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Large-amplitude vibration of thin plates and shells has been critical design issues for many engineering structures. The increasingly more stringent safety requirements and the discovery of new materials with amazingly superior properties have further focused the attention of research on this area. This thesis deals with the vibration problem of rectangular, circular and angle-ply composite plates. This vibration can be triggered by an initial vibration amplitude, or an initial velocity, or both. Four types of boundary conditions including simply supported and clamped combined with in-plane movable/immovable are considered. To solve the differential equation generated from the vibration problem, Lindstedt's perturbation technique and Runge-Kutta method are applied. In previous works, this problem was solved by Lindstedt's Perturbation Technique. This technique can lead to a quick approximate solution. Yet based on mathematical assumptions, the solution will no longer be accurate for large amplitude vibration, especially when a significant amount of imperfection is considered. Thus Runge-Kutta method is introduced to solve this problem numerically. The comparison between both methods has shown the validity of the Lindstedt's Perturbation Technique is generally within half plate thickness. For a structure with a sufficiently large geometric imperfection, the vibration can be represented as a well-known backbone curve transforming from soften-spring to harden-spring. By parameter variation, the effects of imperfection, damping ratio, boundary conditions, wave numbers, young's modulus and a dozen more related properties are studied. Other interesting research results such as the dynamic failure caused by out-of-bound vibration and the change of vibration mode due to damping are also revealed.

Environmental, aesthetic and political pressures continue to push for siting off-shore wind turbines beyond sight of land, where waters tend to be deeper, and use of floating structures is likely to be considered. Savings could potentially be realized by reducing hull size, which would allow more compliance with the wind thrust force in the pitch direction. On the other hand, these structures with large-amplitude motions will make dynamic analysis both more challenging and more critical. Prior to the present work, there were no existing dynamic simulation tools specifically intended for compliant wind turbine design. Development and application of a new computational method underlying a new time-domain simulation tool is presented in this dissertation. The compliant floating wind turbine system is considered as a multibody system including tower, nacelle, rotor and other moving parts. Euler's equations of motion are first applied to the compliant design to investigate the large-amplitude motions. Then, a new formulation of multibody dynamics is developed through application of the conservation of both linear momentum and angular momentum to the entire system directly. A base body is prescribed within the compliant wind turbine system, and the equations of motion (EOMs) of the system are projected into the coordinate system associated with this body. Only six basic EOMs of the system are required to capture 6 unknown degrees of freedom (DOFs) of the base body when mechanical DOFs between contiguous bodies are prescribed. The 6 x 6 mass matrix is actually composed of two decoupled 3 x 3 mass matrices for translation and rotation, respectively. Each element within the matrix includes the inertial effects of all bodies. This condensation decreases the coupling between elements in the mass matrix, and so minimizes the computational demand. The simulation results are verified by critical comparison with those of the popular wind turbine dynamics software FAST. The new formulation is generalized to form the momentum cloud method (M- CM), which is particularly well suited to the serial mechanical N-body systems connected by revolute joints with prescribed relative rotation. The MCM is then expanded to multibody systems with more complicated joints and connection types.

<p> The inter/intramolecular interactions and associations between constituents determine the microstructure of food and its response to mechanical deformation and flow. The characterization of food rheology enables the design of efficient processing equipment, production of high-quality, stable end products, prediction of textural and sensorial attributes, and assurance of consumer acceptability. Foods are subjected to rapid and large deformations during processing operations and consumption. Dynamic oscillatory shear tests are carried out by subjecting food to a sinusoidal deformation (or stress) and probing the mechanical stress (or strain) and recording the response as a function of time. In the SAOS region, the mechanical response is in the form of a perfect sinusoidal curve and interpretation is straightforward as expected from a linear model. On the other hand, LAOS response requires complex mathematical relations to extract meaningful rheological parameters. In this dissertation, Fourier Transform-Chebyshev Decomposition (FTC) and Sequence of Physical Processes (SPP) methods were utilized to quantify the LAOS response of selected food materials. The objective of this study is to gain new insights into the nonlinear rheology and structural architecture of food materials. To offer insights into the microstructure–rheology relations, rheological measurements were accompanied by various techniques probing chemical interactions (FTIR), imaging (Cryo-SEM, SEM), quantitative network analysis, and molecular size (SDS-PAGE). This dissertation showed that LAOS rheology is highly correlated with the network structure of food shown by the quantitative network analysis utilizing SEM images. It is a powerful tool to detect the effect of small molecules on the nonlinear rheology of food (HMW-LMW glutenin ratio, gliadin for dough, fat content in yogurt, and amylopectin/amylose ratio of starch in a suspension). Nonlinear parameters were sensitive to structural changes occurring in dough structure during processing conditions including aging at room and elevated temperatures. Lastly, the SPP method enabling time-resolved interpretation of nonlinear rheology provided detailed transient microstructural interpretations whereas the FTC method gave static measures at specific strains in an oscillation cycle. Thus, nonlinear rheology of doughs with various gluten subfractions in MAOS and LAOS regions as well as shear thickening characteristic of starch suspensions with changing amylopectin/amylose ratio interpreted by the SPP method gave more sensitive results than the FTC method. The application of fundamental knowledge from this work can be a guide to evaluating the architecture and nonlinear rheology of food for the assurance of consumer acceptancy and the fabrication of efficient machinery by building more accurate mechanical models of complex food systems. </p>

