A wide range of dynamic systems can be approximated as linear and time invariant, for which a wealth of tools are available to characterize or modify their dynamic characteristics. Experimental modal analysis (EMA) is a procedure whereby the natural frequencies, damping ratios and mode shapes which parameterize vibratory, linear, time invariant systems are derived from experimentally measured response data. EMA is commonly applied in a multitude of applications, for example, to generate experimental models of dynamic systems, validate finite element models and to characterize dissipation in vibratory systems. Recent EMA has also been used to characterize damage or defects in a variety of systems. The Algorithm of Mode Isolation (AMI), presented by Drexel and Ginsberg in 2001, employs a unique strategy for modal parameter estimation in which modes are sequentially identified and subtracted from a set of FRFs. Their natural frequencies, damping ratios and mode vectors are then refined through an iterative procedure. This contrasts conventional multi-degree-of-freedom (MDOF) identification algorithms, most of which attempt to identify all of the modes of a system simultaneously. This dissertation presents a hybrid multi-input-multi-output (MIMO) implementation of the algorithm of mode isolation that improves the performance of AMI for systems with very close or weakly excited modes. The algorithmic steps are amenable to semi-automatic identification, and many FRFs can be processed efficiently and without concern for ill-conditioning, even when many modes are identified. The performance of the algorithm is demonstrated on noise contaminated analytical response data from two systems having close modes, one of which has localized modes while the other has globally responsive modes. The results are compared with other popular algorithms. MIMO-AMI is also applied to experimentally obtained data from shaker excited tests of the Z24 highway bridge, demonstrating the algorithm's performance on a data set typical of many EMA applications. Considerations for determining the number of modes active in the frequency band of interest are addressed, and the results obtained are compared to those found by other groups of researchers.

This study presents the investigation and the verification of the modal parameters of a plate-like structure by using different modal analysis methods. A fin-like structure which is generally used in aircraft is selected as a subcategory of a plate-like test structure. In the first part of the thesis, the natural frequencies and the corresponding mode shapes of the fin are extracted by Finite Element Analysis method. Classical Modal Analysis and Testing methods comprising both impact hammer and modal shaker applications are then applied in order to obtain the modal parameters such as / resonance frequencies, mode shapes and damping ratios. In the second part, a recent modal analysis technique, Operational Modal Analysis, is also applied in the laboratory environment. Since Operational Modal Analysis method does not require any information of input forcing, the fin structure is tested under both mechanical and acoustical types of excitations without measuring the given input forces. Finally, Operational Modal Analysis and Testing is also performed under various flow conditions generated in the wind tunnel which may simulate the real operating environment for the fin structure. The modal parameters extracted under these flow conditions are then compared with the previously obtained Finite Element, Classical and Operational Modal Analyses results.

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.

This thesis deals with the stability of particle laden flows. Both modal and non-modal linear analyses have been performed on two-way coupled particleladen flows, where particles are considered spherical, solid and either heavy or light. When heavy particles are considered, only Stokes drag is used as interaction term. Light particles cannot be modeled with Stokes drag alone, therefore added mass and fluid acceleration are used as additional interaction forces. The modal analysis investigates the asymptotic behavior of disturbances on a base flow, in this thesis a pressure-driven plane channel flow. A critical Reynolds number is found for particle laden flows: heavy particles increase the critical Reynolds number compared to a clean fluid, when particles are not too small or too large. Neutrally buoyant particles, on the other hand, have no influence on the critical Reynolds number. Non-modal analysis investigates the transient growth of disturbances, before the subsequent exponential behavior takes over. We investigate the kinetic energy growth of a disturbance, which can grow two to three orders of magnitude for clean fluid channel flows. This transient growth is usually the phenomenon that causes transition to turbulence: the energy can grow such that secondary instabilities and turbulence occurs. The total kinetic energy of a flow increases when particles are added to the flow as a function of the particle mass fraction. But instead of only investigating the total energy growth, the non-modal analysis is expanded such that we can differentiate between fluid and particle energy growth. When only the fluid is considered in a particle-laden flow, the transient growth is equal to the transient growth of a clean fluid. Besides thes Stokes drag, added mass and fluid acceleration, this thesis also discusses the influence of the Basset history term. This term is often neglected in stability analyses due to its arguably weak effect, but also due to difficulties in implementation. To implement the term correctly, the history of the particle has to be known. To overcome this and obtain a tractable problem, the square root in the history term is approximated by an exponential. It is found that the history force as a small effect on the transient growth. Finally, Direct numerical simulations are performed for flows with heavy particles to investigate the influence of particles on secondary instabilities. The threshold energy for two routes to turbulence is considered to investigate whether the threshold energy changes when particles are included. We show that particles influence secondary instabilities and particles may delay transition. / QC 20111013

