This thesis concerns the analysis of dynamical systems suitable to be modelled by piecewise-smooth differential equations. In such systems the continuous-in-time dynamics is interrupted by discrete-in-time jumps in the state or governing equations of motion. Not only can this framework be used to describe existing systems with strong nonlinear behaviour such as impacts and friction, but the non-smooth properties can be exploited to design new mechanical devices. As suggested in this work it opens up the possibility of, for example, fast limit switches and energy transfer mechanisms. Particularly, the dynamics at the onset of low-velocity impacts in systems with recurrent dynamics, so called grazing bifurcations in impact-oscillators, are investigated. As previous work has shown, low-velocity impacts is a strong source of instability to the dynamics, and efforts to control the behaviour is of importance. This problem is approached in two ways in this work. One is to investigate the influence of parameter variations on the dynamic behaviour of the system. The other is to implement low-cost control strategies to regulate the dynamics at the grazing bifurcation. The control inputs are of impulsive nature, and utilizes the natural dynamics of the system to the greatest extent. The scientific contributions of this work is collected in five appended papers. The first paper consists of an experimental verification of a map that captures the correction to the smooth dynamics induced by an impact, known in the literature as the discontinuity map. It is shown that the lowest order expansion of the map accurately captures the transient growth rate of impact velocities. The second paper presents a constructive proof of a control algorithm for a rather large class of impact oscillators. The proof is constructive in the sense that it gives control parameters which stabilizes the dynamics at the onset of low-velocity impacts. In the third paper a piecewise-smooth quarter-car model is derived, and the control strategy is implemented to reduce impact velocities in the suspension system. In the fourth and fifth papers the grazing bifurcation of an impact oscillator with dry friction type damping is investigated. It turns out that the bifurcation is triggered by the disappearance of an interval of stable stick solutions. A condition on the parameters of the system is derived which differentiates between stable and unstable types of bifurcation scenarios. Additionally, a low-cost control strategy is proposed, similar to the one previously mentioned, to regulate the bifurcation scenario. / QC 20100811

L’utilisation industrielle ou militaire des explosifs est largement répandue. La sécurité est devenue un axe majeur avec notamment l’ignition involontaire des explosifs composés de HMX lors des impacts à basse vitesse. L’objectif de cette thèse est de contribuer à la compréhension des mécanismes dissipatifs à l’origine des échauffements locaux dans le matériau. Le développement d’un essai aux barres d’Hopkinson a permis de coupler de grandes vitesses de déformations à des pressions élevées pour compléter les données expérimentales. Cet essai a montré un angle de frottement quasiment identique à celui obtenu en quasistatique mais une contrainte de cohésion supérieure d’environ 25 MPa. Ensuite, pour observer les mécanismes pouvant être sources d’échauffement, un essai de compression dans la tranche a été développé avec des observations en temps réel. Celles-ci ont permis de conclure qu’il y a très peu de frottements entre les gros grains et la matrice (l’ensemble des petits grains, du liant et de la porosité). De la plasticité des grains de HMX a pu être observée mais surtout beaucoup d’endommagement dans certaines zones y compris dans la matrice. Une microfissuration très intense de certains grains a été observée. Parallèlement, une représentation numérique biphasique (gros grains de HMX et matrice) de toute la microstructure du matériau a été considérée. Une confrontation entre les observations expérimentales et les simulations a permis de déterminer le seuil de plasticité du HMX. Le comportement de la matrice a été identifié pour prendre en compte l’effet de vitesse et l’endommagement observé. Enfin, les confrontations entre les essais et les simulations de ceux-ci ont montré que les échauffements devraient plutôt se localiser dans la matrice que dans les gros grains de HMX et que le mécanisme le plus probable est le frottement de lèvres de microfissures. / Safety of industrial or military explosives is a major focus to prevent inadvertent ignition due to accidental loading as, for example, low-velocity impact. Our aim is to understand the dissipative mechanisms at work which could heat a pressed HMX-based PBX. A test based on the Split Hopkinson Pressure Bars system is proposed to carry out a dynamic triaxial compression test. This test simultaneously associates a high strain rate and a high pressure. Data have shown almost the same friction angle as during quasi-static experiments, but a higher cohesive stress. Then, A reversed edge-on impact test has been developed. This experiment enables the real-time observation of the deformation mechanisms at the microstructural scale. No relative displacement is observed between the biggest HMX grains and the matrix made of the smallest grains, the binder and the porosity. Plasticity has been observed into some HMX grains as well as damage by microcracking. Meanwhile, a biphasic (HMX grains and matrix) numerical representation of the material microstructure has been considered. A comparison between experimental observations and simulations is used to determine the yield stress of HMX. The behavior of the matrix has been determined to account for the influence of the strain rate and of the damage. Lastly, a comparison between tests and simulations has highlighted (1) that heating should rather be located in the matrix than in the biggest HMX grains and (2) that the most likely heating mechanism is the friction of microcracks lips.