In recent years, an increase to design slender and aesthetically-pleasing structures have resulted in some structures having a low natural frequency. This is because the design calculation did not meet the requirement of serviceability performance. Structures can experience excessive vibrations when they are subjected to different types of dynamic loading. A device can be installed to prevent these vibrations.In this thesis, we study the response of buildings and lateral vibrations of footbridges equipped with Tuned Liquid Damper. The aim is to mitigate the first mode of vibration. Tuned Liquid Damper consists of a container in rectangular, cylindrical or arbitrary shape partially filled with shallow liquid, most often water is used as a regulating device system. The design properties of Tuned Liquid Damper is introduced and it is based on the analogyof the most popular damper, Tuned Mass Damper.An experimental study of a building frame model with four floors is conducted to validate the numerical results obtained from the simulation of the model in ANSYS. The linear and non-linear analysis are performed through a system coupling between Ansys mechanical and Fluent solver. The simulation results obtained are in good agreement with the experimental results.A parametric study is conducted with a simply supported steel footbridge. It is a 45 m long span with 3 m width and the flexural rigidity is modified to get the lateral vibration mode. The first lateral natural frequency obtained is 0.713 Hz. The load case for the study considered is according to Sétra guide. The variable parameters studied is the Tuned Liquid Damper water mass ratios: 0.7%, 1.0%, 2.0%, 3.0% and 4.0%. The results show a satisfactory performance of the footbridge model equipped with Tuned Liquid Damper. The accelerations are below 0.1 m/s2 which satisfied the requirement of 0.15 m/s2.

Since their invention in the early 1900s, Tuned Vibration Absorbers (TVAs) have shown to be effective in suppressing vibrations of machines and structures. A vibration absorber is a vibratory subsystem attached to a primary system. It normally consists of a mass, a spring, and a damper. Mounted to the primary system, a TVA counteracts the motions of the primary system, "absorbing" the primary structure's vibrations. A conventional passive TVA, however, is only effective when it is tuned properly, hence, the name "tuned" vibration absorber. In many practical applications, inevitable off-tuning (or mistuning) of a TVA occurs because of the system's operating conditions or parameter changes over time. For example, the mass in a building floor could change by moving furnishings, people gathering, etc., which can "off-tune" TVAs. When TVAs are off-tuned, their effectiveness is sharply reduced. Moreover, the off-tuned TVAs can excessively amplify the vibration levels of the primary structures; therefore, not only rendering the TVA useless but also possibly causing damage to the structures. Off-tuning is one of the major problems of conventional passive TVAs. This study proposes a novel semiactive TVA, which strives to combine the best features of passive and active TVA systems. The semiactive TVA in this study includes a Magneto-Rheological (MR) damper that is used as a controllable damping element, for providing the real-time adjustability that is needed for improving the TVA performance. This study is conducted in two phases. The first phase provides a numerical investigation on a two-degree-of-freedom (2-DOF) numerical model in which the primary structure is coupled with a TVA. The numerical investigation considers four semiactive control methods for the MR TVAs, in addition to an equivalent passive TVA. These numerical models are optimally tuned using numerical optimization techniques to compare each TVA system. These tuned systems then serve as the basis for numerical parametric studies for further evaluation of their dynamic performance. The parametric study covers the effects of damping, as well as system parameter variations (off-tuning). The results indicates that semiactive TVAs are more effective in reducing the maximum vibrations of the primary structure and are more robust when subjected to off-tuning. Additionally, the numerical study identifies the "On-off Displacement-Based Groundhook control (on-off DBG)" as the most suitable control method for the semiactive TVA among control methods considered in this study. For the second phase of this study, an experimental study is performed on a test setup, which represents a 2-DOF structure model coupled with an MR TVA. Using this setup, a series of tests are conducted in the same manner as the numerical study to evaluate the performance of the semiactive TVA. The primary purposes of the experiment are to further evaluate the most promising semiactive control methods and to serve as a "proof-of-concept" of the effectiveness of this MR TVA for floor vibration applications. The results indicate that the semiactive TVA with displacement-based groundhook control outperforms the equivalent passive TVA in reducing the maximum vibrations of the primary structure. This confirms the numerical result that identifies on-off DBG control method as the "best" control method for the MR TVA among four semiactive control schemes considered. The experimental robustness study is also conducted, focusing on the dynamic performance of both the passive and the semiactive TVAs when the mass of the primary system changes (mass off-tuning). The mass of the primary system varied from -23 % to +23 % of its nominal value by adding and removing external masses. The experimental results show that the semiactive TVA is more robust to changes in the primary mass than the passive TVA. These results justify the benefits of the use of semiactive MR TVAs in structures, such as building floor systems. The off-tuning analysis further suggests that, in practice, semiactive TVAs should be tuned slightly less than their optimum in order to compensate for any added masses to the structure. Additionally, the lessons learned from the experimental study have paved the way for implementing the semiactive MR TVA on a test floor, which is currently in progress under a separate study. / Ph. D.

