Lean premixed combustors have been designed to lower NOx and other pollutant levels in land based gas turbines. These combustors are often susceptible to thermo-acoustic instabilities, which manifest as pressure and heat release oscillations in the combustor. To be able to predict and control these instabilities, it is required that both the acoustics of the system, and a frequency-resolved response of the combustion process to incoming perturbations be understood. Currently, a system-level approach is being used widely to predict the thermoacoustic instabilities. This approach requires simple, yet accurate models which would describe the behavior of each dynamic block within the loop. The present study is directed toward using computational fluid dynamics (CFD) as a tool in developing reduced order models for the dynamics of laminar flat flames and swirl stabilized turbulent flames. A finite-volume based approach is being used to simulate reacting flows in both laminar and turbulent combustors. The study has been divided into three parts -- the first part involves the modeling of a self-excited combustor (the acoustics of the combustor are coupled with the unsteady heat release); the second part of the research aims to study the effect of velocity perturbations on the unsteady heat release rate from a burner stabilized laminar flat flame; the third and final part of work involves an extension of the laminar flat flame study to turbulent reacting flows in a swirl stabilized combustor, and study the effects on the turbulent heat release due to the velocity perturbations. A Rijke tube combustor was selected to study self-excited combustion phenomenon. A laminar premixed methane-air flat flame was stabilized on a honeycomb flame-stabilizer. The flame stabilizer was placed at the center of the 5 feet vertical tube. The position of the flame at the center of the tube leads to a thermoacoustic instability of the 2nd acoustic mode. The fundamental thermoacoustic frequency was predicted accurately by the CFD model and the amplitude was reasonably matched (for a flow rate of Q = 120 cc/s and equivalence ratio phi = 1.0). Other characteristics of the pressure power spectrum were captured to a good degree of accuracy. This included the amplitude modulation of the fundamental and the harmonics due to a subsonic pulsating instability. The flat flame study has been being conducted for Q = 200 cc/s and equivalence ratio phi = 0.75. The objective has been to obtain a frequency response function (FRF) of the unsteady heat release rate (output) due to incoming velocity perturbations (input). A range of frequencies (15 Hz - 500 Hz) have been selected for generating the FRF. The aim of this part of the study has been to validate the computational model against the experimental results and propose a physics based interpretation of the flame response. Detailed heat transfer modeling (including radiation heat transfer) and two-step chemistry models have been implemented in the model. The FRF generated has been able to reproduce the experimentally observed phenomena, like the low frequency pulsating instability occurring at 30 Hz. A heat transfer study has been conducted to explain the pulsating instability and a fuel variability study has been performed. Both the heat transfer study and the fuel variability study proved the role of heat transfer in creating the pulsating instability. The final part of the study involves simulation of reacting flow in a turbulent swirl stabilized combustor. The effect of velocity perturbations on the unsteady heat release has been studied by creating an FRF between the unsteady velocity and the unsteady heat release rate. A Large Eddy Simulation (LES) approach has been selected. A swirl number of S = 1.19 corresponding to a flow rate of Q = 20 SCFM with an equivalence ratio of phi = 0.75 have been implemented. Reduced reaction chemistry modeling, turbulence-chemistry interaction and heat transfer modeling have been incorporated in the model. The LES of reacting flow has shown vortex-flame interaction occurring inside the combustor. This interaction has been shown to occur at 255 Hz. The FRF obtained between unsteady velocity and unsteady heat release rate shows good comparison with the experimentally obtained FRF. / Ph. D.

