Made available in DSpace on 2014-06-11T19:27:14Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-07-30Bitstream added on 2014-06-13T19:55:34Z : No. of bitstreams: 1 freitas_tc_me_ilha.pdf: 1484818 bytes, checksum: 9f0ca1d5825d93918e44fc9b31aae513 (MD5) / Agência Nacional de Energia Elétrica (ANEEL) / Este trabalho apresenta o estudo, a implementação e a aplicação de duas técnicas de identificação de parâmetros modais utilizando apenas as respostas da estrutura, denominadas: Identificação Estocástica de Subespaço (IES) e Decomposição no Domínio da Freqüência (DDF). A IES é baseada na Decomposição em Valores Singulares (DVS) da projeção ortogonal do espaço das linhas das saídas futuras no espaço das linhas das saídas passadas. Uma vez realizada a DVS da projeção ortogonal é possível obter o modelo de espaço de estado da estrutura e os parâmetros modais são estimados diretamente através da decomposição em autovalores e autovetores da matriz dinâmica. A DDF é baseada na DVS da matriz de densidade espectral de potência de saída nas linhas de freqüências correspondentes a região em torno de um modo. O primeiro vetor singular obtido para cada linha de freqüência contém as respectivas informações daquele modo e os correspondentes valores singulares levam a função densidade espectral de um sistema equivalente de um grau de liberdade (1GL), permitindo a obtenção dos parâmetros do respectivo modo. Os métodos são avaliados utilizando dados simulados e experimentais. Os resultados mostram que as técnicas implementadas são capazes de estimar os parâmetros modais de estruturas utilizando apenas as respostas. / This work presents the study, implementation and application of the two techniques for the modal parameters identification using only response data: Stochastic Subspace Identification (SSI) and Frequency Domain Decomposition (FDD). The SSI is based on Singular Value Decomposition (SVD) of the orthogonal projection of the future output row space in the past output row space. After the completion of the SVD of the orthogonal projection, is possible to get the state space model of the structure and the modal parameters are estimated directly through the eigenvalues and eigenvectors decomposition of the dynamic matrix. The FDD is based on the SVD of the output power spectral density matrix in the frequencies lines around a mode. The first singular vector obtained for each frequency line contains the respective information about this mode and the corresponding spectral density function leads to an equivalent system of one degree of freedom (1 DOF), allowing the calculation of the parameters of the mode. The methods are evaluated using simulated and experimental data. The results show that the techniques implemented are capable to estimate the modal parameters of structures using only response data.

