Este trabalho apresenta o desenvolvimento de uma metodologia para a estimativa de funções de resposta em freqüência angulares (FRFAs). Trata-se de uma técnica que utiliza transdutores piezelétricos (PZT) do tipo bimorph para a medição da curvatura local da estrutura através do potencial elétrico induzido pela extensão e compressão do sensor. A partir da estimativa da curvatura, a rotação pode ser obtida diretamente através de várias técnicas de interpolação (polinomial, formas modais, etc). Apresenta-se a modelagem téorica da qual se deriva as equações que governam a dinâmica de estruturas uni-dimensionais, do tipo viga, e estruturas bidimensionais, do tipo placa, ambas isotrópicas, onde se incorpora o sensor bimorph. Modelos em elementos finitos foram propostos no intuito de avaliar a utilização destes sensores (bimorphs) aplicados à estimativa das FRFAs. Apresentam-se também resultados numéricos e experimentais considerando-se uma viga engastada-livre (cantilever) e resultados numéricos considerando-se uma placa simplesmente apoiada. Um algoritmo genético foi ainda desenvolvido no intuito de determinar a posição e dimensão ótimas dos bimorphs em estruturas do tipo viga. / The present work aims to perform the development of an attractive approach for accurate measurement of angular frequency response functions (AFRFs). It uses bimorph piezoceramic patches to measure the structure\'s local curvature through the measurement of the electric potential induced by the extension and compression of the patch\'s top and bottom stripes, respectively. From this curvature, rotation can be obtained directly by several interpolation techniques (single polynomial, modes basis). Theoretical modeling of the vibration incorporating piezoelectric bimorph sensor is presented and equations governing the dynamics for one-dimensional structures, like a beam, and for two-dimensional structures, like a plate, are derived for isotropic structures. Finite element model for the dynamic analysis were proposed to evaluate bimorphs patches applied to the measurement of angular FRFs. Numerical and experimental results are presented considering a cantilever beam and numerical results for a simply supported plate as tested structured. Also, in this work, a genetic algorithm was used as an adaptive heuristic search algorithm for optimal placement and sizing of the bimorph sensor into beam like structures.

Este trabalho apresenta o desenvolvimento de uma metodologia para a estimativa de funções de resposta em freqüência angulares (FRFAs). Trata-se de uma técnica que utiliza transdutores piezelétricos (PZT) do tipo bimorph para a medição da curvatura local da estrutura através do potencial elétrico induzido pela extensão e compressão do sensor. A partir da estimativa da curvatura, a rotação pode ser obtida diretamente através de várias técnicas de interpolação (polinomial, formas modais, etc). Apresenta-se a modelagem téorica da qual se deriva as equações que governam a dinâmica de estruturas uni-dimensionais, do tipo viga, e estruturas bidimensionais, do tipo placa, ambas isotrópicas, onde se incorpora o sensor bimorph. Modelos em elementos finitos foram propostos no intuito de avaliar a utilização destes sensores (bimorphs) aplicados à estimativa das FRFAs. Apresentam-se também resultados numéricos e experimentais considerando-se uma viga engastada-livre (cantilever) e resultados numéricos considerando-se uma placa simplesmente apoiada. Um algoritmo genético foi ainda desenvolvido no intuito de determinar a posição e dimensão ótimas dos bimorphs em estruturas do tipo viga. / The present work aims to perform the development of an attractive approach for accurate measurement of angular frequency response functions (AFRFs). It uses bimorph piezoceramic patches to measure the structure\'s local curvature through the measurement of the electric potential induced by the extension and compression of the patch\'s top and bottom stripes, respectively. From this curvature, rotation can be obtained directly by several interpolation techniques (single polynomial, modes basis). Theoretical modeling of the vibration incorporating piezoelectric bimorph sensor is presented and equations governing the dynamics for one-dimensional structures, like a beam, and for two-dimensional structures, like a plate, are derived for isotropic structures. Finite element model for the dynamic analysis were proposed to evaluate bimorphs patches applied to the measurement of angular FRFs. Numerical and experimental results are presented considering a cantilever beam and numerical results for a simply supported plate as tested structured. Also, in this work, a genetic algorithm was used as an adaptive heuristic search algorithm for optimal placement and sizing of the bimorph sensor into beam like structures.

