paredes que compõem os núcleos, dimensionados de forma a apresentarem três taxas de armadura, uma próxima à mínima, uma média e uma próxima à máquina permitida pela NBR 6118. São estabelecidas estimativas simplificadas para os efeitos da não linearidade física sobre esses elementos, que possam ser utilizadas em projetos usuais de maneira simples e prática. / This work deals with nonlinear geometrical and physical analysis of structural cores that take part in the bracing system of multistory reinforced concrete buildings. The study depicts the structural behavior of concrete cores by using a computational tool that performs a strict non-linear analysis, coping with usual models based on the Finite Element Method. The work evaluates the inertia reduction of concrete core\'s walls, considering minimum, medium and maximum geometrical reinforcement ratio prescribed by NBR 6118. Estimations of the physical nonlinearity of those elements are provided aiming at the practical use in actual structural design.

Este trabalho tem como objetivo principal apresentar formulações do método dos elementos de contorno que contemplem as análises de placas considerando-se as não-linearidades física e geométrica e de placas enrijecidas considerando-se o comportamento não-linear físico do material. As equações integrais utilizadas são baseadas na teoria de Kirchhoff para flexão de placas delgadas, sendo o efeito não-linear geométrico modelado a partir da teoria de Von Kármán. Os efeitos não-lineares físicos são introduzidos no sistema a partir da consideração de um campo de tensões iniciais, com a avaliação das regiões plastificadas realizada a partir do critério elastoplástico de von Mises com encruamento isótropo linear e particularizado para o estado plano de tensão. A formulação dos enrijecedores é efetuada de forma alternativa, com o painel enrijecido considerado como um todo e submetido a campos de momentos e forças normais iniciais para induzir o ganho de rigidez. Apenas a parcela de enrijecimento na direção longitudinal do enrijecedor é considerada. O sistema de equações algébricas é obtido a partir da discretização estrutural com elementos de contorno isoparamétricos lineares. Para a consideração dos efeitos de domínio da placa são utilizadas células triangulares com funções de aproximação linear. Já as integrais no domínio dos enrijecedores são transformadas em integrais no contorno dos mesmos, com as variáveis escritas apenas no seu eixo longitudinal. Toda a solução do sistema não-linear de equações é obtida a partir de uma formulação implícita, sendo os operadores tangentes consistentes explicitados ao longo do trabalho. Por fim, vários exemplos são apresentados de forma a validar o correto desenvolvimento das formulações propostas. / In this work a boundary element method formulation to analyse plates with combined geometrical and material nonlinearities was presented. Additionally an alternative boundary element method formulation was presented to analyse material nonlinear reinforced plates. The boundary integral equations are derived based on Kirchhoff\'s theory. An initial stress field and von Kármán hypothesis are considered to take into account the material and geometrical nonlinearities, respectively. The elastoplastic von Mises criterion with linear isotropic hardening and particularized to the plane stress condition is considered to evaluate the plastic zone. The effects of the reinforcements are taken into account by using a simplified scheme based on applying an initial stress field to correct locally the bending and stretching stiffness of the reinforcement regions. Only bending and stretching rigidities in the direction of the reinforcements are considered. Isoparametric linear elements are used to approximate the boundary unknown values and triangular internal cells with linear shape functions are used to evaluate the plate domain value influences. The domain integrals due to the presence of the reinforcements are transformed to the reinforcement/plate interface. The nonlinear system of equations is solved by using an implicit scheme together with the consistent tangent operator presented along this paper. Finally, several examples are presented to confirm the correct development of the proposed formulations.

No presente trabalho são avaliados os principais parâmetros de projeto na análise da estabilidade global de estruturas em concreto pré-moldado de múltiplos pavimentos, considerando a não-linearidade física (NLF), não-linearidade geométrica (NLG) e ligações semi-rígidas. Os sistemas estruturais analisados são constituídos por pórticos com ligação viga-pilar semi-rígida e pilares engastados na fundação. As ligações viga-pilar têm sua tipologia definida por chumbadores retos e capa de concreto moldado in loco com armadura de continuidade. A NLF é avaliada segundo a construção dos diagramas M x N x 1/r, onde foi considerado de forma consistente o efeito da força normal, da armadura passiva, da armadura ativa e a reologia do concreto. São propostas funções e definidos coeficientes redutores de rigidez que foram comparados com valores apontados em expressões normativas que contemplam de forma aproximada a NLF. A NLG é avaliada com o auxílio do programa ANSYS e na forma aproximada segundo o coeficiente z e o método da carga lateral fictícia (P-). Apresentam-se modelos analíticos de caracterização de rigidez e resistência de ligações viga-pilar ao momento fletor negativo e positivo. Na análise numérica é feito um estudo de caso completo de uma estrutura típica de múltiplos pavimentos em concreto pré-moldado com o auxílio do programa ANSYS, avaliando-se diferentes formas de consideração da NLF e da NLG. É analisada a distribuição de esforços na estrutura frente às combinações de ações utilizadas e os modelos de comportamento das ligações, para algumas variações de geometria e carregamento. Dentre as conclusões, pode ser citado que os coeficientes redutores obtidos segundo o diagrama M x N x 1/r divergem das indicações normativas para consideração simplificada de NLF. Quanto à consideração simplificada de análise NLG, o coeficiente z apresentou resultados melhores na previsão dos esforços de segunda ordem em relação aos obtidos por 0,95.z. / In this research it was evaluated the main design parameters in the analysis of global stability of multi-storey precast concrete framed structures considering the physical nonlinearity (PNL), geometric nonlinearity (GNL) and semi-rigid connections behavior. The structural systems considered are those consisting of frames with beam-to-column semi-rigid connection and columns inset in the foundation. The beam-to-column connections are defined by two dowels and cast-in-place concrete cap with longitudinal reinforced bars. The PNL is evaluated according the M x N x 1/r diagrams, where are considered the effect of normal force, the reinforcing steel, prestressing steel and creep. Functions are proposed and reducing stiffness coefficients are defined, with were compared with codes that include the approximated PNL. The GNL is evaluated according to ANSYS software by no approximate analisys and its approximate according to the coefficient z and (P-) method. This research presents an analytical model characterization of stiffness and strength of beam-to-column connections to the negative and positive bending moment. In the numerical analysis is made a full case study of a typical multi-storey precast concrete framed structure with the aid of the ANSYS software, evaluating different forms of consideration of the PNL and the GNL. It analysed the bending moment distribution according the combinations of actions used and the behavioral models of connections, for some variations at geometry and loading. The reduction coefficients of flexural rigidity obtained according the M x N x 1/r diagrams differ from normative indications for simplified account of PNL. In GNL simplified analysis, the coefficient z showed better results in predicting the second-order effects with respect to those obtained by the coefficient 0,95. z.