La tribologie et l'analyse non-linéaire du signal est le sujet de mon travail de thèse. Dans la nature, les phénomènes linéaires sont l'exception ; rares sont les systèmes réels qui obéissent exclusivement à des lois linéaires. A l'opposée, les non-linéarités sont impliquées dans tous les processus naturels (réactions chimiques, mécanique, économie, etc.). Les systèmes frottant en sont un des exemples les plus courants, avec des applications très variées. Dans les systèmes de freinage, le frottement se trouve être à l'origine de nombreux problèmes d'instabilités. Les types d'instabilités auxquelles on a affaire dans ce cas sont celles des vibrations induites par le frottement. C'est justement sur ces instabilités que repose le principe Modalsens; un capteur- une lamelle- vient frotter sur un échantillon et ce frottement génère la vibration de celui-ci : le post-traitement par analyse de Fourier du signal vibratoire permet de distinguer des composantes liées au relief, au frottement et à la compressibilité des aspérités. Dans le cas de la méthode Modalsens, l'analyse de Fourier, qui est un outil linéaire, agit comme des lunettes aux travers desquelles est observé le signal et qui filtrerait toutes les composantes non-linéaires. Notre contribution s'inscrit dans cette optique: mettre en place une méthode performante d'analyse non-linéaire pour permettre de mieux appréhender l'analyse du comportement dynamique de Modalsens et de dégager de nouveaux estimateurs pour la caractérisation des surfaces textiles. Partant de là, les résultats obtenus nous serviront à proposer une modélisation du contact sur matériaux fibreux. / Tribology and nonlinear time series analysis are the main subject of my thesis. In nature, the Iinear events are the exception; few real systems follow linear laws exclusively. At the opposite, nonlinearities are involved in all natural processes (chemical reactions, mechanical engineering, economies, etc.). Systems involving dry friction are one of the most common examples, with a variety of applications. In braking systems, friction is found to cause many problems of instability. Types of instabilities addressed in this case are those of friction induced vibrations. The Modalsens method is precisely based on the exploitation of those instabilities: a sensor- a thin blade- rubs on a sample and friction induces its vibrations. Post-processing by Fourier analysis of the vibration signal can separate several components of the sample related to the relief, friction and compressibility of asperities. However, in the case of Modalsens method, Fourier analysis, which is a linear tool, acts like eyeglasses through which the signal is observed and that filters out all non-linear components. Our contribution is in this perspective: the establishment of an efficient method of nonlinear signal analysis to better understand the dynamic behavior of Modalsens and also generate new estimators for the characterization of textile surfaces. Hence, a model of contact on fibrous surface is proposed based on the obtained results.

X-rays have been widely exploited to unravel the structure of matter since their discovery in 1895. Nowadays, with the emergence of new X-ray sources with higher intensity and very short pulse duration, notably X-ray Free Electron Lasers, the number of experiments that may be considered in the X-ray regime has increased dramatically, making the characterization of gas phase atoms and molecules in space and time possible. This thesis explores in the theoretical analysis and calculation of X-ray scattering atoms and molecules, far beyond the independent atom model. Amethod to calculate inelastic X-ray scattering from atoms and molecules is presented. The method utilizes electronic wavefunctions calculated using ab-initio electronic structure methods. Wavefunctions expressed in Gaussian type orbitals allow for efficient calculations based on analytical Fourier transforms of the electron density and overlap integrals. The method is validated by extensive calculations of inelastic cross-sections in H, He+, He, Ne, C, Na and N2. The calculated cross-sections are compared to cross-sections from inelastic X-ray scattering experiments, electron energy-loss spectroscopy, and theoretical reference values. We then begin to account for the effect of nuclear motion, in the first instance by predicting elastic X-ray scattering from state-selected molecules. We find strong signatures corresponding to the specific vibrational and rotational state of (polyatomic) molecules. The ultimate goal of this thesis is to study atomic and molecular wavepackets using time-resolved X-ray scattering. We present a theoretical framework based on quantum electrodynamics and explore various elastic and inelastic limits of the scattering expressions. We then explore X-ray scattering from electronic wavepackets, following on from work by other groups, and finally examine the time-resolved X-ray scattering from non-adiabatic electronic-nuclear wavepackets in the H2 molecule, demonstrating the importance of accounting for the inelastic effects.