In this thesis a piezo-electro-mechanical system, constituted of an aluminum beam with five piezoelectric patches glued on it, each of them shunted with an RL electrical circuit, has been numerically and experimentally investigated, in order to determine the optimal electric tuning parameters for vibration damping. A numerical code based upon Galerkin weighted-residual method is developed and the complete piezo-electro-mechanical system is designed, realized and finally tested by a standard modal testing technique. Comparisons between different shunting configurations of the system are given and finally the experimental data are compared with ones obtained by the developed numerical code in order to verify the accuracy of the latter. / Master of Science

In this work, the feasibility to perform substructuring technique with experimental data is demonstrated. This investigation examines two structures with different additional mass‑loads, i.e. transmission simulators (TSs). The two structures are a single blade and the hub together with two blades from an Ampair 600 wind turbine. Simulation data from finite element models of the TSs are numerically decoupled from each of the two structures. The resulting two structures are coupled to each other. The calculations are made exclusively in the frequency domain. A comparison between the predicted behavior from this assembled structure and measurements on the full hub with all three blades is carried out. The result is discouraging for the implemented method. It shows major problems, even though the measurements were performed in a laboratory environment.

During vibration of engineering structures, fatigue cracks may exhibit repetitive crack open-close breathing like phenomenon. In this thesis, the concept of entropy is employed to quantify this bi-linearity/irregularity of the vibration response so as to evaluate crack severity. To increase the sensitivity of the entropy calculation to detect the damage severity, entropy is merged with wavelet transformation (WT). A cantilever beam with a breathing crack is studied to asses proposed crack identification method under two vibration conditions: sinusoidal and random excitations. Through numerical simulations and experimental testing, the breathing crack identification under sinusoidal excitation is studied first and proven to be effective. Then, the crack identification sensitivity under lower excitation frequencies is further improved by parametric optimization of sample entropy and WT. Finally, breathing crack identification under general random excitations are experimentally studied and realized using frequency response functions (FRFs) as an add-in tool with the proposed crack identification technique. / October 2016

Determinar as forças que estão agindo em um dado sistema é uma questão frequente em dinâmica estrutural, de modo que a reconstrução ou a identificação de carregamento se torna um importante problema de engenharia. Quando um sistema é exposto a um carregamento desconhecido e/ou não se é possível medir diretamente a força atuante nesse sistema, se torna necessária a utilização de métodos inversos. Esta metodologia consiste essencialmente na aplicação de cargas dinâmicas pontuais nos modelos de estudo e posterior recuperação de estimativas dessas cargas nos pontos de interesse. Na prática, há situações em que o número de pontos de interesse diferem do número de pontos testados, sendo assim, a matriz da função de resposta de freqüência (FRF) do sistema resulta retangular, fazendo-se necessário o uso da pseudo-inversa de Moore-Penrose. No presente trabalho, essa metodologia é aplicada a modelos númericos a fim de testar sua eficácia. Os resultados dos processos de reconstrução de carregamento dinâmico utilizando a presente metodologia foram obtidos a partir de aplicações analíticas e numéricas. Além disso, diretrizes para utilização da pseudo-inversa de Moore-Penrose na reconstrução de carregamento dinâmico são apresentadas ao final deste trabalho. / Determining the forces acting on a given system is a frequent issue in structural dynamics, so that load reconstruction or load identification becomes an important engineering problem. When a system is exposed to an unknown load and/or if it is not possible to directly measure the force acting on that system, it is necessary to use inverse methods. This methodology consists essentially in the application of punctuals dynamics load in the study models and later recovery of estimates of these loads at points of interest. In practice, there are situations where the number of points of interest differ from the number of points tested, so the matrix of the frequency response function (FRF) of the system is rectangular, making it necessary to use the pseudo-inverse of Moore-Penrose. In the present work, this methodology is applied to numerical models in order to test their effectiveness. The results of the dynamic load reconstruction processes using the present methodology were obtained from analytical and numerical applications. In addition, guidelines for using Moore-Penrose pseudo-inverse in the dynamic load reconstruction are presented at the end of this work.