Timber is a building material that is becoming more common and of interest for use in high-rise buildings. One of the reasons is that timber requires less energy input for the manufacturing process of the material compared to non-wood based materials. When designing high- rise timber buildings it is of great significance to understand the dynamic behavior of the structure. One method to obtain the dynamic properties is to use Operational Modal Analysis, which is based on the structural response from operational use. Finite element (FE) analysis is a tool which can be used for dynamic analysis for large structures. In this study an Operation Modal Analysis (OMA) was conducted on a four-story timber building in Växjö. A finite element model was created of the same building using commercial FE packages. Based on the mode shapes and natural frequencies obtained from the OMA, the FE model was fine-tuned. The purpose of this thesis is to gain knowledge of which parameters that might have a significant role in finite element modelling for a structural dynamic analysis. The aim is to develop a finite element model that accurately simulates the dynamic behavior of the tested building. It was shown from the result that is possible with an enough detailed FE model to capture the dynamic behaviour of a structure. The parameters that had the largest effect on the result can be pointed to the mass and the stiffness of the structure. / Trä är ett byggnadsmaterial som börjar bli allt mer vanligt och är av intresse att använda som stommaterial för höga byggnader. En anledning till detta är att det krävs mindre energi i tillverkningsfasen för trä jämfört med stål och betong. Vid dimensionering av höga träbyggnader är det essentiellt att förstå byggnadens dynamiska egenskaper. För att ta fram en byggnads dynamiska egenskaper kan en metod som benämns Operational Modal Analysis (OMA) tillämpas vilken baseras på byggnadens rörelser vid daglig användning. Finita element (FE) metoden är ett verktyg som kan användas vid dynamisk analys för större byggnader. I detta arbete genomfördes en OMA för ett fyravåningshus med trästomme beläget i Växjö. Genom användning av kommersiella FE-mjukvaror togs en finita element modell av samma byggnad fram. Baserat på de egenfrekvenser och egenmoder erhållna från OMA, uppdaterades FE-modellen därefter. Syftet med detta arbete är att erhålla kunskap kring vilka parametrar som har betydelse vid FE-modellering med hänsyn till dynamisk analys. Syftet är även att validera den prototyp av datainsamlingsenhet som använts vid fältmätningen. Målet med arbetet är att ta fram en FE-modell som på ett korrekt sätt beskriver den testade byggnadens dynamiska beteende. Resultatet av arbetet påvisar att med en tillräckligt detaljerad FE-modell är det möjligt att erhålla en byggnads dynamiska egenskaper. De parametrar som har störst inverkan på resultatet är byggnadens styvhet och inkluderad massa.

<p>Asymptotic Modal Analysis (AMA) is a computationally efficient and accurate method for studying the response of dynamical systems experiencing banded, random harmonic excitation at high frequencies when the number of responding modes is large. In this work, AMA has been extended to systems of coupled continuous components as well as nonlinear systems. Several prototypical cases are considered to advance the technique from the current state-of-the-art. The nonlinear problem is considered in two steps. First, a method for solving problems involving nonlinear continuous multi-mode components, called Iterative Modal Analysis (IMA), is outlined. Secondly, the behavior of a plate carrying a nonlinear spring-mass system is studied, showing how nonlinear effects on system natural frequencies may be accounted for in AMA. The final chapters of this work consider the coupling of continuous systems. For example, two parallel plates coupled at a point are studied. The principal novel element of the two-plate investigation reduces transfer function sums of the coupled system to an analytic form in the AMA approximation. Secondly, a stack of three parallel plates where adjacent plates are coupled at a point are examined. The three-plate investigation refines the reduction of transfer function sums, studies spatial intensification in greater detail, and offers insight into the diminishing response amplitudes in networks of continuous components excited at one location. These chapters open the door for future work in networks of vibrating components responding to banded, high-frequency, random harmonic excitation in the linear and nonlinear regimes.</p> / Dissertation

