This diploma thesis deals with the issue of operational modal analysis, which is one of the newer areas of structural dynamics that makes it possible to estimate modal properties of structures directly during their operation. The aim of this work is to create theoretical basis of operational modal analysis, more specifically of Frequeny Domain Decomposition method. Furthermore, apply this method to a selected structure and verify the achieved results using computational modelling and experimental modal analysis. The technique of dividing the experiment to separate measurements using reference sensor was used. Evaluation of the operational modal analysis was performed using self-created function for the MATLAB software and using the commercial PULSE Operational Modal Analysis software. Obtained results were verified by computational modelling and experimental modal analysis.

In one of the first hours of study at the Institute of Mechanics of Bodies, Mechatronics and Biomechanics, the author of this work received three basic recommendations regarding measurement: 1) Do not measure! 2) If you measure, do not repeat the measurement!! 3) If you repeat the measurement, do not compare the measurements!!! However, this thesis boldly violates all three recommendations. In the introductory theoretical part, it briefly introduces the vibration of multi-degree of freedom damped systems and describes experimental ways of determining the modal damping. It also summarizes the Operational Modal Analysis (OMA) approach, explains the principle of the FDD method, and introduces EFDD (Enhanced Frequency Domain Decomposition) method which allows to determine not only natural frequencies and shapes as FDD does, but also modal damping of the shapes. A script in Matlab environment for processing vibrations using EFDD method is one of the thesis outputs. The script is first tested by computational model, where a model system with known damping is tested and damping is determined by the script. Subsequently, the work moves to the actual measurement of the real system - a bonded bar which is analysed by Experimental Modal Analysis and OMA, while the second variant uses commercial EFDD method (Brüel a Kjr company) and programmed script. In the conclusion of the thesis the damping results are compared to each other. The diploma thesis continues in Ing. M. Pop’s thesis – Modal Analysis Experimental Method Verification. From this work a part of measured data is taken. Specific cases of data use are always listed in the appropriate section of the text.

Modal analysis of printed circuit board results, gained from computional and experimental modeling, have been compared. Anylyses have been performed on dummy boards (models without electronic components), created as one-layered at first, then as three-layered PCB. Board is usually clamped by its longer edges with wedgelock. In order to enable the realization of boundary conditions in computional and experimental modeling, real clamping has been simplified to simply supported. Computional models have used FEM elements, which are comomnly used in this type of problem. Determined results have been evaluated by comparing the experimental modeling results. Models‘ sensitivity on modification of element length and number of elements through thickness have been performed.

This thesis highlights one of the most significant concerns that has preoccupied drivetrain engineers in recent times, namely drivetrain clonk. Clonk is an unacceptable audible sound, which is accompanied by a tactile drivetrain response. This may occur under several different driving conditions. Many drivetrain NVH concerns are related to impact loading of subsystems down-line of engine. These concerns are induced by power torque surge through engagement and disengagement processes, which may propagate through various transmission paths as structural waves. The coincidence of these waves with the acoustic modes of sub-system components leads to audible responses, referred to as clonk. The approach usually undertaken and reported in literature is either purely theoretical or constitutes experimental observation of vehicle conditions. A few research workers have reported rig-based investigations, but not under fully dynamic conditions with controlled and reproducible impulsive action. The research reported in this thesis combines experimental and numerical investigation of high frequency behaviour of light truck drivetrain systems, when subjected to sudden impulsive action, due to driver behaviour. The problem is treated as a multi-physics interactive phenomenon under transient conditions. The devised numerical method combines multi-body dynamics, structural modal analysis, impact dynamics in lash zones and acoustic analysis within an overall investigation framework. A representative drivetrain system rig is designed and implemented, and controlled tests simulating driver behaviour undertaken. The combined numerical predictions and experimental noise and vibration monitoring has highlighted the fundamental aspects of drivetrain behaviour. Good agreement is' also found between the detailed numerical approach and the experimental findings. Novel methods of measurement such as Laser Doppler Vibrometery have been employed. Simultaneous measurements of vibration and noise radiation confirm significant elasto-acoustic coupling at high impact energy levels. One of the major finds of the thesis is the complex nature of the clonk signal, being a combination of accelerative and ringing noise, with the latter also comprising of many other lower energy content as observed in the case of transmission rattle and bearing-induced responses. Therefore, the link between rattle and clonk, long suspected, but not hitherto shown has been confirmed in the thesis. Another major find of particular commercial interest is the insignificant contribution of torsional damping devices such as dual mass flywheels upon the accelerative component of the clonk response.