Noise, vibration and harshness (NVH)levels in the luxury automotive industry are used by customers as a subjective method of determining the vehicle quality. This can be achieved by adjusting the vehicle design, where simulations are used to predict the NVH behaviour. Changes can be expensive and time consuming when made after the design stage has been completed, so it is important to produce accurate simulations of the product. Variability exists to some extent in all products, even those just off the production line, however, if a high level of variability exists then only a small portion of products will meet the predicted behaviour. The aim of the project is to provide information that may lead to the reduction of variability in an automotive vehicle. This is achieved by quantifying the statistical spread of FRFs (frequency response function) in a set of nominally identical vehicles. Once overall levels have been calculated, the location of the most variable sources can be identified. Project also seeks to develop new methods of analysis for the system phase response to determine whether further information may be extracted compared to the magnitude response. There are three main themes that run throughout this thesis, with the first being the quantification of variability due to the measurement taking process which is covered in chapter 3. A novel application of a method to separate the measurement variability from the overall system uncertainty was achieved as well as the quantification of the vehicle to- vehicle variability. The second theme that runs through the study concerns the identification of variability sources. This is realised in chapter 4 and chapter 6 as a set of structural and acoustic tests on a luxury sedan door. The trim was found to be held to the door panel by a series of 11 polymer clips and 4 metal screws. The variability of small changes to a significant boundary condition at the door trim was quantified, showing that the removal of rigid clips had a more significant effect on the overall variability that if a loose clip has been removed. It was also found that clips at the corners were the most sensitive to change. The final theme outlines and tests new analysis methods on the phase and compares the statistical spread of the phase with the equivalent spread of the magnitude. Data taken from the same tests was used and for most of the cases the two results were found to be approximately the same.

A limited and extendable master thesis is representing the first step in the experimental substructuring of an A600 wind turbine. Additional masses have been designed, manufactured and added to the sub components for the laboratory experimental tests. Further preparations for dynamic experimental tests have been described and implemented. Vibrational tests of a modified wind turbine blade have been made using the Leuven Measurements System (LMS) for excitations and data acquisition purposes. The theory of frequency response function based substructuring applied on the wind turbine blade model is demonstrated. The theory and an example of a Matlab coded spring-mass system, an experimental model of a wind turbine blade and FRFs stemming from measurements are reported.

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En önskan om en enad internationell uppsättning av redovisningsstandarder har uppkommit på senare tid på grund av globaliseringen. FASB har i ett försök att närma sig IASB regelverk implementerat mer principer i US GAAP medan IASB har implementerat fler regler i IFRS. Trenden pekar mot harmoniseringen för att lyckas med en enad internationell uppsättning redovisningsstandarder. Globaliseringen påverkar inte enbart börsnoterade företag utan även små och medelstora företag (SME). Arbetet för harmonisering av små och medelstora företags (SME) regelverk har dock inte berörts i lika stor grad. Studiens syfte är att undersöka till vilken grad regelverken IFRS for SME, FRS 102 och FRF for SME är princip- eller regelbaserade gentemot varandra samt att utreda till vilken grad dessa är harmoniserade med varandra.För att uppfylla syftet har en kvalitativ studie utförs med hjälp av en innehållsanalys. Kvalitativ data används i uppbyggnad av den teoretiska referensramen med skriftliga källor i form av vetenskapliga artiklar. Empirin består av delar ur lagtexter av regelverken IFRS for SME, FRS 102 och FRF for SME som analyseras med utgångspunkt i den teoretiska referensramen.Det vi kom fram till var att IFRS for SME och FRS 102 är principbaserade regelverk medan FRF for SME är ett regelbaserat regelverk. När de sedan ställdes emot varandra betraktas FRS 102 precis som IFRS for SME som ett principbaserat regelverk men till en större grad. IFRS for SME och FRS 102 bedöms således som harmoniserade. FRF for SME anser vi å andra sidan vara ett regelbaserat regelverk och när det ställs emot IFRS for SME och FRS 102 anses det därmed svagt regelbaserade. Vi kan följaktligen inte betrakta FRS for SME som harmoniserade med varken IFRS for SME eller FRS 102.Vår studie bidrar därmed till litteratur om harmoniseringen av SME företag samt till IFRS for SME, FRS 102 och FRF for SME är huvudsakligen princip- eller regelbaserad. Dessutom görs en reflektion över om den enda aspekten med redovisningen är jämförbarhet då är det optimala läget för harmonisering när regelverken är stark regelbaserade. / AbstractA desire for a united international set of accounting standards has arisen in recent times due to globalization. FASB has in an attempt to approach the IASB regulations implemented more principles in US GAAP, while the IASB has implemented more rules in IFRS. The trend is pointing towards harmonization to succeed in the desire for an united international set of accounting standards. Globalisation does not only affect listed companies but also small and medium-sized enterprises (SMEs). Harmonisation of these small and medium-sized enterprises (SMEs) framework have not been written about to the same degree as the listed companies. The study aims to examine to which extent regulations IFRS for SME, FRS 102 and FRF for SME's are principle or rule-based to one another. The second purpose of the study is to investigate the degree to which these are harmonized with each other.A qualitative study with a content analyse have been conducted to fulfill the purpose of the study. Qualitative data is used in the construction of the theoretical framework in form of written sources such as scientific articles. The empirical data is also of qualitative character and consists of parts of the legal texts of the regulations IFRS for SME, FRS 102 and FRF for SMEs. The empirical data is analyzed on the basis of the theoretical framework.The conclusion was that IFRS for SME and FRS 102 are principle-based frameworks while FRF for SMEs is a rules-based framework. When they were facing each other FRS 102 was considered as a principle-based regulations but to a greater degree then IFRS for SME. IFRS for SME and FRS 102 is consequently considered harmonized. FRF for SMEs on the other hand is a rules-based framework and when it is set against the IFRS for SME and FRS 102 it is considered weak rule-based. We cannot therefore regard FRS for SMEs harmonized with either IFRS for SMEs or FRS 102.Our study contributes to the literature on the harmonization of SME companies, and whether the IFRS for SME, FRS 102 and FRF for SMEs are mainly principle- or rulebased. In addition, a reflection on if the only aspect of the financial report is comparability then optimal framework for harmonization are one that is strong rulebased.