Este trabalho realiza uma investigação sobre técnicas experimentais para a determinação de Funções de Resposta em Freqüência (FRFs) angulares com aplicações em estruturas do tipo viga. Estas FRFs são definidas considerando-se como variável de saída o movimento angular (deslocamento, velocidade ou aceleração) exibido pela estrutura sob estudo quando a mesma é excitada por uma força linear ou um momento puro. Dada a grande dificuldade em se aplicar um momento puro à estrutura sob estudo, este trabalho utiliza como forma de excitação apenas esforços lineares que podem ser aplicados através de técnicas usuais de excitação em análise modal, tais como o excitador eletrodinâmico e o martelo impulsivo. Portanto as FRFs obtidas descrevem relações de saída e entrada do tipo Angular/Linear. Uma das técnicas utilizadas na determinação das FRFs angulares consiste na excitação de uma estrutura com um excitador eletrodinâmico e utilização de um corpo rígido na forma de um bloco T que é montado sobre a estrutura sob estudo. Dois acelerômetros lineares devem ser montados sobre o bloco T e a partir das duas acelerações lineares medidas buscam-se estimar um sinal proporcional à aceleração angular da estrutura no ponto de conexão. Outra técnica utiliza uma formulação via diferenças finitas, onde dois ou três acelerômetros (de acordo com a formulação de diferenças finitas utilizada) igualmente espaçados são montados diretamente sobre a estrutura sob estudo e são usados para se derivar à aceleração angular. Os resultados obtidos a partir destas técnicas são comparados com resultados obtidos a partir da utilização de um acelerômetro angular piezelétrico recentemente disponível no mercado. Também foram desenvolvidos modelos analíticos e computacionais via método dos elementos finitos a fim de se gerar subsídios adicionais para a análise dos resultados. Foram feitas várias constatações e dentre elas destacam-se resultados onde as FRFs angulares/lineares resultantes podem sofrer alterações significativas dependendo de como os dados experimentais são processados. / The present work aims to perform an investigation on experimental techniques for the determination of angular Frequency Response Functions (FRFs) in Modal Testing. Angular FRFs are those where the output variable is given by angular displacement, velocity or acceleration, whereas the input is given in terms of linear or angular quantities (a pure moment). Since the application of a pure moment as an excitation source still remains as a challenge, this work is focused in studying techniques to estimate angular/linear types of angular FRFs. One of these techniques consists of exciting the structure with a shaker and using a rigid T-block to measure the linear accelerations and then calculating the angular FRFs from these linear accelerations. Another technique employs finite differences formulations to get the angular motions. This technique uses the closely spaced accelerometers mounted directly to the structure under test, where at least two (according to the finite difference formula employed) accelerometers are used. The translational measurements are gathered and finite difference formulas are used to derive the necessary angular quantities. Additional tests are performed with an angular piezoelectric accelerometer recently available in the market in order to provide a comparison basis for the results obtained using the two techniques. The results are also compared whit theoretical models developed using analytical and Finite Element Formulations. Among all results obtained, it was understood that depending on the level of angular vibrations exhibited by the structure, and how the signals are processed, the resulting angular FRFs can suffer some significant changes

A análise dinâmica experimental tem sido amplamente pesquisada como uma ferramenta de avaliação de integridade de estruturas de concreto armado. Existem técnicas de identificação de danos baseadas em propriedades modais como frequências de ressonâncias, deformadas modais, curvaturas modais e amortecimento. Há também técnicas baseadas na não linearidade da resposta dinâmica, que apesar do grande potencial na detecção de danos, têm sido pouco exploradas nos últimos anos. Este trabalho tem por objetivo avaliar a integridade estrutural de vigas de concreto armado através do comportamento da resposta dinâmica. Foram realizados ensaios dinâmicos em duas vigas de concreto armado com 3,5 m de comprimento, 25 cm de largura, 35 cm de altura e idênticas taxas de armaduras, mas configuradas com barras de aço de diferentes diâmetros, 2 &#981 16 mm e 8 &#981 8 mm, respectivamente. Tais vigas, inicialmente íntegras, foram submetidas a ciclos de carregamento e descarregamento com intensidades crescentes até atingir a ruptura do elemento. Após cada ciclo, as propriedades dinâmicas foram avaliadas experimentalmente, com o emprego de técnicas de excitação por sinais do tipo aleatório e tipo transiente, respectivamente, visando determinar parâmetros que indiquem a deterioração gradativa do elemento. Nesses ensaios dinâmicos aplicaram-se diferentes amplitudes da força de excitação. Verificou-se que o aumento da amplitude da força dinâmica de excitação provocou reduções nos valores das frequências de ressonância de 1,1% e 2,4%, associadas, respectivamente, às excitações aleatórias e transientes; e um comportamento não linear dos índices de amortecimento, associados às excitações aleatórias, mantendo um crescimento linear com as excitações transientes. Constatou-se, ainda, que os valores das frequências de ressonância decrescem com a redução de rigidez mecânica, diminuída com o aumento do nível de fissuração induzido nos modelos. Já os valores dos índices de amortecimento, após cada ciclo, se comportaram de forma não linear e assumiram diferentes valores, conforme a técnica de excitação empregada. Acredita-se que esta não linearidade está relacionada aos danos provocados no elemento pela solicitação estrutural e, por consequência, ao processo de como a dissipação de energia é empregada no processo de instauração, configuração e propagação das fissuras nos elementos de concreto armado. / The experimental dynamic analysis has been widely investigated as a tool to assess integrity of reinforced concrete structures. State-of-the-art modal-based techniques for structural damage analysis use resonance frequencies, modal deformed, curvature and modal damping analysis. There are also techniques based on nonlinear dynamic response that despite the large potential for damage detection, have not been considered in recent years. This work aims to evaluate the structural integrity of reinforced concrete beams through the dynamic response behavior. Dynamic tests were performed on two reinforced concrete beams with 3.5 meters of length, 250 mm of width, 350 mm of height and identical reinforcement rates, but different steel bars diameters, 2 &#981 16 mm e 8 &#981 8 mm, respectively. Beams were initially intact and were subjected to loading and unloading cycles with increasing intensity until the rupture of the concrete beam. After each cycle, the dynamic properties were evaluated experimentally with random and transient excitation signals to determine parameters that indicate gradual deterioration of the beam. Different amplitudes of the excitation force were applied during dynamic testing of concrete beams. These results indicated that an increase in amplitude of dynamic excitation force caused reductions in frequency resonances by 1.1% and 2.4%, associated with the random and transient excitations, respectively. Furthermore, a non-linear behavior of the damping ratios related to random excitations was observed while a linear relationship with transient excitation was found. Moreover, it was found that the resonance frequency decreased with the cracking-related reduction of beam stiffness, caused by increasing level of loading. Additionally, the values of the damping ratios after each cycle behaved non-linearly assuming different values according to the used excitation technique. It is believed that this non-linearity can be related to the loading-related structural damage of the reinforced concrete beam. Therefore, the energy dissipation related to cracking initiation, configuration and propagation in reinforced concrete elements played an important role in the damping ratios of concrete beams.

