Brake squeal is an old and well-known problem in the vehicle industry and is a frequent source for customer complain. Although, brake squeal is not usually affecting the performance of the brakes, it is still important to address the problem and to predict the brakes tendency to squeal on an early stage in the design process. Brake squeal is usually defined as a sustained, high-frequency vibration of the brake components, due to the braking action. By using simulation in finite element (FE) method it should be possible to predict at what frequencies the brakes tend to emit sound. The method chosen for the analysis was the complex eigenvalues analysis (CEA) method, since it is a well-known tool to predict unstable modes in FE analysis. The results from the CEA were evaluated against measured data from an earlier study. Even though there are four main mechanism formulated in order to explain the up come of squeal, the main focus in this project was modal coupling, since it is the main mechanism in the CEA. A validation of the key components in model was performed before the analysis, in order to achieve better correlation between the FE model and reality. A parametric study was conducted with the CEA, to investigate how material properties and operating parameters effected the brakes tendency to squeal. The following parameters was included in the analysis; coefficient of friction, brake force, damping, rotational velocity, and Young’s modulus for different components. The result from the CEA did not exactly reproduce the noise frequencies captured in experimental tests. The discrepancy is believed to mainly be due to problems in the calibration process of the components in the model. The result did however show that the most effective way to reduce the brakes tendency for squeal was to lower the coefficient of friction. The effect of varying the Young’s modulus different components showed inconsistent results on the tendency to squeal. By adding damping one of the main disadvantages for the CEA, which the over-prediction of the number of unstable modes, where minimized.

In large and complex systems, failures can have dramatic consequences, such as black-outs, pandemics or the loss of entire classes of an ecosystem. Nevertheless, it is a centuries-old intuition that by using networks to capture the core of the complexity of such systems, one might understand in which part of a system a phenomenon originates. I investigate this intuition using spectral methods to decouple the dynamics of complex systems near stationary states into independent dynamical modes. In this description, phenomena are tied to a specific part of a system through localized eigenvectors which have large amplitudes only on a few nodes of the system's network. Studying the occurrence of localized eigenvectors, I find that such localization occurs exactly for a few small network structures, and approximately for the dynamical modes associated with the most prominent failures in complex systems. My findings confirm that understanding the functioning of complex systems generally requires to treat them as complex entities, rather than collections of interwoven small parts. Exceptions to this are only few structures carrying exact localization, whose functioning is tied to the meso-scale, between the size of individual elements and the size of the global network. However, while understanding the functioning of a complex system is hampered by the necessary global analysis, the prominent failures, due to their localization, allow an understanding on a manageable local scale. Intriguingly, food webs might exploit this localization of failures to stabilize by causing the break-off of small problematic parts, whereas typical attempts to optimize technological systems for stability lead to delocalization and large-scale failures. Thus, this thesis provides insights into the interplay of complexity and localization, which is paramount to ascertain the functioning of the ever-growing networks on which we humans depend.

