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.

A major area of research recently has been the study of nonlinear waves in liquid crystals. The availability of commercial liquid crystals and the formation of solitons at mWpower levels has meant that experimental research and the need to understand how the solitons are formed and interact has been boosted. The first part of the thesis looks at how two laser beams in a nematic liquid crystal interact. Specifically research has centred on the problem of directing a signal beam to a target area by varying the input angle of the control beam. Different approximate models are developed to describe this phenomena, with the results from these models compared to a full numerical analysis. The first model developed is called the particle model and is based on the unmodified modulation equations. The results from this model were acceptable when compared with the results obtained from a full numerical analysis. This comparison is indicative that the underlying assumptions of the model did not capture an essential part of interaction between the two laser beams. The second model used to describe the interaction between the two laser beams was based on the law of conservation of momentum in the laser beams. Here the potential between the laser beams was modified to take into account the profile of the beams. The results from this model were in excellent agreement with results from the full numerical analysis, showing the key role potential between the beams plays in the trajectories of the beams. The interaction between dark solitons was also studied. The model used in this case was based on the modulation equations with a suitable trial function for dark solitons. The results from this model were in excellent agreement with the results from the full numerical analysis. The behaviour of the dark solitons shown by the approximate model and the full numerical analysis showing similar key features. This thesis sets out the equations describing the interaction of laser beams in liquid crystals. These are the equations used to carry out a full numerical analysis. This analysis is valuable in its own right and is the standard to compare the results obtained from other models but to achieve a deeper understanding of how laser beams interact in liquid crystals approximate models are developed so that the important parameters in each model can be identified. The Lagrangian describing the interaction of laser beams in liquid crystals is used in all the approximate models. The approximate models can then be developed through the use of suitable trial functions that adequately describe how the laser beams interact. The derivation of the equations and how these equations are solved is described for each model. The results from each model are compared to a full numerical analysis with a discussion of how the results compare.

Marsh vegetation is widely considered to offer protection against coastal storm damage, and vegetated flow has thus become a key area of hydrodynamic research. This study investigates the utility of simulated Spartina alterniora marsh vegetation as storm protection using an ADV measurement technique, and is the first to apply jet self-similarity analysis to characterize the overall mean and turbulent flow properties of a three-dimensional axisymmetric jet through a vegetated array. The mean axial flow of a horizontal axisymmetric turbulent jet is obstructed by three configurations of staggered arrays of vertical rigid plant stems. The entire experiment is repeated over five sufficiently high jet Reynolds number conditions to ensure normalization and subsequent collapse of data by nozzle velocity so that experimental error is obtained. All self-similarity parameters for the unobstructed free jet correspond to typical published values: the axial decay coefficient B is 5:8 +/- 0:2, the Gaussian spreading coefficient c is 85 +/- 5, and the halfwidth spreading rate eta_(1/2) is 0:093 +/- 0:003. Upon the introduction of vegetation, from partially obstructed to fully obstructed, B falls from 5:1+/- 0:2 to 4:2 +/- 0:2 and finally 3:7 +/-0:1 for the fully obstructed case, indicating that vegetation reduces axial jet velocity. Cross-sectionally averaged momentum for the unobstructed free jet is M=M0 = 1:05 +/- 0:07, confirming conservation of momentum. Failure of conservation of momentum is most pronounced in the fully obstructed scenario – M=M0 = 0:54 +/- 0:05. The introduction of vegetation increases spreading of the impinging jet. The entrainment coefficient alpha for the free jet case is 0.0575; in the fully obstructed case, alpha = 0:0631. Mean advection of mean and turbulent kinetic energy demonstrates an expected reduction in turbulence intensity within the vegetated array. In general, turbulent production decreases as axial depth of vegetation increases, though retains the bimodal profile of the free jet case; the fully vegetated case, however, exhibits clear peaks behind plant stems. Turbulent transport was shown to be unaffected by vegetation and appears to be primarily a function of axial distance from the jet nozzle. An analysis of rate of dissipation revealed that not only does the cumulative effect of upstream wakes overall depress the magnitude of spectral energy density across all wavenumbers but also that plant stems dissipate large anisotropic eddies in centerline streamwise jet flow. This study, thus, indicates that sparse emergent vegetation both reduces axial flow velocity and has a dissipative effect on jet flow. Typically, however, storm surge does not exhibit the lateral spreading demonstrated by an axisymmetric jet; therefore, the results of this study cannot conclusively support the claim that coastal vegetation reduces storm surge axial velocity.

[pt] Em problemas geotécnicos podem ocorrer grandes deformações devido a chuvas prolongadas, sismos, deslizamentos de encostas, etc. Material point method (MPM) é um método de solução baseado no Método dos Elementos Finitos (MEF) que oferece vantagens para o cálculo estático e dinâmico que envolve deformações desse tipo. O objetivo desta dissertação é utilizar o MPM em problemas geotécnicos em condições estáticas e dinâmicas. Esta pesquisa mostra o procedimento de analises do MPM para a condição não acoplada (só solido sem presença de água) e depois acoplada. Para a revisão matemática de MPM se faz antes um resumo da teoria do MEF na metodologia de conservação de quantidade de movimento. Nestas duas formas de resolver os problemas geotécnicos foram expostos três exemplos simples. O primeiro é uma coluna de solo simulado sob os fundamentos da elasticidade, com o objetivo de verificar o deslocamento vertical pelo peso próprio. Isto foi resolvido mediante quatro diferentes métodos: analítica, MEF por resíduos ponderados, MEF por conservação de quantidade de movimento, e MPM. Todos eles consideram somente a fase solida. No segundo exemplo, tem-se solo na geometria de quadrado de lado 1 metro, onde busca-se obter as poropressões quando atingir a condição permanente enquanto os deslocamentos ocorrem ao longo do tempo; ou seja, a análise é acoplada e é resolvida pelo método MPM. Para uma aplicação mais realista, foi feita a análise (não acoplada) da barragem Palo Redondo, pertencente ao projeto Chavimochic, localizada na região de La Libertad, Perú. Nesta análise dinâmica considerou-se dois modelos constitutivos: Elástico e Mohr Coulomb, além de um sismo. / [en] In geotechnical problems can happen large strains because of prolonged rains, earthquake, slide slope, etc. Material point method is a solution method based on the finite element method (FEM) which offers advantages for static and dynamic calculation that involve that kind of strains. The objective in this dissertation is to use the MPM in geotechnical problems in statics and dynamics conditions. This research shows the analysis procedure of MPM for uncoupled condition (only solids, without water) and then coupled. Before the mathematical theory of MPM, a review of the theory of FEM in the conservation of quantidade de movimento is done. In this two methodology were raised three examples. The first one is a soil column that was modeled elastically, in which the main objective in to analyze the vertical displacement because of own weight. This was solved by four different methods: analytically, FEM weighted residual, FEM conservation of momentum, and MPM. All of them consider only the solid phase. The second example is a square of soil with side 1 meter, where the objective is to know the pore-pressure in the permanent condition and at the same time the vertical displacement were generated, it means that the analysis is coupled and were solved by MPM. In order to make a more realistic application, Palo Redondo dam is analyzed (uncoupled condition), which belongs to the Chavimochic project located in La Libertad, region of Perú. This dynamic analysis was done considering two constitutive models: Elastic and Mohr Coulomb, additionally seismic forces.