This thesis deals with a vibration diagnostics of objects, structures and machines. The theoretical part is divided into three chapters according to type of the measurement. The first part called Modal Analysis discusses the basis of vibration, methods of measurement, relevant technical equipment and principle of experimental modal analysis. The second and third chapters of the thesis are focused on the diagnosis of defects. Each chapter mentioned above describes diagnosed defects, used methods and procedure for the diagnosis. Another part of the thesis summarizes practical issues and results gained in the laboratory experiments. It begins with discovering parameters of the measured object using technical diagnostics – experimental modal analysis. In the next step the hardware concept design was created, including custom measuring application programmed in LabVIEW. One part of the design is the laboratory model which includes a structure for free mounting and a possibility of excitation by an electrodynamic exciter. The application is also modified to enable measurements with shaker excitation. Finally, applications cooperating with professional software ModalVIEW and BK Connect were developed in order to simplify the operation and increase the comfort.

This diploma thesis deals with dynamic analysis of the steam turbine blade. This blade is part of the last row of low pressure level of steam turbine. Computational analysis has been performed in first part using FEM and software ANSYS. A Transient analysis has been used to solve forced vibrations. Main goal is to obtain a behavior of main stresses and its directions as a function of loading of the blade in the crack initiation area. Second part deals contain a an experiment. Experiment has been set up to perform a modal analysis which is necessary to obtain a fundamental numbers. Then the vibration of the blade has been performed. To perform this experiment same edge conditions as which has been used during the computational analysis. Goal is the same as in the first part – obtain a behavior of main stresses and its directions as a function of loading of the blade in the crack initiation area. The comparison of results obtained during experimental analysis and computational analysis has been performed in the last part of the thesis. Also the question if any geometrical nonlinearities appeared during analyses is answered.

