Made available in DSpace on 2016-04-18T21:39:47Z (GMT). No. of bitstreams: 4 Daniela Mitie Kato1.pdf: 3074727 bytes, checksum: 838e46df28bd97be8c86b966efbdb36b (MD5) Daniela Mitie Kato2.pdf: 1644798 bytes, checksum: 9fab5a871347c336126e7f1eebb46dd2 (MD5) Daniela Mitie Kato3.pdf: 1390068 bytes, checksum: a71d113839f5bb7d740a9d8ddd7deda0 (MD5) Daniela Mitie Kato4.pdf: 3042893 bytes, checksum: 9c6b7834f6fd7ff78c42d7435ef034b7 (MD5) Previous issue date: 2008-06-26 / Fundo Mackenzie de Pesquisa / In this work, we investigate characteristics of the Power Spectral Density (PSD) of chaotic signals generated by one-dimensional maps. Usually, these signals are mentioned as having broadband and impulsive Autocorrelation Sequence (ACS). In this work, we verify that chaotic signals can be narrowband or broadband, with their power concentrated in the high or low frequencies. For a particular piecewise linear family of maps, we analytically evaluate the influence of the Lyapunov exponent on the ACS and on the PSD. We relate essential bandwidth to this exponent and to the parameter that defines a map in the family. We also consider the Manneville family of maps. In this case, the analysis is performed via computational simulations, interpreting the signals as sample-functions of a stochastic process. We relate the essential bandwidth to the Lyapunov exponent and to the family's parameter. We also relate this parameter to the return time of the intermittences. From the Telecommunication Engineering point of view, the results are relevant because they allow the emergence of new ideas for applications of chaotic signal in digital communication. / Neste trabalho investiga-se características da Densidade Espectral de Potência (DEP) de sinais caóticos gerados por mapas unidimensionais. Usualmente, refere-se aos sinais caóticos como sendo sinais banda larga e com Seqüência de Autocorrelação (SAC) na forma impulsiva. Verifica-se aqui que estes sinais podem ser banda estreita ou banda larga, com sua potência concentrada nas altas ou nas baixas freqüências. Para uma particular família de mapas lineares por partes, a influência do expoente de Lyapunov na SAC e na DEP é avaliada analiticamente. Relaciona-se a banda essencial dos sinais a este expoente e ao parâmetro que define um mapa da família. Considera-se também a família de mapas de Manneville, para a qual a análise é realizada por meio de simulações computacionais, interpretando os sinais gerados como funções-amostras de um processo estocástico. Relaciona-se a banda essencial ao expoente de Lyapunov e ao parâmetro da família e relaciona-se também este parâmetro ao tempo de retorno das intermitências. Do ponto de vista da Engenharia de Telecomunicações, os resultados obtidos são relevantes, pois possibilitam o surgimento de novas idéias de aplicações de sinais caóticos em sistemas de comunicação digital.

Compliant suspensions are often used in micromechanical devices and precision mechanisms as substitutes for kinematic joints. While their small-displacement behavior is easily captured in simple formulae, large-displacement behavior requires nonlinear finite element analysis. In this work, we present a method that helps capture the geometrically nonlinear behavior of compliant suspensions using parameterized non-dimensional maps. The maps are created by performing one nonlinear finite element analysis for any one loading condition for one instance of a suspension of a given topology and fixed proportions. These maps help retrieve behavioral information for any other instance of the same suspension with changed size, cross-section dimensions, material, and loading. Such quantities as multi-axial stiffness, maximum stress, natural frequency, etc. ,can be quickly and accurately estimated from the maps. These quantities are non-dimensionalized using suitable factors that include loading, size, cross-section, and material properties. The maps are useful in not only understanding the limits of performance of the topology of a given suspension with fixed proportions but also in design. We have created the maps for 20 different suspensions. Case studies are included to illustrate the effectiveness of the method in microsystem design as well as in precision mechanisms. In particular, the method and 2D plots of non-dimensional kinetoelastic maps provide a comprehensive view of sensitivity, cross-axis sensitivity, linearity, maximum stress, and bandwidth for microsensors and microactuators.

<p>The 9:2 lunar synodic resonant near rectilinear halo orbit (NRHO) is the chosen orbit for the Gateway, a future lunar space station constructed by the National Aeronautics and Space Administration (NASA) as well as several commercial and international partners. Designing trajectories in this sensitive lunar region combined with the absence of a singular systematic methodology to approach mission design poses challenges as researchers attempt to design transfers to and from this nearly stable orbit. This investigation builds on previous research in Poincar\'e mapping strategies to design transfers from the 9:2 NRHO using higher-dimensional maps and maps with non-state variables. First, Poincar\'e maps are applied to planar transfers to demonstrate the utility of hyperplanes and establish that maps with only two or three dimensions are required in the planar problem. However, with the addition of two state variables, the spatial problem presents challenges in visualizing the full state. Higher-dimensional maps utilizing glyphs and color are employed for spatial transfer design involving the 9:2 NRHO. The visualization of all required dimensions on one plot accurately reveals low cost transfers into both a 3:2 planar resonant orbit and an L2 vertical orbit. Next, the application of higher-dimensional maps is extended beyond state variables. Visualizing time-of-flight on a map axis enables the selection of faster transfers. Additionally, glyphs and color depicting angular momentum rather than velocity lead to transfers with nearly tangential maneuvers. Theoretical minimum maneuvers occur at tangential intersections, so these transfers are low cost. Finally, a map displaying several initial and final orbit options, discerned through the inclusion of Jacobi constant on an axis, eliminates the need to recompute a map for each initial and final orbit pair. Thus, computation time is greatly reduced in addition to visualizing more of the design space in one plot. The higher-dimensional mapping strategies investigated are relevant for transfer design or other applications requiring the visualization of several dimensions simultaneously. Overall, this investigation outlines Poincar\'e mapping strategies for transfer scenarios of different design space dimensions and represents initial research into non-state variable mapping methods.</p>