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

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

Ce travail de thèse propose une approche dynamique pour les structures périodiques et l'application à la modélisation d'un pneumatique. Les propriétés statiques et dynamiques des matériaux constituants du pneu sont mesurées. Des modèles spécifiques d'homogénéisation sont aussi utilisés pour déterminer les caractéristiques équivalentes. Les fonctions de réponse en fréquence sont mesurées à plusieurs endroits sur le pneumatique dans les deux cas de force d'excitation : sur la bande de roulement et sur le flanc. La théorie dynamique utilisant la périodicité des structures est présentée. On propose une transformation en repère cartésien pour les structures ayant la périodicité dans un repère non-cartésien. L'utilisation de cette transformation dans le pneumatique assure les conditions de périodicité dans l'exploitation des matrices des cellules. Les mobilités à plusieurs points du pneu sont calculées et comparées avec les mesures. Ce travail permet d'une part l'étude dynamique d'un pneumatique à haute fréquence et d'autre part l'étude paramétrique de l'influence des propriétés de matériaux et de la pression interne dans le pneu.

In recent years more emphasis has been placed on in-situ condition based monitoring of engineering systems and structures. Aerospace components are manufactured from composite materials more often. Structural health monitoring (SHM) systems are required in the aerospace industry to monitor the safety and integrity of the structure and will ensure that composites reach its full potential within the industry. Damage detection techniques form an integral part of such SHM systems. With this work a damage detection technique is developed for intended eventual use on composite structures, but starting first on isotropic structures. The damage mechanism that is of interest is delamination damage in composites. A simple numerical equivalent is implemented here however. Two damage indicators, the strain cumulative damage factor (SCDF) and the strain-frequency damage level (SFDL) are introduced. The respective damage indicators are calculated from output-only strain and acceleration response data. The effectiveness of the system to detect damage in the structure is critically evaluated and compared to other damage detection techniques such as the natural frequency method. The sensitivity to damage and performance of both these indicators is examined numerically by evaluating two deterministic damage cases. The numerical study is enhanced through the use of an updated finite element model. The minimum number of sensors capable of detecting the presence and locate damage spatially is determined from numerical simulations. Monte Carlo type analysis is performed by letting the damaged area vary stochastically and calculating the respective damage indicators. The model updating procedure from measured mobility frequency response functions (FRFs) is described. The application of the technique to real structures is examined experimentally. Two test structures with two different damage scenarios are examined. The spatial location and presence of damage can be established from both the SCDF and SFDL values, respectively. The spatial location obtained from the SCDF values corresponded to the known damage location for both the numerical and experimental study. The SFDL proved to be more sensitive than the natural frequency method and could be used to calculate the level of damage within the structure. / Dissertation (MEng)--University of Pretoria, 2009. / Mechanical and Aeronautical Engineering / unrestricted