Dans cette thèse ont été développés de nouveaux outils de calcul théorique de spectres moléculaires rovibrationnels qui permettent de mieux traiter les états vibrationnels très excités ainsi que les mouvements de grandes amplitudes avec la méthode d’interactions de configurations en champ moyen. Dans un premier temps, nous avons discuté la question du choix des bases modales et les différents compromis à trouver afin de pallier aux défauts possibles des surfaces d'énergie potentielle. Dans ce cadre nous avons également développé un critère de sélection visant à améliorer la qualité des fonctions d'ondes rovibrationnelles de base. Ces approches ont été appliquées avec succès à la molécule de méthane CH4.Dans un second temps, nous avons implémenté un algorithme de calcul formel des opérateurs d'énergie cinétique en coordonnées quelconques qui permet d'avoir des expressions exactes ainsi que leurs développements en série de Taylor ou Fourier, qui exploite au mieux les potentialités du logiciel MATHEMATICA et a permis d'obtenir des hamiltoniens rovibrationnels en coordonnées de valence de façon particulièrement efficace. Enfin, nous avons généralisé la méthode d’interactions de configurations en champ moyen en ajoutant de façon perturbative un champ effectif d'ordre deux. Nous avons appliqué cette généralisation à la molécule de péroxyde d'hydrogène HOOH, ce qui a permis de montrer son intérêt tant pour l'amélioration des niveaux d'énergie que des fonctions d'onde associées, lorsqu'on a affaire à des groupes de degrés de liberté bien séparés énergétiquement. / In this thesis we developed new theoretical tools for molecular rovibrational spectra for a better description of the excited vibrational states and movements with large amplitudes using mean field configuration interaction method. First, we discussed the choice of modal basis and different trade-off to overcome the possible shortcomings of potential energy surfaces. In this context we have also developed selection criteria to improve the quality of rovibrational wave functions. These approaches have been successfully applied to the methane molecule (CH4). Secondly, we have implemented a formal algorithm for calculating the kinetic energy operators in arbitrary coordinates that allows the derivation of exact expressions and their Taylor and Fourier series, using, in a very efficient way, the capabilities of the software MATHEMATICA which yield to the derivation of rovibrational Hamiltonians in valence coordinated. Finally, we have generalized the mean-field configuration interaction method by adding perturbatively a second order effective field. We applied this generalization to the hydrogen peroxide molecule (HOOH), which has shown an improvement for both energy levels and the associated wave functions, when dealing with groups of degrees of freedom that are energetically well separated.

A recently developed approach, in the area of nonlinear oscillations, is used to analyze the single degree of freedom equation of motion of a oating unit (such as a ship) about a critical axis (such as roll). This method makes use of a closed form analytic solution, exact upto the rst order, and takes into account the the complete unperturbed (no damping or forcing) dynamics. Using this method very-large-amplitude nonlinear vessel motion in a random seaway can be analysed with techniques similar to those used to analyse nonlinear vessel motions in a regular (periodic) or random seaway. The practical result being that dynamic capsizing studies can be undertaken considering the shortterm irregularity of the design seaway. The capsize risk associated with operation in a given sea state can be evaluated during the design stage or when an operating area change is being considered. Moreover, this technique can also be used to guide physical model tests or computer simulation studies to focus on critical vessel and environmental conditions which may result in dangerously large motion amplitudes. Extensive comparitive results are included to demonstrate the practical usefulness of this approach. The results are in the form of solution orbits which lie in the stable or unstable manifolds and are then projected onto the phase plane.

Acetylacetone (AcAc) exists as a mixture of enol and keto tautomers. Besides providing a good example for the study of tautomerization, it is a model system for investigating intramolecular hydrogen bonds in its enol form. Trapping AcAc in the soft para-Hydrogen (pH2 ) environment brings out new opportunities to investigate its properties. Infrared spectra of the samples give a good characterization of the two stable enol and keto tautomers. The keto/enol ratio in solid pH2 is found to be higher than in other matrices. While vibrational bands of keto are narrow, those of enol are broad, reflecting the intrinsic properties of the enol which exhibits three entangled large amplitude motions (two methyl torsions and the intramolecular hydrogen transfer). Surprisingly, narrowing of some of these bands is observed in a slow time evolution. This effect is interpreted as a consequence of nuclear spin conversion in the hydrogen atoms of the methyl groups, giving access to AcAc species differing by their nuclear spin symmetry. This offers new pertinent investigations on the large amplitude motions, especially on the intramolecular hydrogen transfer. AcAc/pH2 samples have been irradiated by UV laser beams. Irradiation at 266 nm induces isomerization from the stable chelated enol form to non chelated conformers, similarly to the case of other matrices. A clear IR signature of the conformers is obtained thanks to the pH2 host. Irradiation at 248 nm induces the enol/keto tautomerization. The kinetics of this interconversion highlights a non-direct process. Fragmentation is clearly observed under irradiation at 193 nm, followed by chemical reaction with the hydrogen host.

