Le présent travail traite l’optimisation des paramètres des amortisseurs à masses accordées (AMA) accrochés sur des structures, linéaires. Les AMAs sont des dispositifs de contrôle passif utilisés pour atténuer les vibrations induites par des chargements dynamiques (en particulier stochastiques) appliqués sur des structures. L’efficacité de tels dispositifs est étroitement liée aux caractéristiques dynamiques qu’on doit imposer à ces systèmes. Dans ce cadre, plusieurs stratégies d’optimisation peuvent être utilisées dans des contextes déterministes et non déterministes, où les paramètres de la structure à contrôler sont incertains. Parmi les différentes approches qu’on peut trouver dans la littérature, l’optimisation structurale stochastique (OSS) et l’optimisation basée sur la fiabilité (OBF) étaient particulièrement traitées dans le présent travail.Dans la première partie de ce travail, en plus de la nature stochastique des chargements extérieurs appliqués à la structure linéaire à contrôler, la présence de paramètres structuraux de type incertains mais bornés (IMB) est prise en considération et les bornes optimales des paramètres AMA ont été calculées. Le calcul de ces bornes a été fait en utilisant une technique basée sur un développement de Taylor suivi d’une extension aux intervalles. La technique, permettant l’obtention d’une approximation des bornes optimales, a été appliquée dans les cas d’un système à un degré de liberté (1DDL) et un autre à plusieurs degrés de libertés (nDDL). Les résultats obtenus ont montrés que la technique utilisée était bien adaptée pour la stratégie OSS et elle l’est moins pour l’approche OBF.Comme suite logique aux résultats de la première partie, la seconde partie de la présente dissertation est consacrée à la présentation de deux méthodes permettant l’obtention des bornes exactes et des bornes approximées des paramètres optimaux de l’AMA et ce, en présence de paramètres structuraux de type IMB. La première méthode est celle de la boucle d’optimisation continue imbriquée, la seconde est celle des extensions aux intervalles basées sur la monotonie. Les méthodes présentées, qui ont été appliquées avec l’approche OBF, sont valables pour n’importe quel problème d’optimisation faisant intervenir des paramètres de type IMB. Mis à part le calcul de bornes optimisées du dispositif AMA, la question de la robustesse, vis-à-vis des incertitudes structurales, a été également traitée et il a été prouvé que la solution optimale correspondante au contexte déterministe était la plus robuste.L’introduction d’une nouvelle stratégie OBF des paramètres AMA a fait l’objet de la troisième partie de cette dissertation. En effet, un problème OBF est toujours relié à un mode de défaillance caractérisé par le franchissement d’une certaine réponse, de la structure à contrôler, d’un certain seuil limite pendant une certaine durée de temps. Le nouveau mode de défaillance, correspondant à la nouvelle stratégie OBF, consiste à considérer qu’une défaillance ait lieu lorsque la puissance dissipée au niveau de la structure à contrôler, pendant une période de temps, excède une certaine valeur. Faisant intervenir l’approche par franchissement ainsi que la formule de Rice, la nouvelle stratégie a été appliquée dans le cas d’un système 1DDL et l’expression exacte de la probabilité de défaillance est calculée. En se basant sur une approximation mettant en œuvre la technique du minimum d’entropie croisé, la nouvelle stratégie a été, également, appliquée dans le cas d’un système à nDDL et les résultats obtenus ont montrés la supériorité de cette stratégie par rapports à deux autres tirées de la bibliographie. / The present work deals with the parameters optimization of tuned mass dampers (TMD) used in the control of vibrating linear structures under stochastic loadings. The performance of the TMD device is deeply affected by its parameters that should be carefully chosen. In this context, several optimization strategies can be found in the literature and among them the stochastic structural optimization (SSO) and the reliability based optimization (RBO) are particularly addressed in this dissertation.The first part of this work in dedicated to the calculation of the optimal bounds solutions of the TMD parameters in presence of uncertain but bounded (UBB) structural parameters. The bounds of the optimal TMD parameters are obtained using an approximation technique based on Taylor expansion followed by interval extension. The numerical investigations applied with one degree of freedom (1DOF) and with multi-degree of freedom (multi-DOF) systems showed that the studied technique is suitable for the SSO strategy and that it’s less appropriate for the RBO strategy.As immediate consequence of the obtained results in the first part of this work, in the second part a method, called the continuous-optimization nested loop method (CONLM), providing the exact range of the optimal TMD parameters is presented and validated. The numerical studies demonstrated that the CONLM is time consuming and to overcome this disadvantage, a second method is also presented. The second method is called the monotonicity based extension method (MBEM) with box splitting. Both methods have been applied in the context of the RBO strategy with 1DOF and multi-DOF systems. The issue of effectiveness and robustness of the presented optimum bounds of the TMD parameters is also addressed and it has been demonstrated that the optimum solution corresponding to the deterministic context (deterministic structural parameters) provide good effectiveness and robustness.Another aspect of RBO approach is dealt in the third part of the present work. Indeed, a new RBO strategy of TMD parameters based on energetic criterion is presented and validated. The new RBO approach is linked to a new failure mode characterized by the exceedance of the power dissipated into the controlled structure over a certain threshold during some interval time. Based on the outcrossing approach and the Rice’s formula, the new strategy is firstly applied to 1DOF system and exact expression of the failure probability is calculated. After that, a multi-DOF system is considered and the minimum cross entropy method has been used providing an approximation to the failure probability and then the optimization is carried out. The numerical investigations showed the superiority of the presented strategy when compared with other from the literature.