Aero-engine assemblies are complex structures typically involving two or three nested rotors mounted within a flexible casing via squeeze-film damper (SFD) bearings. The deployment of SFDs into such structures is highly cost-effective but requires careful calculation since they can be highly nonlinear in their performance, particularly if they are unsupported (i.e. without a retainer spring). The direct study of whole-engine models with nonlinear bearings has been severely limited by the fact that current nonlinear computational techniques are not well-suited for complex large-order systems. The main contributions of this thesis are: • A procedure for unbalance response computation, suitable for generic whole-engine models with nonlinear bearings, which significantly extends the capability of current finite element packages. This comprises two novel nonlinear computational techniques: an implicit time domain integator referred to as the Impulsive Receptance Method (IRM) that enables rapid computation in the time domain; a whole-engine Receptance Harmonic Balance Method (RHBM) for rapid calculation of the periodic response in the frequency domain. Both methods use modal data calculated from a one-off analysis of the linear part of the engine at zero speed.• First-ever analyses on real twin-spool and three-spool engines. These studies illustrate the practical use of these solvers, provide an insight into the nonlinear dynamics of whole-engines and correlate with a limited amount of industrial experimental data. Both IRM and RHBM are directly formulated in terms of the relative response at the terminals of the nonlinear bearings. This makes them practically immune to the number of modes that need to be included, which runs into several hundreds for a typical engine. The two solvers are extensively tested on two/three-shaft engine models (with 5-6 SFDs) provided by a leading engine manufacturer using an SFD model that is used in industry. The tests show the IRM to be many times faster than an established robust conventional implicit integrator while achieving a similar level of accuracy. It is also shown to be more reliable than another popular implicit algorithm. The RHBM enables, for the first time, the frequency domain computation of the nonlinear response of whole-engine models. Its use is illustrated for both Single-Frequency Unbalance (SFU) excitation (unbalance confined to only one shaft) and Multi-Frequency Unbalance (MFU) excitation (unbalance located on two or more shafts, rotating at different speeds). Excellent correlation is demonstrated between RHBM and IRM.The parametric studies compare and contrast the frequency spectra for SFU and MFU cases. They also reveal the varying degree of lift at the unsupported SFDs. The sensitivity of the response to end-sealing and bearing housing alignment is also illustrated. It is demonstrated that the use of suitably preloaded vertically oriented “bump-springs” at the SFDs of heavy rotors produces a significant improvement in journal lift. It is also shown that the consideration of a slight amount of distributed damping in the structure significantly affects the predicted casing vibration levels, bringing them closer to measured levels, while having little effect on the SFD orbits.

Ce travail de thèse porte sur l'élaboration d'un matériau composite à matrice thermodurcissable incorporant des renforts nanométriques et/ou une phase élastomère, permettant d'améliorersa rigidité, son amortissement et sa résilience. Pour cela, nous avons réalisé des formulations baséessur des matrices époxyvinylester, renforcées ou non par une phase élastomère et chargées de montmorillonite ou de sépiolite. Nous avons étudié leurs propriétés visco-élastiques par analyse modaleexpérimentale et leurs propriétés à l'impact par des essais d'impact par chute de masse. Nous avonsdéterminé la microstructure des composites fabriqués en nous appuyant sur la diffraction des rayonsX et des observations en microscopie électronique. Des modèles d'homogénéisation, fondés sur lemodèle de H ALPIN -T SAI et adaptés aux matériaux composites étudiés, ont été développés afin dedisposer d'un outil permettant de relier explicitement la rigidité des composites à leur morphologie.Une analyse paramétrique approfondie a permis de déterminer les caractères morphologiques lesplus influents et d'évaluer la performance des procédés de mise en œuvre au regard des renforcements mécaniques obtenus. Expérimentalement, l'incorporation de montmorillonite ou de sépiolite a conduit à une augmentation significative du module élastique et la présence d'une phase élastomère dans la résine a permis de doubler l'amortissement et d'augmenter la résilience. Finalement, les formulations les plus performantes ont été retenues pour la fabrication de composites renforcés de fibres de verre. L'amélioration des propriétés mécaniques se retrouve, dans une moindre mesure, dans lesprototypes réalisés. La pertinence de l'utilisation de ces matériaux à l'échelle industrielle a été évaluée. / This thesis focuses on the development of a thermosetting matrix composite incorporating nanoscale reinforcements and/or an elatomeric phase to improve its stiffness, damping and resilience.To do so, we made formulations based on epoxy vinyl ester matrices, filled or not by an elastomeric phase, and reinforced with montmorillonite or sepiolite. Their viscoelastic properties were studied usingexperimental modal analysis and their impact properties were investigated using drop weight impacttesting. The microstructure of these composites was examined using X-ray diffraction and electronmicroscopy observations.Homogenization models based on H ALPIN -T SAI model and adapted to the studied composites were developed to provide a tool able to explicitly link the stiffness of the material to its morphology.A detailed parametric analysis allowed to determine the most influential morphological characteristics and to assess the efficiency of the process regarding the mechanical stiffening obtained.Experimentally, the incorporation of montmorillonite or sepiolite led to a significant increase in the elastic modulus and, with the presence of an elastomeric phase in the resin, the damping was doubled and the resilience was increased.Finally, the most efficient formulations were used to manufacture glass fibers reinforced composites.The improvement in mechanical properties was found, to a lesser extent, for the manufactured prototypes.The relevance of the use of these materials on an industrial scale was evaluated.