The handling of variability effects in structural models is a natural and necessary extension of deterministic analysis techniques. In the context of finite element and uncertainty modelling, the stochastic finite element method (SFEM), grouping the perturbation SFEM, the spectral SFEM and the Monte-Carlo simulation, has by far received the major attention. <br> The present work focuses on second moment approaches, in which the first two statistical moments of the structural response are estimated. Due to its efficiency for handling problems involving low variability levels, the perturbation method is selected for characterising the propagation of the parameter variability from an uncertain dynamic model to its structural response. A dynamic model excited by a time-harmonic loading is postulated and the extension of the perturbation SFEM to the frequency domain is provided. This method complements the deterministic analysis by a sensitivity analysis of the system response with respect to a finite set of random parameters and a response surface in terms of a Taylor series expansion truncated to the first or second order is built. Taking into account the second moment statistical data of the random design properties, the response sensitivities are appropriately condensed in order to obtain an estimation of the response mean value and covariance structure. <br> In order to handle a wide definition of variability, a computational tool is made available that is able to deal with material variability sources (material random variables and fields) as well as shape uncertainty sources. This second case requires an appropriate shape parameterisation and a shape design sensitivity analysis. The computational requirements of the tool are studied and optimised, by reducing the size of the random dimension of the problem and by improving the performances of the underlying deterministic analyses. In this context, modal approaches, which are known to provide efficient alternatives to direct approaches in frequency domain analyses, are developed. An efficient hybrid procedure, coupling the perturbation and the Monte-Carlo simulation SFEM, is proposed and analysed. <br> Finally, the developed methods are validated, by resorting mainly to the Monte-Carlo simulation technique, on different numerical applications: a cantilever beam structure, a plate bending problem (involving a 3-dimensional model), an articulated truss structure and a problem involving a plate with a random flatness default. The propagation of the model uncertainty in the response FRFs and the effects involved by random field modelling are examined. Some remarks are stated pertaining to the influence of the parameter PDF in simulation-based methods. <br> <br> La gestion de la variabilité présente dans les modèles structuraux est une extension naturelle et nécessaire des techniques de calcul déterministes. En incorporant la modélisation de l'incertitude dans le calcul aux éléments finis, la méthode des éléments finis stochastiques (groupant l'approche perturbative, l'approche spectrale et la technique de simulation Monte-Carlo) a reçu une large attention de la littérature scientifique. <br> Ce travail est orienté sur les approches dites de second moment, dans lesquelles les deux premiers moments statistiques de la réponse de la structure sont estimés. De par son aptitude à traiter des problèmes caractérisés par de faibles niveaux de variabilité, la méthode perturbative est choisie pour propager la variabilité des paramètres d'un modèle dynamique incertain sur sa réponse. Un modèle sous chargement dynamique harmonique est supposé et l'extension dans le domaine fréquentiel de l'approche perturbative est établie. Cette méthode complète l'analyse déterministe par une analyse de sensibilité de la réponse du système par rapport à un ensemble fini de variables aléatoires. Une surface de réponse en termes d'un développement de Taylor tronqué au premier ou second ordre peut alors être écrit. Les sensibilités de la réponse sont enfin condensées, en tenant compte des propriétés statistiques des paramètres de design aléatoires, pour obtenir une estimation de la valeur moyenne et de la structure de covariance de la réponse. <br> Un outil de calcul est développé avec la capacité de gestion d'une définition large de la variabilité: sources de variabilité matérielle (variables et champs aléatoires) ainsi que géométrique. Cette dernière source requiert une paramétrisation adéquate de la géométrie ainsi qu'une analyse de sensibilité à des paramètres de forme. Les exigences calcul de cet outil sont étudiées et optimisées, en réduisant la dimension aléatoire du problème et en améliorant les performances des analyses déterministes sous-jacentes. Dans ce contexte, des approches modales, fournissant une alternative efficace aux approches directes dans le domaine fréquentiel, sont dérivées. Une procédure hybride couplant la méthode perturbative et la technique de simulation Monte-Carlo est proposée et analysée. <br> Finalement, les méthodes étudiées sont validées, principalement sur base de résultats de simulations Monte-Carlo. Ces résultats sont relatifs à plusieurs applications numériques: une structure poutre-console, un problème de flexion de plaque (modèle tridimensionnel), une structure en treillis articulé et un problème de plaque présentant un défaut de planéité aléatoire. La propagation de l'incertitude du modèle dans les fonctions de réponse fréquentielle ainsi que les effets propres à la modélisation par champs aléatoires sont examinés. Quelques remarques relatives à l'influence de la loi de distribution des paramètres dans les méthodes de simulation sont évoquées.