Secondary structure dynamics of biopolymers play a vital role in many of the complex processes within a cell. However, due to the substantial number of atoms in the involved biopolymers along with the multitude of interactions that occur between the molecules, understanding these processes in detail is challenging and often involves computationally demanding simulations. In this thesis, the secondary structure dynamics of three different biopolymer systems were modeled using a single approach, which is based on intuitive principles that facilitate the interpretation. To this end, the kinetic behavior of each system was experimentally determined, and described by simplified reaction schemes, which were then connected to Markov chain models encompassing all principal secondary structural conformations. Firstly, we investigated the toehold-mediated strand displacement reaction, which is widely applied in nanotechnology to create DNA-based nano-devices and biochemical reaction networks. Our model correctly described the impact of base pair mismatches on the kinetics of these reactions, as measured by bulk fluorescence experiments. Additionally, it revealed that incumbent dissociation, base pair fraying, and internal loop formation are important processes during strand displacement. Furthermore, we established two dissipative elements to enhance temporal control over toehold-mediated strand displacement reactions. The first element allowed a reversible and repeatable incumbent strand release, whereas the second element provided the possibility to start the displacement reaction after a programmable temporal delay. Secondly, we studied the target recognition by the CRISPR-Cas effector complex Cascade, a highly promising protein for applications in genome engineering. Our model successfully reproduced all aspects of the torque- and mismatch-dependent R-loop formation time by Cascade obtained by single-molecule torque and bulk fluorescence measurements. Furthermore, we demonstrated that the seed effect observed for Cascade results from DNA supercoiling, rather than a structural property of the protein complex. Lastly, we explored the folding/unfolding of α-helices, which plays a critical role in the folding and function of proteins. Our model accurately described α-helix unfolding kinetics obtained by fast triplet-triplet energy transfer. Moreover, we showed that the complex α-helix unfolding does not follow a simple Einstein-type diffusion but is a combination of the sub-diffusive boundary diffusion and the rather peptide-length-independent coil nucleation. The presented models enabled access to the diverse timescales of the characterized processes, which are generally difficult to access experimentally, despite utilizing just a single approach. In particular, we obtained: tens of microseconds for the branch migration step time of the toehold-mediated strand displacement, hundreds of microseconds for the R-loop formation steps by Cascade, and tens of nanoseconds for folding or unfolding of an α-helix by a single residue. Given the simplicity and accessibility of the established models, we are confident that they will become useful tools for researchers to analyze the dynamics of biomolecules, and anticipate that similar modeling approaches can be applied to other biopolymer systems, being well-described by probabilistic models. / Die Sekundärstrukturdynamik von Biopolymeren spielt eine entscheidende Rolle bei vielen komplexen Prozessen innerhalb einer Zelle. Aufgrund der beträchtlichen Anzahl von Atomen in den beteiligten Biopolymeren und der Vielzahl