A large body of literature exists regarding linear and nonlinear dynamic absorbers, but the vast majority of it deals with linear primary structures. However, nonlinearity is a frequency occurrence in engineering applications. Therefore, the present thesis focuses on the mitigation of vibrations of nonlinear primary systems using nonlinear dynamic absorbers. Because most existing contributions about their design rely on optimization and sensitivity analysis procedures, which are computationally demanding, or on analytic methods, which may be limited to small-amplitude motions, this thesis sets the emphasis on a tuning procedure of nonlinear vibration absorbers that can be computationally tractable and treat strongly nonlinear regimes of motion. The proposed methodology is a two-step procedure relying on a frequency-energy based approach followed by a bifurcation analysis. The first step, carried out in the free vibration case, imposes the absorber to possess a qualitatively similar dependence on energy as the primary system. This gives rise to an optimal nonlinear functional form and an initial set of absorber parameters. Based upon these initial results, the second step, carried out in the forced vibration case, exploits the relevant information contained within the nonlinear frequency response functions, namely, the bifurcation points. Their tracking in parameter space enables the adjustment of the design parameter values to reach a suitable tuning of the absorber. The use of the resulting integrated tuning methodology on nonlinear vibration absorbers coupled to systems with nonlinear damping is then investigated. The objective lies in determining an appropriate functional form for the absorber so that the limit cycle oscillation suppression is maximized. Finally, the proposed tuning methodology of nonlinear vibration absorbers may impose the use of complicated nonlinear functional forms whose practical realization, using mechanical elements, may be difficult. In this context, an electro-mechanical nonlinear vibration absorber relying on piezoelectric shunting possesses attractive features as various functional forms for the absorber nonlinearity can be achieved through proper circuit design. The foundation of this new approach are laid down and the perspectives are discussed.

Dans ce travail, des méthodes itératives ont été étudiées afin de préparer des oligomères à séquences bien définies en utilisant des supports solides ou solubles. Trois stratégies de couplage de monomères ont été exploitées (i) AB + AB, (ii) AB + CD et (iii) AA + BB. La première méthode a permis la synthèse d’oligopeptides en utilisant les protocoles classiques de la synthèse peptidique à partir notamment d’amino-acides protégés par des groupements Fmoc. Les deux autres stratégies ont permis de préparer des oligo(alcoxyamine amide)s et des oligoamides, en l’absence de groupements protecteurs. Dans ces cas, le contrôle de la structure primaire de l’oligomère a été rendu possible soit par l’utilisation de réactions chimio-sélectives (AB + CD) soit en introduisant un large excès de monomères bifonctionnels (AA + BB). Ainsi, les oligo(alkoxyamine amide)s ont été préparés en utilisant des couplages successifs de bromo-anhydride et d’amino-nitroxide ; et les oligoamides ont été obtenus par couplages de diacides et de diamines.L'approche pratique permettant la formation de ces oligomères à séquence contrôlée ainsi que leur caractérisation seront décrites dans cette thèse. / In this work, iterative methods have been studied to prepare sequence-defined oligomers on solid and soluble supports. Three model monomer coupling strategies have been exploited, (i) AB + AB, (ii) AB + CD and (iii) AA + BB, for the synthesis of oligopeptides, oligo(alkoxyamine amide)s and oligoamides, respectively. In the first strategy (AB + AB), oligopeptides have been synthesized using classical peptide synthesis protocols, in which Fmoc-protected amino acids were used. The other two strategies (AB + CD and AA + BB) are protecting-group free methods. In this case, the control over the oligomer primary structure has been achieved using chemoselective reactions (AB + CD) or a large excess of bifunctional monomers (AA + BB). The oligo(alkoxyamine amide)s have been prepared using successive coupling of bromo-anhydride and amino-nitroxide building blocks. The oligoamides have been obtained by sequential coupling of diacid and diamine building blocks. The practical approach to these primary structures using solid- and liquid-phase methodologies followed by the characterization of formed oligomers is the scope of this thesis.