The aim of my master’s thesis was to create models of the damping device and observing their behavior in interaction with the structure. First was the construction separately modeled with Java application named FyDiK2D like a model with one degree of freedom. Model of construction takes form like a high, thin rod with full circular cross section. The lower part was restrained into the subsoil. The design was to verify the correct functionality of the model by comparing the analytical and numerical solutions. For capturing the precise behavior of the structure was converted to a multi-stage model. Then the pendulum damper was applied on this construction and found amplitude lies in highest point of multi-stage model. He was then replaced by tuned mass damper. By comparing these amplitudes from both dampers was found which kind of damper is efficient for multi-stage model.

The diploma thesis deals with dynamic analysis of cable-stayed steel pedestrian footbridge. The dynamic response of pedestrian-induced vibration was studied. The response of structure exeeded standard acceptance limit. Due to the effect of installed Tuned Mass Damper was studied. Motion equations of single and two degree of freedom model were solved in program MATLAB and the results were compared with numeric model in ANSYS.

El capítulo I presenta una introducción y aspectos generales en base a los antecedentes, realidad problemática, formulación del problema; así como la definición de la hipótesis y los objetivos concluyentes. El capítulo II se realiza el estado del arte basándose en los fundamentos teóricos más importantes en base a la eficiencia de los AMS sometidos a fuerzas o movimientos armónicos en la base; así también describe generalidades en base a la clasificación general de los sistemas de protección sísmica, fundamentos del AMS, y resumen de trabajos relevantes sobre aplicaciones en edificios y otras obras de ingeniería civil. El capítulo III, IV y V se refieren al comportamiento de estructuras sin AMS frente a acciones sísmicas. En particular se analizan las edificaciones existentes reales de 7, 10 y 20 niveles en base al análisis computacional. El capítulo VI presenta los parámetros de diseño de un AMS para tres aplicaciones de edificios reales de 7, 10 y 20 niveles, concluyendo con la determinación de las características óptimas para la construcción y los efectos generados por estas. Finalmente, en el capítulo VII se presentan las principales conclusiones y recomendaciones basadas en la investigación realizada. / Chapter I presents an introduction and general aspects based on the background, problematic reality, formulation of the problem, as well as the definition of the hypothesis and the conclusive objectives. Chapter II the state of the art is made based on the most important theoretical foundations based on the efficiency of the AMS subjected to forces or harmonic movements in the base; it also describes generalities based on the general classification of seismic protection systems, foundations of the AMS, and summary of relevant works on applications in buildings and other civil engineering works. Chapter III, IV and V refers to the behavior of structures without AMS against seismic actions. In particular, the real existing buildings of 7, 10, and 20 levels are analyzed based on the computational analysis. Chapter VI presents the design parameters of an AMS for three applications of real buildings of 7, 10 and 20 levels, concluding with the determination of the optimal characteristics for the construction and the effects generated by these. Finally, Chapter VI presents the main conclusions and recommendations based on the research carried out. / Tesis