an Wechselwirkungen zwischen den Molekülen ist es jedoch eine Herausforderung diese Prozesse im Detail zu verstehen, und erfordert oft rechenintensive Simulationen. In dieser Arbeit wurde die Sekundärstrukturdynamik von drei verschiedenen Biopolymersystemen mit einem einzigen Ansatz modelliert, welcher auf intuitiven Prinzipien beruht und somit eine erleichterte Interpretation der Ergebnisse ermöglicht. Hierzu wurde das kinetische Verhalten jedes Systems experimentell bestimmt und durch vereinfachte Reaktionsschemata beschrieben. Diese wurden anschließend mit Markov-Kettenmodellen verknüpft, welche alle wichtigen Konformationen der Sekundärstruktur abbilden. Als erstes System untersuchten wir die DNA Strangaustauschreaktion, welche in der Nanotechnologie häufig zur Herstellung von DNA-basierten Nanomaschinen und biochemischen Reaktionsnetzwerken eingesetzt wird. Unser Modell beschrieb die durch Ensemble-Fluoreszenz-Experimente gemessenen Auswirkungen von Basenfehlpaarungen auf die Kinetik dieser Reaktionen korrekt. Des Weiteren zeigte sich, dass die vorzeitige Strangablösung, das Ausfransen von Basenpaaren und die Bildung interner Schleifen wichtige Prozesse während des Strangaustausches sind. Darüber hinaus konnten wir zwei dissipative Elemente etablieren, um die zeitliche Kontrolle über die Strangaustauschreaktionen zu verbessern. Das erste Element ermöglicht eine reversible und wiederholbare Strangablösung, während das zweite Element die Möglichkeit bietet die Strangaustauschreaktionen nach einer programmierbaren zeitlichen Verzögerung zu starten. Zweitens untersuchten wir den Zielerkennungsprozess durch den CRISPR-Cas Komplex Cascade, ein vielversprechendes Protein für Anwendungen in der Genomtechnologie. Unser Modell reproduzierte erfolgreich alle Aspekte der torsions- und fehlpaarungs-abhängigen R-Schleifenbildung durch Cascade, welche durch Einzelmolekül-Torsions- und Ensemble-Fluoreszenz-Messungen ermittelt wurden. Zusätzlich konnten wir nachweisen, dass der für Cascade beobachtete „seed“-Effekt auf DNA-Verdrehung und nicht auf eine strukturelle Eigenschaft des Proteinkomplexes zurückzuführen ist. Schließlich untersuchten wir die Faltung/Entfaltung von α-Helices, welche eine entscheidende Rolle bei der Faltung und Funktion von Proteinen spielen. Unser Modell beschrieb die durch schnelle Triplett-Triplett-Energietransfer Experimente ermittelte α-Helix-Entfaltungskinetik exakt. Darüber hinaus konnten wir zeigen, dass die komplexe α-Helix-Entfaltung nicht einer einfachen Diffusion vom Einstein-Typ folgt, sondern eine Kombination aus subdiffusiver Grenzdiffusion und der eher peptidlängenunabhängigen Coil-Nukleation ist. Obwohl nur ein einziger Ansatz verwendet wurde, ermöglichten die vorgestellten Modelle den Zugang zu den vielschichtigen Zeitskalen der charakterisierten Prozesse, welche im Allgemeinen experimentell schwer zugänglich sind. Insbesondere konnten die folgenden zeitlichen Bereiche bestimmt werden: Dutzende von Mikrosekunden für die Schrittzeit der Strangaustauschreaktion, Hunderte von Mikrosekunden für die Schritte der R-Schleifenbildung durch Cascade, und Dutzende von Nanosekunden für die Faltung oder Entfaltung einer α-Helix um ein einzelnes Segment. Angesichts der Simplizität und Zugänglichkeit der etablierten Modelle sind wir zuversichtlich, dass sie zu nützlichen Werkzeugen für Forscher werden, um die Dynamik von Biomolekülen zu analysieren. Zusätzlich gehen wir davon aus, dass ähnliche Modellierungsansätze auf andere Biopolymersysteme angewendet werden können, sofern sie gut durch probabilistische Modelle beschrieben werden.