In large and complex systems, failures can have dramatic consequences, such as black-outs, pandemics or the loss of entire classes of an ecosystem. Nevertheless, it is a centuries-old intuition that by using networks to capture the core of the complexity of such systems, one might understand in which part of a system a phenomenon originates. I investigate this intuition using spectral methods to decouple the dynamics of complex systems near stationary states into independent dynamical modes. In this description, phenomena are tied to a specific part of a system through localized eigenvectors which have large amplitudes only on a few nodes of the system's network. Studying the occurrence of localized eigenvectors, I find that such localization occurs exactly for a few small network structures, and approximately for the dynamical modes associated with the most prominent failures in complex systems. My findings confirm that understanding the functioning of complex systems generally requires to treat them as complex entities, rather than collections of interwoven small parts. Exceptions to this are only few structures carrying exact localization, whose functioning is tied to the meso-scale, between the size of individual elements and the size of the global network. However, while understanding the functioning of a complex system is hampered by the necessary global analysis, the prominent failures, due to their localization, allow an understanding on a manageable local scale. Intriguingly, food webs might exploit this localization of failures to stabilize by causing the break-off of small problematic parts, whereas typical attempts to optimize technological systems for stability lead to delocalization and large-scale failures. Thus, this thesis provides insights into the interplay of complexity and localization, which is paramount to ascertain the functioning of the ever-growing networks on which we humans depend.:1 Introduction 2 Concepts and Tools 2.1 Networks 2.2 Food webs 2.3 Dynamics on networks 2.4 Steady state operating modes 2.5 Bifurcations affecting operating modes 2.6 Dynamical modes 2.7 Generalized models for food webs 3 Perturbation Impact 3.1 Impact of perturbations on food webs 3.2 Examples 3.3 Impact formulation with dynamical modes 3.4 Influence and sensitivity of species 3.5 Localized dynamical modes 3.6 Iterative parameter estimation 3.7 Most important parameters and species 3.8 Discussion 4 Exact Localization 4.1 Graph symmetries 4.2 Localized dynamics on symmetries 4.3 Exactly localized dynamics 4.4 Symmetry reduction in networks 4.5 Application to food webs 4.6 Localization on asymmetric structures 4.7 Nearly-exact localization 4.8 Other systems 4.9 Discussion 5 Approximate Localization 5.1 Spread of a dynamical mode 5.2 Examples for localized instabilities 5.3 Localization of extreme eigenvalues 5.4 Dependence on the system size 5.5 Localization in the model of R. May 5.6 Finding motifs that carry localization 5.7 (Self-)stabilization of food webs 5.8 Repairing localized instabilities 5.9 Discussion 6 Conclusions Acknowledgments Appendix A Parametrization of the Gatun Lake food web B The Master Stability Function approach C Approximate localization on larger structures Bibliography

Ce travail s’intéresse à l’étude d’un système de pompage turbinage à vitesse variable avec une machine asynchrone doublement alimentée face aux perturbations de réseau électrique. L’objectif est d’assurer la continuité de service de cet élément stabilisateur de réseau électrique de sorte qu’il reste connecté au réseau même en cas de perturbations. Le contrôle du système dans les différentes phases de fonctionnement en mode sain a été tout d’abord développé ainsi qu'une étude de stabilité de système utilisant l’analyse modale. Les différents outils nécessaires pour cette analyse ont été tout d’abord mis en oeuvre. Ensuite, les limites de stabilité du système ont été étudiées tenant compte de la variation de longueur de ligne. Le comportement du système en présence des défauts a été par la suite étudié. Les défauts de réseau considérés sont les défauts symétriques et les défauts asymétriques. Une solution basée sur la modification de la stratégie de contrôle a été adoptée pour le cas des défauts symétriques et une solution basée sur l’ajout d’éléments au circuit de puissance a été adoptée pour les cas des défauts asymétriques. Un dispositif expérimental de 4kW a été mis en oeuvre pour la validation des développements menés dans le cadre de cette thèse. / This work focuses on the study of a variable speed pumped storage system based on a doubly fed induction machine in case of grid disturbances. Thus the main objective is to improve the fault ride through capabilities of this grid stabilizer and to guarantee its connection with the grid even under disturbances. The system control in the different operating phases in healthy conditions is developed and then a system stability study is conducted using the eigenvalue analysis. The system stability limits have been investigated taking into account the variation of grid line length so the grid impedance variation. Then the system behavior under disturbances is analyzed. Theconsidered grid faults are symmetric and asymmetric faults. The investigated fault ride through capabilities of the pumped storage system consist of two solutions, one based on the modification of the control strategy was adopted for the symmetric faults and one based on hardware modification has been adopted for the asymmetric ones. A 4kW laboratory set-up has been developed for experimental validation.

The aim of final thesis is design and assessment of footbridge over highway D1 in Bohumín. The design is processed in two options. From these two options there is cable-stayed construction solved in greater detail. Because counstruction is in circular arch with small radius, it is necessary to contain real geometry to computational model. Model is created by beams and construction stages are included too. The construction is assessed for the ultimate and serviceability limit state according to valid standards. In the thesis is performed eigenvalue analysis and harmonic response of the construction. Detailed drawings are included too.