Vibration generated from various sources (engine, road surface, tires, exhaust, etc.) should be considered in the design of a car body. These vibrations travel through transfer systems (drivetrain, suspension, body, etc.) to the steering wheel, seats and other areas where it is detected by the passengers of the vehicle. Transmission routes must be studied and efforts made to keep transfer systems from amplifying vibration and to absorb it instead. Since the superior vibration transfer system is the car body, finite element analysis and experimental vibration analysis are performed on car body-in-white. Body vibration analysis entails understanding and improving the body&rsquo / s dynamic characteristics that act as vibration transfer channels. In the previous study, a finite element model has been created for a car body-in-white available in Automotive Laboratory (Mechanical Engineering Department, Middle East Technical University, Ankara) and its natural frequencies and mode shapes have been determined using finite element analysis software. In this study, vibration tests have been performed on actual car body-in-white. Frequency response functions between 34 response locations and force application point have been measured. Using these frequency response functions, natural frequencies and mode shapes of the body-in-white have been determined. Finite element analysis and experimental results have been compared to evaluate the finite element model reliability.

Determinar as forças que estão agindo em um dado sistema é uma questão frequente em dinâmica estrutural, de modo que a reconstrução ou a identificação de carregamento se torna um importante problema de engenharia. Quando um sistema é exposto a um carregamento desconhecido e/ou não se é possível medir diretamente a força atuante nesse sistema, se torna necessária a utilização de métodos inversos. Esta metodologia consiste essencialmente na aplicação de cargas dinâmicas pontuais nos modelos de estudo e posterior recuperação de estimativas dessas cargas nos pontos de interesse. Na prática, há situações em que o número de pontos de interesse diferem do número de pontos testados, sendo assim, a matriz da função de resposta de freqüência (FRF) do sistema resulta retangular, fazendo-se necessário o uso da pseudo-inversa de Moore-Penrose. No presente trabalho, essa metodologia é aplicada a modelos númericos a fim de testar sua eficácia. Os resultados dos processos de reconstrução de carregamento dinâmico utilizando a presente metodologia foram obtidos a partir de aplicações analíticas e numéricas. Além disso, diretrizes para utilização da pseudo-inversa de Moore-Penrose na reconstrução de carregamento dinâmico são apresentadas ao final deste trabalho. / Determining the forces acting on a given system is a frequent issue in structural dynamics, so that load reconstruction or load identification becomes an important engineering problem. When a system is exposed to an unknown load and/or if it is not possible to directly measure the force acting on that system, it is necessary to use inverse methods. This methodology consists essentially in the application of punctuals dynamics load in the study models and later recovery of estimates of these loads at points of interest. In practice, there are situations where the number of points of interest differ from the number of points tested, so the matrix of the frequency response function (FRF) of the system is rectangular, making it necessary to use the pseudo-inverse of Moore-Penrose. In the present work, this methodology is applied to numerical models in order to test their effectiveness. The results of the dynamic load reconstruction processes using the present methodology were obtained from analytical and numerical applications. In addition, guidelines for using Moore-Penrose pseudo-inverse in the dynamic load reconstruction are presented at the end of this work.