Ce document propose une modélisation indirecte par sous-structuration des vibrations d'origine ferroviaire transmises aux bâtiments par le sol. La méthodologie globale est empruntée à la méthode des mobilités dans laquelle chaque sous-structure est caractérisée par sa mobilité. L'excitation est représentée par une force ponctuelle en surface du sol ou par une ligne de forces décorréllées. Elle est néanmoins calibrée sur des résultats expérimentaux. Une attention particulière a été portée à la caractérisation des comportements vibratoires des éléments du problème. La plupart des représentations de l'ensemble sol-fondations est effectuée à l'aide d'un code FEM-BEM en 2 et 2.5 dimensions. Le bâtiment est modélisé par différentes techniques : FEM, BEM, SEA et ondulatoire. Une approche probabiliste permet d'évaluer l'impact de la variabilité des sols environnent sur la mobilité des fondations. Les impédances stochastiques qui en découlent sont intégrées aux modèles de propagation. Leurs impacts sur les vibrations du bâtiment sont alors accessibles. La méthodologie permet d'obtenir les niveaux vibratoires des composantes du bâtiment / This document proposes an approach by sub-structuralization of the problem of the vibrations of railroad origin passed on in buildings by the soil. The global methodology is borrowed from the method of the mobilities, every sub-structure is characterized by its mobility. The excitement is represented by an on-surface punctual strength of the ground or by a line of uncorrelated forces. Nevertheless it can be calibrated on experimental results. A particular attention was carried in the characterization of the vibratory behavior of the elements of the problem. A major left the representations of the group soil-foundation is made by a FEM-BEM code. The building is modelled by various techniques: FEM, BEM, SEA and waves approach. A probability approach allows to estimate the impact of the variability of soil close to foundations in the model of soil-structure interaction. The stochastic impedances which ensues from it are integrated into the models of propagation. Their impacts on the vibrations of the building are also accessible. The methodology allows to obtain the vibratory levels of the components of the building

We use an agent-based model to investigate the interdependent dynamics between individual agency and emergent socioeconomic structure, leading to institutional change in a generic way. Our model simulates the emergence and exit of institutional units, understood as generic governed social structures. We show how endogenized trust and exogenously given leader authority influences institutional change, i.e., diversity in institutional life-cycles. It turns out that these governed institutions (de)structure in cyclical patterns dependent on the overall evolution of trust in the artificial society, while at the same time, influencing this evolution by supporting social learning. Simulation results indicate three scenarios of institutional life-cycles. Institutions may, (1) build up very fast and freeze the artificial society in a stable but fearful pattern (ordered system); (2) exist only for a short time, leading to a very trusty society (highly fluctuating system); and (3) structure in cyclical patterns over time and support social learning due to cumulative causation of societal trust (complex system).

Este trabalho descreve um modelo matemático para simulação da laringe humana durante a fonação. O objetivo foi produzir uma técnica computacional de grande escala de processamento para capturar os fenômenos fisiológicos que ocorrem na laringe durante a vocalização e servir de base para estudos mais aprofundados sobre esta importante estrutura do corpo humano. Usando o método dos elementos finitos como base para discretizar as equações dos tecidos musculares da laringe e das equações de Navier-Stokes, e um modelo de descrição da colisão entre as pregas vocais, o sinal glotal foi obtido a partir de diferentes geometrias de laringes com diferentes propriedades viscoelásticas. Os resultados confirmaram a teoria mioelástica-aerodinâmica que descreve a dinâmica da fonação, reproduzindo inclusive fenômenos fisiológicos que os modelos existentes são incapazes de simular. Estudos adicionais foram feitos para verificar a viabilidade do modelo para simular algumas doenças que danificam a laringe. / This work describes a mathematical model to simulate the human larynx during a phonation. The objective was to produce a large-scale computational technique to capture several physiological phenomena that take place on the larynx during the vocalization and to assist further studies about this important structure of the human body. Using the finite element methods as the way to discretize the muscle tissue equations of the larynx and the Navier-Stokes equations and a model to describe the collision between both vocal folds, the glottal signal for different larynx geometries with different viscoelastic properties was obtained. The results confirmed the myoelastic-aerodynamic theory which describes the dynamic of the phonation, also reproducing physiologic phenomena that current models are unable to simulate. Additional studies were conducted to confirm the feasibility of the model to simulate some diseases that affect the larynx.