The master thesis deals with modal analysis of turbine wheel of aircraft engine. The first part is concerned with the modal analysis of the computational model of turbine wheel and separated turbine blade using the cyclic symmetry of the ANSYS software. This part of the thesis set the task of determining the natural frequency depending on the operating parameters of the motor. The second part of the thesis occupies with the experimental simulation of the task. The results of experimental simulation are verified and compared with the results from the computational modal analysis. The goal is to create a Campbell diagram and to determine the intervals of the critical revolution of the turbine wheel.

The aim of this diploma thesis is to determine and compare modal properties of four swirl turbine wheels, each with a different geometry. Natural frequencies and mode shapes were obtained based on computer modelling using Ansys software and they were compared with experimental modal analysis' results. The computer modelling and the experimental modal analysis were carried out for different boundary conditions and in different environments. The beginning of the thesis is dedicated to a brief overview of literature with similar issues. Then a brief introduction of a dynamics theory is mentioned in which equations of motion for a damped and an undamped single degree of freedom system are derived. The creation of a geometry model which is obtained by a reverse engineering is shown in the second part of the thesis. The geometry model was subsequently used for the computer based modelling of the modal parameters. In the third part an experimental equipment, setting, measurement and processing of data are described. The conclusion of the thesis is dedicated to the comparison of the results obtained by the experimental modal analysis and the computing modelling is presented. Moreover, influence of boundary conditions and influence of the environment on the natural frequencies are evaluated.

The aim of this diploma thesis is a creation of modal parameter estimation application. Modal properties (natural frequencies, damping factors and mode shapes) are used in many dynamics analysis and their accurate determination is very important therefore the modal parameter estimation is one of the most significant part of the experimental modal analysis. Many methods have been developed for modal parameter estimation, each of them with different assumptions and with different accuracy. In the beginning of this thesis, a theory connected with modal analysis and a theory which is necessary for understanding to presented modal parameter methods are given. Then four different modal parameter estimation methods are presented - Peak Picking, Circle Fit, Least Square method and Eigensystem Realization Algorithm. The application for the modal parameter estimation is the output of this diploma thesis. In addition, the application allows performing all experimental modal analysis such as estimation of frequency response functions, animation of the found mode shapes, different kinds of comparison etc. In the conclusion, three structures are shown on which the application and modal parameter estimation methods were tested.

Cieľom tejto diplomovej práce je predstavenie Experimentálnej modálnej analýzy a štúdium a použitie algoritmov pre výpočet modálnych parametrov z odmeraných vibrácií pri Experimentálnej modálnej analýze. Bodom záujmu sú predovšetkým algoritmy, pracujúce s odmeranými dátami v časovej oblasti. Diplomová práca sa zaoberá programovaním algoritmu ITD a jeho implementáciou pre Experimentálnu modálnu analýzu. Ďaľšou časťou práce je štúdium citlivosti algoritmu na okrajové podmienky meranej sústavy pri výpočte modálnych parametrov a štúdium možnosti využitia algoritmu pri Operačnej modálnej analýze.

Existing methods of evaluating the structural system of a building after a seismic event consist of removing architectural elements such as drywall, cladding, insulation, and fireproofing. This method is destructive and costly in terms of downtime and repairs. This research focuses on removing the guesswork by using forced vibration testing (FVT) to experimentally determine the health of a building. The experimental structure is a one-story, steel, bridge-like structure with removable braces. An engaged brace represents a nominal and undamaged condition; a dis-engaged brace represents a brace that has ruptured thus changing the stiffness of the building. By testing a variety of brace configurations, a set of experimental data is collected that represents potential damage to the building after an earthquake. Additionally, several unknown parameters of the building’s substructure, lateral-force-resisting-system, and roof diaphragm are determined through FVT. A suite of computer models with different levels of damage are then developed. A quantitative analysis procedure compares experimental results to the computer models. Models that show high levels of correlation to experimental brace configurations identify the extent of damage in the experimental structure. No testing or instrumentation of the building is necessary before an earthquake to identify if, and where, damage has occurred.