PATTERN EVALUATION FOR IN-PLANE DISPLACEMENT MEASUREMENT OF THIN FILMS

The term Gossamer is used to describe ultra-lightweight spacecraft structures that solve the aerospace challenge of obtaining maximum performance while reducing the launch costs of the spacecraft. Gossamer structures are extremely compliant, which complicates control design and ground testing in full scale. One approach is to design and construct smaller test articles and verify their computational models experimentally, so that similar computational models can be used to predict the dynamic performance of full-scale structures. Though measurement of both in-plane and out-of-plane displacements is required to characterize the dynamic response of the surface of these structures, this thesis lays the groundwork for dynamic measurement of the in-plane component. The measurement of thin films must be performed using non-contacting sensors because any contacting sensor would change the dynamics of the structure. Moreover, the thin films dealt with in this work are coated with either gold or aluminum for special applications making the film optically smooth and therefore requiring a surface pattern. A Krypton Fluoride excimer laser system was selected to fabricate patterns on thin-film mirror test articles. Parameters required for pattern fabrication were investigated. Effects of the pattern on the thin-film dynamics were studied using finite element analysis. Photogrammetry was used to study the static in-plane displacement of the thin-film mirror. This was performed to determine the feasibility of the photogrammetric approach for future dynamic tests. It was concluded that photogrammetry could be used efficiently to quantify dynamic in-plane displacement with high-resolution cameras and sub-pixel target marking

Outils analytiques et numériques pour l'étude des bifurcations rasantes d'orbites périodiques et de tores invariants

The objective of this dissertation is to develop theoretical and computational tools for the study of qualitative changes in the dynamics of systems with discontinuities, also known as nonsmooth or hybrid dynamical systems, under parameter variations. Accordingly, this dissertation is divided into two parts.The analytical section of this dissertation discusses mathematical tools for the analysis of hybrid dynamical systems and their application to a series of model examples. Specifically, qualitative changes in the system dynamics from a nonimpacting to an impacting motion, referred to as grazing bifurcations, are studied in oscillators where the discontinuities are caused by impacts. Here, the study emphasizes the formulation of conditions for the persistence of a steady state motion in the immediate vicinity of periodic and quasiperiodic grazing trajectories in an impacting mechanical system. A local analysis based on the discontinuity-mapping approach is employed to derive a normal-form description of the dynamics near a grazing trajectory. Also, the results obtained using the discontinuity-mapping approach and direct numerical integration are found to be in good agreement. It is found that the instabilities caused by the presence of the square-root singularity in the normal-form description affect the grazing bifurcation scenario differently depending on the relative dimensionality of the state space and the steady state motion at the grazing contact. The computational section presents the structure and applications of a software program, $\hat{\text{TC}}$, developed to study the bifurcation analysis of hybrid dynamical systems. Here, we present a general boundary value problem (BVP) approach to locate periodic trajectories corresponding to a hybrid dynamical system under parameter variations. A methodology to compute the eigenvalues of periodic trajectories when using the BVP formulation is illustrated using a model example. Finally, bifurcation analysis of four model hybrid dynamical systems is performed using $\hat{\text{TC}}$.L'objectif de ce travail est de développer des outils théoriques et informatiques dédiés à l'étude des changements de dynamique de systèmes avec discontinuitéss, aussi répondant au nom de "systèmes hybrides" ou "systèmes non-réguliers"