Uncertainty involved in the safe and comfort design of the structures is a major concern of civil engineers. Traditionally, the uncertainty has been overcome by utilizing various and relatively large safety factors for loads and structural properties. As a result in conventional design of for example tall buildings, the designed structural elements have unnecessary dimensions that sometimes are more than double of the ones needed to resist normal loads. On the other hand the requirements for strength and safety and comfort can be conflicting. Consequently, an alternative approach for design of the structures may be of great interest in design of safe and comfort structures that also offers economical advantages. Recently, there has been growing interest among the researchers in the concept of structural control as an alternative or complementary approach to the existing approaches of structural design. A few buildings have been designed and built based on this concept. The concept is to utilize a device for applying a force (known as control force) to encounter the effects of disturbing forces like earthquake force. However, the concept still has not found its rightful place among the practical engineers and more research is needed on the subject. One of the main problems in structural control is to find a proper algorithm for determining the optimum control force that should be applied to the structure. The investigation reported in this thesis is concerned with the application of active control to civil engineering structures. From the literature on control theory. (Particularly literature on the control of civil engineering structures) problems faced in application of control theory were identified and classified into two categories: 1) problems common to control of all dynamical systems, and 2) problems which are specially important in control of civil engineering structures. It was concluded that while many control algorithms are suitable for control of dynamical systems, considering the special problems in controlling civil structures and considering the unique future of structural control, many otherwise useful control algorithms face practical problems in application to civil structures. Consequently a set of criteria were set for judging the suitability of the control algorithms for use in control of civil engineering structures. Various types of existing control algorithms were investigated and finally it was concluded that predictive optimal control algorithms possess good characteristics for purpose of control of civil engineering structures. Among predictive control algorithms, those that use ARMA stochastic models for predicting the ground acceleration are better fitted to the structural control environment because all the past measured excitation is used to estimate the trends of the excitation for making qualified guesses about its coming values. However, existing ARMA based predictive algorithms are devised specially for earthquake and require on-line measurement of the external disturbing load which is not possible for dynamic loads like wind or blast. So, the algorithms are not suitable for tall buildings that experience both earthquake and wind loads during their life. Consequently, it was decided to establish a new closed loop predictive optimal control based on ARMA models as the first phase of the study. In this phase it was initially established that ARMA models are capable of predicting response of a linear SDOF system to the earthquake excitation a few steps ahead. The results of the predictions encouraged a search for finding a new closed loop optimal predictive control algorithm for linear SDOF structures based on prediction of the response by ARMA models. The second part of phase I, was devoted to developing and testing the proposed algorithm The new developed algorithm is different from other ARMA based optimal controls since it uses ARMA models for prediction of the structure response while existing algorithms predict the input excitation. Modeling the structure response as an AR or ARMA stochastic process is an effective mean for prediction of the structure response while avoiding measurement of the input excitation. ARMA models used in the algorithm enables it to avoid or reduce the time delay effect by predicting the structure response a few steps ahead. Being a closed loop control, the algorithm is suitable for all structural control conditions and can be used in a single control mechanism for vibration control of tall buildings against wind, earthquake or other random dynamic loads. Consequently the standby time is less than that for existing ARMA based algorithms devised only for earthquakes. This makes the control mechanism more reliable. The proposed algorithm utilizes and combines two different mathematical models. First model is an ARMA model representing the environment and the structure as a single system subjected to the unknown random excitation and the second model is a linear SDOF system which represents the structure subjected to a known past history of the applied control force only. The principle of superposition is then used to combine the results of these two models to predict the total response of the structure as a function of the control force. By using the predicted responses, the minimization of the performance index with respect to the control force is carried out for finding the optimal control force. As phase II, the proposed predictive control algorithm was extended to structures that are more complicated than linear SDOF structures. Initially, the algorithm was extended to linear MDOF structures. Although, the development of the algorithm for MDOF structures was relatively straightforward, during testing of the algorithm, it was found that prediction