Na Indústria Aeronáutica, é de extrema importância a qualidade e o desempenho de seus produtos, que estão diretamente relacionados ao projeto e ao desenvolvimento de estruturas adequadas, pois além de seu caráter funcional deve-se também garantir a sua integridade nas mais diversas condições de operação. O comportamento dinâmico destas estruturas é um dos seus principais aspectos, principalmente devido à demanda contínua para estruturas mais leves e consequentemente mais flexíveis. Tradicionalmente, as estruturas aeroespaciais devem ser submetidas a alguma forma de verificação antes do voo, de forma a assegurar que a aeronave esteja livre de qualquer fenômeno de instabilidade aeroelástica, que pode ocorrer provocando problemas de fadiga ou falhas estruturais. Um dos fenômenos de instabilidade mais importantes é denominado flutter. As técnicas de ensaio em voo para identificação de flutter são de extrema importância para o conhecimento dos limites de voo seguro. Um dos elementos essenciais para a realização de ensaios de flutter em voo é o processo de identificação dos parâmetros modais estruturais da aeronave sob teste. A identificação precisa e rápida dos parâmetros modais permite determinar com antecedência e segurança as condições de voo em que o fenômeno de flutter irá ocorrer. Atualmente as pesquisas nesta área apontam na direção do desenvolvimento de tecnologia que permita a identificação em tempo real dos parâmetros modais associados ao flutter. Neste trabalho foi realizado o estudo de um método de identificação de parâmetros modais para ser aplicado em tempo real. O método de identificação utilizado para este estudo é o EERA - Extended Eigensystem Realization Algorithm, um método de identificação no domínio do tempo considerado eficiente e poderoso, pois é capaz de identificar o comportamento dinâmico complexo em estruturas. O algoritmo foi validado através de um ensaio experimental num modelo de asa no túnel de vento, onde foram determinados os parâmetros modais envolvidos no flutter. Também foi realizado um ensaio experimental numa placa de alumínio, onde foram identificados os seus parâmetros modais, frequências naturais e fatores de amortecimento. Após sua validação, o método EERA foi adaptado e programado no equipamento de aquisição e processamento de sinais dSPACE®, que é destinado a realizar identificação em tempo real. Por último foi realizado um ensaio experimental em tempo real na placa de alumínio utilizada anteriormente, onde os parâmetros modais identificados on-line foram comparados com os identificados off-line, comprovando assim a eficiência do método na identificação em tempo real. / In the Aeronautical Industry, the quality and the performance of its products, that are directly related to the project and the development of adequate structures, are of extreme importance, since, beyond their functional characteristics, their integrity, in the most diverse operation conditions, must also be guaranteed. The dynamic behavior of these structures is one of its main aspects, mainly due to continuous demand for lighter and consequently more flexible structures. Traditionally, the aerospace structures must be submitted to some form of verification before the flight, to assure that the aircraft is free of any aeroelastic instability phenomenon, which when occurring will provoke structural fatigue problems or failure. One of the more important instability phenomena is called flutter. The techniques of flight test for identification of flutter are of extreme importance for the knowledge of the limits of safe flight. One of the essential elements for the accomplishment of flutter tests in flight is the process of identification of the structural modal parameters of the aircraft under test. The accurate and fast identification of the modal parameters allows determining, with antecedence and security, the flight conditions where the phenomenon of flutter will occur. Currently the research in this area points in the direction of developing the technology that allows the identification in real time of the modal parameters associated to flutter. In this work the study of a method of identification of modal parameters was carried through to be applied in real time. The method of identification used for this study is the EERA - Extended Eigensystem Realization Algorithm, a method of identification in the time domain considered efficient and powerful, since it is capable to identifying complex dynamic behavior in structures. The algorithm was validated with an experimental test in a model of wing in the wind tunnel, where the involved modal parameters in flutter had been determined. Also an experimental test was carried out with an aluminum plate, where its modal parameters, natural frequencies and damping factors, had been identified. After its validation, the method EERA was adapted and programmed in the dSPACE® signals acquisition and processing equipment, which is used for carrying out identification in real time. Finally an experimental test, in real time, with the previously used aluminum plate was carried out, when the modal parameters identified on-line were compared with those identified off-line, thus proving the efficiency of the method for identification in real time.