The purpose of this investigation is to identify appropriate location of capacitor banks and sources of reactive power by studying power system stability in the vicinity of system equilibrium states. The locations for reactive power sources are determined by identifying those modes of the system that participate most in the system behavior in general and in dictating the final state of the system after experiencing faults or disturbances. To identify the relevant modes of the system that participate most in the system dynamic, we shall make use of modal and participation analysis for different system conditions. We also apply modal and participation analysis to a system in order to identify the components of greatest impact that result in the most efficient system control. The ideas developed in this study are used to analyze and identify weak boundaries of the IEEE 39- Bus system that contribute to the system’s instability.

Les vibrations qui sont en général source de dérangement, d’usure et même destruction des machines et structures mécaniques doivent être contrôlées ou éliminées. Pour cette raison, la lutte contre les vibrations est devenue depuis des années un enjeu majeur pour les chercheurs de laboratoire et de développement dans l’industrie afin de développer des solutions efficaces contre ces problèmes. De nombreuses technologies ont donc été développées. Parmi ces technologies, les absorbeurs de vibration non linéaires présentent des performances importantes dans l’atténuation de vibration sur une large bande de fréquences. C’est dans ce contexte que cette thèse se focalise sur l’analyse et l’optimisation des absorbeurs de vibration non linéaires. L’objectif de cette thèse est d’analyser le comportement dynamique non linéaire des systèmes présentant des absorbeurs de vibration non linéaires. Pour cela, un modèle dynamique d’un système à deux degrés de liberté est développé mettant en équations le comportement non linéaire. La résolution des équations de mouvement est faite par la Méthode Asymptotique Numérique (MAN). La performance de cette méthode est montrée via une comparaison avec la méthode de Newton-Raphson. L’analyse des modes non linéaires du système ayant une non-linéarité cubique est faite par une formulation explicite des Fonctions de Réponse en Fréquence non linéaires (FRFs) et les Modes Normaux Non linéaires (MNNs). Un démonstrateur sur la base d’un système simple à deux degré de liberté est mis en place afin de recaler les modèles envisagés sur la base des résultats expérimentaux trouvés. / Vibrations are usually undesired phenomena as they may cause discomfort, disturbance, damage, and sometimes destruction of machines and structures. It must be reduced or controlled or eliminated. For this reason, the vibrations attenuation became a major issue for scientists and researchers in order to develop effective solutions for these problems. Many technologies have been developed. Among these technologies, the nonlinear vibration absorbers have significant performance in the vibration attenuation over a wide frequency band. In this context, this thesis focuses on the analysis and optimization of nonlinear vibration absorbers. The objective of the thesis is to analyze the nonlinear dynamic behavior of systems with nonlinear vibration absorbers. For this, a dynamic model of a two degrees of freedom system is developed. The Asymptotic Numerical Method (ANM) is used to solve the nonlinear equations of motion. The performance of this method is shown via a comparison with the Newton-Raphson method. The nonlinear modal analysis system with cubic nonlinearity is made by an explicit formulation of the nonlinear Frequency Response Functions (FRFs) and Nonlinear Normal Modes (MNNs). An experimental study is performed to validate the numerical results.