of the response by ARMA models can not be done as was done for SDOF case. In the SDOF case each of the two components of the state vector (i.e. displacement and velocity) was treated separately as an ARMA stochastic process. However, applying the same approach to each component of the state vector of a MDOF structure did not yield satisfactory results in prediction of the response. Considering the whole state vector as a multi-variable ARMA stochastic vector process yielded the desired results in predicting the response a few steps ahead. In the second part of this phase, the algorithm was extended to non-linear MDOF structures. Since the algorithm had been developed based on the principle of superposition, it was not possible to directly extend the algorithm to non-linear systems. Instead, some generalized response was defined. Then credibility of the ARMA models in predicting the generalized response was verified. Based on this credibility, the algorithm was extended for non-linear MDOF structures. Also in phase II, the stability of a controlled MDOF structure was proved. Both internal and external stability of the system were described and verified. In phase III, some problems of special interest, i.e. soil-structure interaction and control time delay, were investigated and compensated for in the framework of the developed predictive optimal control. In first part of phase III soil-structure interaction was studied. The half-space solution of the SSI effect leads to a frequency dependent representation of the structure-footing system, which is not fit for control purpose. Consequently an equivalent frequency independent system was proposed and defined as a system whose frequency response is equal to the original structure -footing system in the mean squares sense. This equivalent frequency independent system then was used in the control algorithm. In the second part of this phase, an analytical approach was used to tackle the time delay phenomenon in the context of the predictive algorithm described in previous chapters. A generalized performance index was defined considering time delay. Minimization of the generalized performance index resulted into a modified version of the algorithm in which time delay is compensated explicitly. Unlike the time delay compensation technique used in the previous phases of this investigation, which restricts time delay to be an integer multiplier of the sampling period, the modified algorithm allows time delay to be any non-negative number. However, the two approaches produce the same results if time delay is an integer multiplier of the sampling period. For evaluating the proposed algorithm and comparing it with other algorithms, several numerical simulations were carried during the research by using MATLAB and its toolboxes. A few interesting results of these simulations are enumerated below: ARM A models are able to predict the response of both linear and non-linear structures to random inputs such as earthquakes. The proposed predictive optimal control based on ARMA models has produced better results in the context of reducing velocity, displacement, total energy and operational cost compared to classic optimal control. Proposed active control algorithm is very effective in increasing safety and comfort. Its performance is not affected much by errors in the estimation of system parameters (e.g. damping). The effect of soil-structure interaction on the response to control force is considerable. Ignoring SSI will cause a significant change in the magnitude of the frequency response and a shift in the frequencies of the maximum response (resonant frequencies). Compensating the time delay effect by the modified version of the proposed algorithm will improve the performance of the control system in achieving the control goal and reduction of the structural response.

Este trabalho descreve um modelo matemático para simulação da laringe humana durante a fonação. O objetivo foi produzir uma técnica computacional de grande escala de processamento para capturar os fenômenos fisiológicos que ocorrem na laringe durante a vocalização e servir de base para estudos mais aprofundados sobre esta importante estrutura do corpo humano. Usando o método dos elementos finitos como base para discretizar as equações dos tecidos musculares da laringe e das equações de Navier-Stokes, e um modelo de descrição da colisão entre as pregas vocais, o sinal glotal foi obtido a partir de diferentes geometrias de laringes com diferentes propriedades viscoelásticas. Os resultados confirmaram a teoria mioelástica-aerodinâmica que descreve a dinâmica da fonação, reproduzindo inclusive fenômenos fisiológicos que os modelos existentes são incapazes de simular. Estudos adicionais foram feitos para verificar a viabilidade do modelo para simular algumas doenças que danificam a laringe. / This work describes a mathematical model to simulate the human larynx during a phonation. The objective was to produce a large-scale computational technique to capture several physiological phenomena that take place on the larynx during the vocalization and to assist further studies about this important structure of the human body. Using the finite element methods as the way to discretize the muscle tissue equations of the larynx and the Navier-Stokes equations and a model to describe the collision between both vocal folds, the glottal signal for different larynx geometries with different viscoelastic properties was obtained. The results confirmed the myoelastic-aerodynamic theory which describes the dynamic of the phonation, also reproducing physiologic phenomena that current models are unable to simulate. Additional studies were conducted to confirm the feasibility of the model to simulate some diseases that affect the larynx.