This thesis presents a state-of-the-art-review and twodifferent approaches for solving the moving load problem ofcable-stayed and suspension bridges. The first approach uses a simplified analysis method tostudy the dynamic response of simple cable-stayed bridgemodels. The bridge is idealized as a Bernoulli-Euler beam onelastic supports with varying support stiffness. To solve theequation of motion of the bridge, the finite difference methodand the mode superposition technique are used. The second approach is based on the nonlinear finite elementmethod and is used to study the response of more realisticcable-stayed and suspension bridge models considering exactcable behavior and nonlinear geometric effects. The cables aremodeled using a two-node catenary cable element derived using"exact" analytical expressions for the elastic catenary. Twomethods for evaluating the dynamic response are presented. Thefirst for evaluating the linear traffic load response using themode superposition technique and the deformed dead load tangentstiffness matrix, and the second for the nonlinear traffic loadresponse using the Newton-Newmark algorithm. The implemented programs have been verified by comparinganalysis results with those found in the literature and withresults obtained using a commercial finite element code.Several numerical examples are presented including one for theGreat Belt suspension bridge in Denmark. Parametric studieshave been conducted to investigate the effect of, among others,bridge damping, bridge-vehicle interaction, cables vibration,road surface roughness, vehicle speed, and tuned mass dampers.From the numerical study, it was concluded that road surfaceroughness has great influence on the dynamic response andshould always be considered. It was also found that utilizingthe dead load tangent stiffness matrix, linear dynamic trafficload analysis give sufficiently accurate results from theengineering point of view. / QC 20100511

Le phénomène de résonance sol (PRS) est une instabilité pouvant survenir lorsque l’hélicoptère est au sol et le rotor est en marche ; elle peut vite aboutir à la destruction de l’appareil. L’origine de l’instabilité est un couplage entre les mouvements de roulis du fuselage posée sur le train d’atterrissage et le mouvement asymétrique de l’ensemble des pales dans le plan du rotor principal. Etudier théoriquement des alternatives de stabilisation par des absorbeurs de vibration linéaires (tuned mass dampers - TMD) et non linéaires (nonlinear energy sinks - NES) c’est le sujet de ce travail de thèse. Ces possibilités sont étudiées en ajoutant à un modèle minimal d’un hélicoptère à quatre pales identiques (rotor isotrope),précédemment étudié par l’équipe de l’ISAE, d’abord, un TMD au fuselage, puis des TMD identiques auniveau de l’articulation des pales du rotor. Ensuite, des dispositifs à raideur purement non linéaire (NES)sont considérées, d’abord, au fuselage, puis, aux pales du rotor (NES identiques). / Helicopter ground resonance (HGR) is an instability phenomenon that can occur when helicopters exhibit a spinning rotor when grounded; it can lead the structure to rapidly break apart. The phenomenon originates from a coupling between asymmetric modes of in plane blade oscillations (lead/ lag) and the roll of a grounded fuselage. The verification of alternative stabilization devices such as tuned mass dampers (TMD) and nonlinear absorbers (nonlinear energy sinks - NES) is the objective of this thesis. These possibilities are theoretically investigated by embedding a four-bladed helicopter minimal model - proposed and previously studied by the ISAE team - first, with a TMD in the fuselage, then with four identical TMDs in each blade lag hinge. Then, a NES attached to the fuselage is considered and eventually a set of four identical NES attached to the blade lag hinges of the model is proposed and analyzed.

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.