Metamaterials are typically described as materials with ’unusual’ wave propagation properties. Originally developed for electromagnetic waves, these materials have also spread into the field of acoustic wave guiding and cloaking, with the most relevant of these ’unusual’ properties, being the so called band-gap phenomenon. A band-gap signifies a frequency region where elastic waves cannot propagate through the material, which in principle, could be used to protect buildings from earthquakes. Based on this, two relevant concepts have been proposed in the field of seismic engineering, namely: metabarriers, and metamaterial-based foundations. This thesis deals with the development of the Metafoundation, a metamaterial-based foundation system for the seismic protection of fuel storage tanks against excessive base shear and pipeline rupture. Note that storage tanks have proven to be highly sensitive to earthquakes, can trigger sever economic and environmental consequences in case of failure and were therefore chosen as a superstructure for this study. Furthermore, when tanks are protected with traditional base isolation systems, the resulting horizontal displacements, during seismic action, may become excessively large and subsequently damage connected pipelines. A novel system to protect both, tank and pipeline, could significantly augment the overall safety of industrial plants. With the tank as the primary structure of interest in mind, the Metafoundation was conceived as a locally resonant metamaterial with a band gap encompassing the tanks critical eigenfrequency. The initial design comprised a continuous concrete matrix with embedded resonators and rubber inclusions, which was later reinvented to be a column based structure with steel springs for resonator suspension. After investigating the band-gap phenomenon, a parametric study of the system specifications showed that the horizontal stiffness of the overall foundation is crucial to its functionality, while the superstructure turned out to be non-negligible when tuning the resonators. Furthermore, storage tanks are commonly connected to pipeline system, which can be damaged by the interaction between tank and pipeline during seismic events. Due to the complex and nonlinear response of pipeline systems, the coupled tank-pipeline behaviour becomes increasingly difficult to represent through numerical models, which lead to the experimental study of a foundation-tank-pipeline setup. Under the aid of a hybrid simulation, only the pipeline needed to be represented via a physical substructure, while both tank and Metafoundation were modelled as numerical substrucutres and coupled to the pipeline. The results showed that the foundation can effectively reduce the stresses in the tank and, at the same time, limit the displacements imposed on the pipeline. Leading up on this, an optimization algorithm was developed in the frequency domain, under the consideration of superstructure and ground motion spectrum. The advantages of optimizing in the frequency domain were on the one hand the reduction of computational effort, and on the other hand the consideration of the stochastic nature of the earthquake. Based on this, two different performance indices, investigating interstory drifts and energy dissipation, revealed that neither superstructure nor ground motion can be disregarded when designing a metamaterial-based foundation. Moreover, a 4 m tall optimized foundation, designed to remain elastic when verified with a response spectrum analysis at a return period of 2475 years (according to NTC 2018), reduced the tanks base shear on average by 30%. These results indicated that the foundation was feasible and functional in terms of construction practices and dynamic response, yet unpractical from an economic point of view. In order to tackle the issue of reducing the uneconomic system size, a negative stiffness mechanism was invented and implemented into the foundation as a periodic structure. This mechanism, based on a local instability, amplified the metamaterial like properties and thereby enhanced the overall system performance. Note that due to the considered instability, the device exerted a nonlinear force-displacement relationship, which had the interesting effect of reducing the band-gap instead of increasing it. Furthermore, time history analyses demonstrated that with 50% of the maximum admissible negative stiffness, the foundation could be reduced to 1/3 of its original size, while maintaining its performance. Last but not least, a study on wire ropes as resonator suspension was conducted. Their nonlinear behaviour was approximated with the Bouc Wen model, subsequently linearized by means of stochastic techniques and finally optimized with the algorithm developed earlier. The conclusion was that wire ropes could be used as a more realistic suspension mechanism, while maintaining the high damping values required by the optimized foundation layouts. In sum, a metamaterial-based foundation system is developed and studied herein, with the main findings being: (i) a structure of this type is feasible under common construction practices; (ii) the shear stiffness of the system has a fundamental impact on its functionality; (iii) the superstructure cannot be neglected when studying metamaterial-based foundations; (iv) the complete coupled system can be tuned with an optimization algorithm based on calculations in the frequency domain; (v) an experimental study suggests that the system could be advantageous to connected pipelines; (vi) wire ropes may serve as resonator suspension; and (vii) a novel negative stiffness mechanism can effectively improve the system performance.

This master thesis deals with the dynamic analysis of a footbridge. Computational model of the footbridge was created using ANSYS software. The model was subjected to dynamic wind load in longitudal and lateral direction. Furthermore pedestrian load in lateral direction was analyzed. Afterwards, due to unsatisfactory response to the pedestrian laod, a tuned mass damper was introduced to reduce the vibration. This lead to decrease in the vibration to a satisfactory levels, as is shown in the analyses of the model.

Thesis deals with the modeling of pedestrian excitation of structures and obtaining the corresponding dynamic response of the structure. The trend of modern slender structures places more emphasis on the accuracy of modeling pedestrian dynamic excitation, which is difficult because of the intelligent behavior of pedestrians and the biological nature of the modeled pedestrian. First part of the thesis deals with traditional models of pedestrian excitation, based on application of pedestrian ground force to the model of construction. Models are explored on a model of slender footbridge for many different excitation variants in order to explore the specifics of the force excitation application and the structure response calculation. In second part of the thesis biomechanical pedestrian models are developed, including inertial forces, to calculate the pedestrian interaction with the structure. Parametric studies carried out on simplified structural models research the influence of design parameters of biomechanical models on dynamic response. The aim is to obtain a more accurate model of the pedestrian-construction system for refinement of the design of structures. The design of a tuned mass dampers for the reduction of pedestrian induced vibrations is also explored. Tuned mass dampers are devoted to parametric studies that deal with the influence of design parameters of the damper on the efficiency and design requirements of the device. The aim is to explore the design parameters and their influence on the efficient and economical design of the device. In the thesis were developed two biomechanical models, a simple biomechanical model with one vertical degree of freedom and a bipedal model of a human walking. Models have proven a certain degree of interaction when exciting light footbridges by one pedestrian. Bipedal model then also brought a partial insight into the mechanics of walking and the causes of pedestrian contact forces.

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