Ce travail s’inscrit dans le cadre d’un partenariat international Airbus Safran Launchers ", " Ecole Centrale de Lyon " et " Ecole Nationale d’Ingénieurs de Tunis ". Les composés élastomériques sont largement utilisés dans l’industrie pour leurs déformabilité et leurs capacités d’amortissement. Soumis aux combinaisons complexes de fabrication et de charges de service, les élastomères montrent la capacité de subir des conditions de chargement sévères et le cas de pré-déformation statique superposée par une excitation dynamique de petite amplitude est couramment utilisé pour des applications industrielles, par exemple des pneus, des amortisseurs, applications aérospatiales ... Pour concevoir efficacement ces composés industriels, il est primordial de prédire la réponse des produits à travers des processus de modélisation simples qui ont multiplié les méthodes d’analyse: expérimentale, théorique et numérique. Dans ce contexte, le présent travail se concentre sur la conception et l’analyse des propriétés dynamiques d’un dispositif élastomère autour d’une configuration préformée. À cette fin, trois mélanges de caoutchouc ont été expérimentés: Caoutchouc naturel (NR), Bromobutyl (BIIR) et un mélange des deux (NR / BIIR). Une discussion est faite avec préoccupation pour la mise en place expérimentale ainsi que les procédures utilisées pour des essais expérimentaux efficaces. Avec ces conclusions, nous avons fait un jugement sur les capacités de prévision, dans les domaines temporels et fréquentiels, de certains modèles hyper-visco-élastique à base d’intégrale unique sous l’hypothèse de séparabilité des effets temps-déformation. Les modèles considérés sont largement utilisés pour les applications d’ingénierie. Ce travail est suivi d’une application sur un composant industriel. Dans le cadre de cette thèse, le code de calcul d’éléments finis ABAQUS 6.14 a été utilisé pour étudier les propriétés dynamiques de cette structure. Une méthodologie d’analyse a été présentée pour identifier soigneusement l’ensemble des paramètres dans le but de satisfaire certaines exigences industrielles, principalement des capacités de masse, de rigidité et d’amortissement. / This work is conducted as international collaboration with " Airbus Safran Launchers ", " Ecole Centrale de Lyon " and " National Engineering School of Tunis ". Elastomeric compounds are widely used in industry for their high deformability and damping capabilities. Subjected to complex combinations of manufacturing and service loadings, elastomers show the fact to undergo severe loading conditions and the load case of large static predeformation superimposed by small amplitude dynamic excitation is commonly encountred for industrial applications e.g tires, shock-absorbing bushes, construction industry, aerospace applications... To design such industrial compounds efficiently, it is of major importance to predict the response of the products through simple modeling processes which have multiplied analysis methods: experimental, theoretical and numerical. Within this context, the present work focuses on design and analysis of dynamic properties of an elastomeric device at a predeformed configuration. To this end, three rubber mixtures have been experimentally investigated: Natural Rubber (NR), Bromobutyl (BIIR) and a mixture of both (NR/BIIR). A discussion is made with concern to experimental set-up as well as the used procedures for an efficient specimens testings. Within these findings, we made judgement on the predictive capabilities, in time and frequency domains, of some single integral based hyper-visco-elastic models under time-strain seperability assumption. The considered models are widely used for engineering applications and focus have been made on the Simo model implemented in finite element commercial software Abaqus. This work is followed by an application on an industrial component. In the framework of this thesis, the finite element calculation code ABAQUS 6.14 was used to investigate the dynamic properties of such structure. An analysis methodology have been presented to carefully identify the set of parameters with the objective of satisfaction of some industrial requirements mainly mass, stiffness and damping capabilities.