Les travaux de recherche de ce manuscrit se concentrent sur l’analyse des fréquences de vibrations des robots. Nos applications concernent plus particulièrement les architectures à cinématique parallèle. Dans un premier temps nous avons considéré les robots parallèles redondants en actionnement pour lesquels nous envisageons d’augmenter la fréquence de leurs oscillations en utilisant les efforts internes intrinsèques à ce type de structure. L’objectif est d’utiliser leur actionnement pour mettre en tension leur structure, et par conséquent, par analogie avec une corde vibrante, augmenter la fréquence de leurs oscillations. Nous avons étudié plusieurs robots plans redondants et nous montrons que dans le cadre de robots typiquement conçus pour être rigides,l’influence des efforts internes rajoutés n’a que peu d’importance. La suite de nos travaux soutient la proposition suivante : "les trajectoires très dynamiques influencent les fréquences des oscillations de la plateforme mobile". En effet, les robots parallèles quand ils sont conçus pour être légers, peuvent atteindre de grandes accélérations. Nous avons choisi de nous intéresser à l’étude de l’impact que peut avoir les effets dynamiques sur la fréquence des oscillations de la plateforme mobile de ces robots. Les robots considérés pour nos développements sont des robots parallèles plans, redondants en actionnement ou non. Nous proposons d’étudier cette influence en nous basant sur un développement au premier ordre du modèle dynamique. Cette linéarisation du modèle dynamique se veut plus complète que celles proposées dans la littérature. Nous expliquons et vérifions la validité de notre approche par une étude sur le lien entre accélération et vitesse et la fréquence d’oscillation pour les robots série PR (pendule sur glissière verticale) et RR (double pendule en rotation horizontale). Ensuite, nous généralisons notre modélisation au premier ordre et l’appliquons aux quatre robots PRR-2 PRR-3, PRR-4 et Dual-V pour voir si nous sommes capable d’en dégager une tendance concernant l’évolution des fréquences d’oscillation. Nous constatons que, en fonction des trajectoires, la dynamique a une influence faible mais visible, souvent positive sur l’augmentation des fréquences d’oscillation de la plateforme mobile. Cependant, les trajectoires et les lois horaires étant imposées, nous ne pouvons que subir cette influence. / The research work of this thesis manuscript focus on the analysis of the frequency of robots’ vibrations. Our applications mainly revolve around architectures with parallel kinematics. First we examined parallel robots which are redundant in actuation and for which we are considering an increase of their oscillations’ frequency using the internal forces inherent to this type of structure. The aim is to use their actuation is the tensioning of their structure, and consequently, by analogy with a vibrating-wire, to enhance theiroscillation frequency. We have studied several redundancy planar robots and we demonstrate that in the case of robots which are typically designed to be stiff, the impact of added internal forces is of low relevance. The continuation of our research supports the following proposal: “High dynamics trajectories have an impact on the oscillation frequency of the mobile platform.” Indeed parallel robots, when designed to be light, can reach greater accelerations. We chose to concentrate on the study of the impact that dynamic effects canhave on the oscillation frequency of those robots’ mobile platform. The robots examined for our developments are planar parallel robots whether they have redundant actuation or not. We offer to study this impact based on a prime order development of the dynamic model. This linearisation of the dynamic model is intended to be more complete than those suggested by literature. We explain and verify the validity of our approach with a study on the link between speed and oscillation frequency on PR robots (pendulum on a vertical sliding guide) and RR robots ( double pendulum rotating horizontally). Then we will generalize our first order model and apply it to the four robots ( PRR-2 PRR-3, PRR-4, and Dual-V) to see if we are able to identify a pattern regarding the evolution ofoscillation frequencies. We observe that, depending on the trajectories, the dynamics have a low but noticeable, and often positive, impact on the increase of oscillation frequency of the mobile platform. However, since the trajectories and speed input laws are imposed, we have no choice but to be subjected to this impact.