[pt] A Dissertação aqui apresentada descreve um acidente em um rotor de máquina de grande porte (compressor de ar) de uma fábrica de fertilizante cujas conseqüências foram perdas financeiras de alta monta tanto para a empresa quanto para o Estado, pela importância econômica onde a fábrica é situada. O objetivo da Dissertação foi simular matematicamente o acidente ocorrido e esclarecer o mesmo. Para se chegar ao diagnóstico do problema se modelou o rotor e o discretizou pelo Método de Elementos Finitos. As técnicas de investigação do problema e a sua seqüência de investigação podem ser tomadas como base em investigação de eventuais acidentes envolvendo rotores futuramente. O capítulo relativo a Análise Modal será extraído como base de apostila para curso envolvendo pessoal da área de Manutenção Mecânica. / [en] A problem related with an air compressor gave birth to the MSc Thesis. Problems related with rotative machines are usual in the industrial field. Difficulties come from the data gathering in order to analyze, and propose a theory of failure in order to explain and avoid the recurrence of such problem. Modelling a rotor with a Timoshenko beam element and the discretization by finite element method permit the dynamical analysis and the modal analysis of the rotor considering its interaction with the radial and thrust bearings (assuming stiffness and rigidity). The work is divided in seven chapters: chapter one introduces the work and gives the overview of it; chapter two describes the industrial problem; chapter three is a brief explanation of bearing types and the fundamental principle of lubrication; chapter four introduces vibration theory and modal analysis; chapter five introduces the finite element method; chapter six is the simulation of the problem, using tailor-made MATLABr programs to reconstruct the problem and to compare the test field results with the here mentioned formulation; chapter seven discusses the results and proposes future works. Appendix shows the kinetic theory and the beam deformation model used in the program and the Laval simple rotor as a limited description of the dynamic of a rotor with distributed mass, rigidity and stiffness. The aim of this work is to help understand and avoid the recurrence of the failure described and to easy the understanding of modal analysis for new engineers and technicians which will deal with rotor dynamics.

[pt] Em uma ferrovia, o veículo interage dinamicamente com a superestrutura (trilhos, palmilha e dormentes) e a subestrutura (lastro, sublastro e sub- base). O conforto dos passageiros, a vibração no solo e a freqüência dos trabalhos, de manutenção tanto dos veículos como também dos trilhos são determinadas considerando-se que todos os elementos estruturais interagem entre si. A resposta de cada componente estrutural é sensível µa pressão do eixo da roda no trilho, µas irregularidades na superfície do trilho e µa velo- cidade do trem, que está relacionada com à velocidade crítica na ferrovia (velocidade da fase mínima com que as ondas se propagam no trilho e no dormente). No projeto de uma nova ferrovia, como também na própria ava- liação das condições de trabalho de ferrovias existentes, todos os aspectos brevemente mencionados acima têm que ser levados em conta em um modelo matemático. A interação trilho-palmilha-dormente-lastro é representada por um modelo unidimensional em que os trilhos são representados por vigas de Timoshenko, assim como os dormentes; o lastro é representado por uma fundação elástica com amortecimento viscoso. A interação local entre tri- lho e dormente é simulada utilizando um elemento de treliça com rigidez e amortecimento. As propriedades mecânicas de cada componente da ferro- via são na maioria dos casos desconhecidas, principalmente as propriedades do lastro. Para cada elemento, são desenvolvidas as equações de equilíbrio entre esforços e deslocamentos. As equações de equilíbrio global são dadas por um desenvolvimento em série das matrizes de massa, rigidez e amorte- cimento em função de uma freqüência circular de vibração. O interesse final é a resposta transiente no domínio do tempo, obtida utilizando técnicas de superposição modal. Por fim, são propostos três modelos globais para a ferrovia, obtidos considerando algumas modificações no dormente. / [en] In a railway, the vehicle interacts dynamically with a track superstructure (rails, rail pad and sleepers) and sub-structure (ballast, sub-ballast, sub- grade). Passengers' comfort, environmental loading (ground vibration) and frequency of maintenance works of vehicles as well as of the track are deter- mined by the way all the structural elements interact. The response of each single structural component is sensitive to the wheel-axle pressure on the track, the effects of joint in un welded rails, the unevenness of wheel and rail, and the train speed as referred to the track critical velocity (minimum phase velocity of bending waves propagating in the track rails, supported by the ballast). An important issue is for example how the ballast will be affected when old, soft, timber sleepers and replaced by much, stiffer, pres- tressed concrete elements, and how newly introduced irregularities propa- gate along the track, among uncountable mathematical model possibilities, the presents a rail-pad-sleeper-ballast model mainly based on an assemble of Timoshenko beam elements (for the rail) including, in case of the sle- epers, elastic foundation (for the ballast) and viscous damping. The local interaction of the rail-pad-sleeper set is simulated with a bar element that includes damping. The dissertation reports on the numerical model, which relies on exact, dynamic beam and truss elements derived on a variational basis for the frequency-domain analysis. The model enable the assessment of the vibration characteristics of a rail track, the inverse evaluation of se- veral mechanical properties of the structural components and eventually, if everything goes well, the assessment of a dynamic behavior of the rail track actual service load. Theoretical basis for transient analysis is the advanced mode superposition technique. Finally, are proposed three global models for the railway, obtained considering some modifications in the sleeper.