Made available in DSpace on 2015-05-08T14:59:36Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1565570 bytes, checksum: 641bee91a3e1ec7240272fff8310ca82 (MD5) Previous issue date: 2006-11-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work it is discussed the improvement in the modal test for obtaining the Frequency Response Function (FRF) in low natural frequency structures by using as exciter an instrumented hammer. There are two conflicting needs in this kind of test: on the one hand, the low natural frequencies of the structure, which are usually associated with low damping, demand long acquisition time so that good resolution in the spectrum may exist. On the other hand, the sampling rate must be increased to correctly catch the short duration signal of the hammer. This leads to an elevated number of points in the signal to be acquired, and there may eventually be limitation on such number of points when using spectrum analyzers in the acquisition and obtaining of the FRFs. Thus, in this work, the selective decimation technique explored for the improvement of the test. The work includes the construction of a prototype with two degrees of freedom (S2GL) to serve as case study for the tests enabling the theoretical and experimental Frequency Response Functions (FRF) to be compared, as well as adjusting the parameters of the model. The MATLAB programming language was used for obtaining the FRFs. The efficiency of the improvement applied was verified through the frequency spectra, in which it was observed significant resemblance between the non-decimated FRF with the acquisition having a high number of points, and the decimated FRF with smaller number of points and selected so that it could preserve the correct detection of the hammer signal. / Neste trabalho discute-se o aprimoramento do teste modal para obtenção da Função Resposta em Freqüência (FRF) em estruturas de baixas freqüências naturais utilizando como excitador um martelo instrumentado. Há duas necessidades conflitantes neste tipo de teste: de um lado, as baixas freqüências naturais da estrutura, usualmente associadas com baixo amortecimento, requerem um tempo longo de aquisição para haver boa resolução no espectro. Por outro lado, a taxa de amostragem deve ser elevada para captar corretamente o sinal de curta duração do martelo. Isto leva a um número elevado de pontos no sinal a ser adquirido, havendo eventualmente limitação de tal número de pontos ao se utilizar analisadores de espectro na aquisição e obtenção das FRFs. Neste sentido, neste trabalho foi explorada a técnica de decimação seletiva para aprimoramento do teste. O trabalho inclui a construção de um protótipo com dois Graus de Liberdade (S2GL) para servir como objeto de estudo para os testes deste aprimoramento, permitindo assim, comparar as Funções Resposta em Freqüências (FRF) teóricas e experimentais, bem como ajustar os parâmetros do modelo. Utilizou-se da linguagem de programação MATLAB® para a obtenção das FRFs. A eficiência do aprimoramento empregado foi verificada através dos espectros de freqüência, onde observou-se uma significativa similaridade entre a FRF não decimada com a aquisição possuindo um número elevado de pontos e a FRF decimada com menor número de pontos e selecionada de modo a preservar a correta detecção do sinal do martelo.

Determinar as forças que estão agindo em um dado sistema é uma questão frequente em dinâmica estrutural, de modo que a reconstrução ou a identificação de carregamento se torna um importante problema de engenharia. Quando um sistema é exposto a um carregamento desconhecido e/ou não se é possível medir diretamente a força atuante nesse sistema, se torna necessária a utilização de métodos inversos. Esta metodologia consiste essencialmente na aplicação de cargas dinâmicas pontuais nos modelos de estudo e posterior recuperação de estimativas dessas cargas nos pontos de interesse. Na prática, há situações em que o número de pontos de interesse diferem do número de pontos testados, sendo assim, a matriz da função de resposta de freqüência (FRF) do sistema resulta retangular, fazendo-se necessário o uso da pseudo-inversa de Moore-Penrose. No presente trabalho, essa metodologia é aplicada a modelos númericos a fim de testar sua eficácia. Os resultados dos processos de reconstrução de carregamento dinâmico utilizando a presente metodologia foram obtidos a partir de aplicações analíticas e numéricas. Além disso, diretrizes para utilização da pseudo-inversa de Moore-Penrose na reconstrução de carregamento dinâmico são apresentadas ao final deste trabalho. / Determining the forces acting on a given system is a frequent issue in structural dynamics, so that load reconstruction or load identification becomes an important engineering problem. When a system is exposed to an unknown load and/or if it is not possible to directly measure the force acting on that system, it is necessary to use inverse methods. This methodology consists essentially in the application of punctuals dynamics load in the study models and later recovery of estimates of these loads at points of interest. In practice, there are situations where the number of points of interest differ from the number of points tested, so the matrix of the frequency response function (FRF) of the system is rectangular, making it necessary to use the pseudo-inverse of Moore-Penrose. In the present work, this methodology is applied to numerical models in order to test their effectiveness. The results of the dynamic load reconstruction processes using the present methodology were obtained from analytical and numerical applications. In addition, guidelines for using Moore-Penrose pseudo-inverse in the dynamic load reconstruction are presented at the end of this work.