L’acétylacétone (AcAc) existe sous deux formes tautomères, énol et kéto. Sous sa forme énol chélaté, c’est une des molécules les plus simples présentant une liaison hydrogène intramoléculaire. Nous l’avons isolée dans la matrice « quantique » de parahydrogène (pH2) pour étudier ses propriétés en bénéficiant des avantages spécifiques de ce solide cryogénique. Les spectres infrarouges apportent une caractérisation claire des formes énol et kéto. Le rapport kéto/énol est plus important en matrice de pH2 que dans les autres matrices. Les bandes du kéto sont fines alors que certaines bandes de l’énol sont très larges à cause de la présence de la liaison hydrogène. Plusieurs bandes s’affinent très lentement avec le temps. Cet effet surprenant a été interprété en terme de conversion nucléaire de spin dans un groupement méthyle d’AcAc, donnant accès aux spectres de niveaux de torsion différents. Les résultats offrent alors un nouveau moyen d’investigation des mouvements de grande amplitude de la molécule (mouvements couplés de torsion des méthyles et du transfert d’hydrogène interne). La photolyse UV des matrices AcAc/pH2 a été étudiée. Une irradiation à 266 nm conduit à l’isomérisation de l’énol sous différentes formes non chélatées ; des spectres très bien résolus de ces formes sont obtenus grâce aux propriétés du pH2 solide. En irradiant à 248 nm, on observe la tautomérisation vers la forme kéto, l’étude cinétique démontrant que le processus n’est pas direct à partir de l’énol chélaté. Enfin, une irradiation à 193 nm provoque la fragmentation de la molécule, processus qui peut être suivi de réactions avec l’hydrogène de la matrice. / Acetylacetone (AcAc) exists as a mixture of enol and keto tautomers. Besides providing a good example for the study of tautomerization, it is a model system for investigating intramolecular hydrogen bonds in its enol form. Trapping AcAc in the soft para-Hydrogen (pH2 ) environment brings out new opportunities to investigate its properties. Infrared spectra of the samples give a good characterization of the two stable enol and keto tautomers. The keto/enol ratio in solid pH2 is found to be higher than in other matrices. While vibrational bands of keto are narrow, those of enol are broad, reflecting the intrinsic properties of the enol which exhibits three entangled large amplitude motions (two methyl torsions and the intramolecular hydrogen transfer). Surprisingly, narrowing of some of these bands is observed in a slow time evolution. This effect is interpreted as a consequence of nuclear spin conversion in the hydrogen atoms of the methyl groups, giving access to AcAc species differing by their nuclear spin symmetry. This offers new pertinent investigations on the large amplitude motions, especially on the intramolecular hydrogen transfer. AcAc/pH2 samples have been irradiated by UV laser beams. Irradiation at 266 nm induces isomerization from the stable chelated enol form to non chelated conformers, similarly to the case of other matrices. A clear IR signature of the conformers is obtained thanks to the pH2 host. Irradiation at 248 nm induces the enol/keto tautomerization. The kinetics of this interconversion highlights a non-direct process. Fragmentation is clearly observed under irradiation at 193 nm, followed by chemical reaction with the hydrogen host.

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<p dir="ltr">The ability to predict and manipulate how a particulate material will flow in a process is challenging for industry and researchers alike. This dissertation presents the results of a model-directed, experimental approach using a concentric cylinder rheometer titled along an axis to enable continuous chute flow of granular media. Experiments were performed using draining flows for constant and oscillatory applied shear rates. Multiple flow and stress sensors were used to investigate the interaction of mass holdup, shear rate, specific torque, particle velocity, discharge mass flow rate, and wall pressure. Depending on the flow configuration, linear ranges were observed wherein the specific torque remained steady during draining. This finding enabled systematic testing of flow behavior as a function of dimensionless shear rates. Results suggest changes in the specific torque, wall slip, and outflow variance occur with the transition from the quasi-static to dense-inertial flow regimes. A pump-curve analogy was also identified for the relationship between the outlet mass flow rate and the specific power relationship for the constant shear rate experiments. Oscillatory shear rate experiments show a significant influence of the phase shift between the applied shear rate and the specific torque. Adding an asperity to the rotor revealed rate-dependent patterns in bulk flow and force chain dynamics. Overall, the study offers valuable insights into the effects of shear rate and boundary conditions on dense granular flows. The effects of particle characteristics (e.g., size and shape distributions, friction, cohesivity) and material properties (e.g., density, modulus) remain topics for future work. </p>