Thesis (Ph.D.) -- McMaster University, 1998. / Includes bibliographical references (p. 177-184). Also available via World Wide Web.

Thesis (M.Sc.)--Victoria University of Wellington, 2007. / Includes bibliographical references.

Thesis (M.S.)--Humboldt State University, 2007. / Includes bibliographical references (leaves 72-74). Also available via Humboldt Digital Scholar.

Thesis (Ph. D.)--Michigan State University. Dept. of Agricultural Economics, Dept. of Economics, 2006. / Title from PDF t.p. (viewed on June 19, 2009) Includes bibliographical references (p. 65-68). Also issued in print.

Thesis (Ph. D.)--University of Hong Kong, 1993.

Thesis (Ph. D.)--University of Hong Kong, 1994. / Includes bibliographical references (leaves 258-274).

Efficient uncertainty propagation schemes for dynamical systems are investigated here within the framework of stochastic finite element analysis. Uncertainty in the mathematical models arises from the incomplete knowledge or inherent variability of the various parametric and geometric properties of the physical system. These input uncertainties necessitate the use of stochastic mathematical models to accurately capture their behavior. The resolution of such stochastic models is computationally quite expensive. This work is concerned with development of model order reduction techniques for obtaining the dynamical response statistics of stochastic finite element systems. Efficient numerical methods have been proposed to propagate the input uncertainty of dynamical systems to the response variables. Response statistics of randomly parametrized structural dynamic systems have been investigated with a reduced spectral function approach. The frequency domain response and the transient evolution of the response of randomly parametrized structural dynamic systems have been studied with this approach. An efficient discrete representation of the input random field in a finite dimensional stochastic space is proposed here which has been integrated into the generic framework of the stochastic finite element weak formulation. This framework has been utilized to study the problem of random perturbation of the boundary surface of physical domains. Truncated reduced order representation of the complex mathematical quantities which are associated with the stochastic isoparametric mapping of the random domain to a deterministic master domain within the stochastic Galerkin framework have been provided. Lastly, an a-priori model reduction scheme for the resolution of the response statistics of stochastic dynamical systems has also been studied here which is based on the concept of balanced truncation. The performance and numerical accuracy of the methods proposed in this work have been exemplified with numerical simulations of stochastic dynamical systems and the convergence behavior of various error indicators.

Orientador: José Roberto deFrança Arruda / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-16T17:59:49Z (GMT). No. of bitstreams: 1 Santos_ThaisBarbosados_M.pdf: 1128463 bytes, checksum: c42428e12fa3b35b0b8d8ab0bb7e8538 (MD5) Previous issue date: 2010 / Resumo: O presente trabalho consiste no estudo estocástico da influência da variabilidade do pneumático no conforto vibracional dos ocupantes do veículo. Elementos de viga curva Euler-Bernoulli formam um anel que representa o pneu. Este é sujeito a uma força girante na direção radial e sua resposta é calculada através do Método do Elemento Espectral. Tal força girante é modelada como um pulso triangular fora de fase aplicada nos diferentes nós do anel. A pressão interna, os efeitos inerciais e o efeito da rigidez da parede lateral em duas direções são considerados na modelagem. A componente radial da força resultante no eixo do pneumático é analisada como critério de conforto. Ela resulta da atuação do pneu na absorção das imperfeições do solo, ou seja, é uma medida do desempenho do pneumático. Os valores obtidos através da simulação são comparados com dados experimentais fornecidos pela Pirelli Pneus Ltda. Partindo desse modelo validado, uma metodologia de aplicação da teoria estocástica para analisar a variabilidade de pneumáticos é desenvolvida e desuniformidades como emendas são inseridas no modelo como informações de caráter aleatório. O Método de Monte Carlo é utilizado como solver / Abstract: The present work consists in a stochastic study of the influence of the pneumatic variability on the vehicle passengers vibrational comfort. Euler-Bernoulli curved beam elements constitute a ring which represents a pneumatic tire. It is subjected to a rotating radial force and its response is calculated through Spectral Elements Method. The internal pressure, the inertial effects and the side-wall stiffness in two directions effect are considered in the model. The radial component of the resultant hub force is analysed as the comfort criterion. It is the tire performance result on the soil impecfections absorbation. The obtained numerical data are compared with experimental data provided by Pirelli Pneus Ltda. Starting from this validated model, a methodology for the stochastic theory application in order to represent the tire variability is developed. Imperfections like amendments are introduced in the model as informations with an aleatory character. The Monte Carlo Method is used as solver / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

Orientador: Pedro José Catuogno / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-20T05:04:07Z (GMT). No. of bitstreams: 1 Almeida_LuisRobertoLucingerde_D.pdf: 4124910 bytes, checksum: 249249a4a4959e28b63a5f2e7290a5fe (MD5) Previous issue date: 2012 / Resumo: Nesta tese, estudamos equações diferenciais estocásticas, sob o ponto de vista da teoria das simetrias de Lie. Introduzimos o conceito de simetria de Lie estocástica, que consiste em uma ação que mantém invariante as soluções de uma equação diferencial, onde tal ação é estocástica, isto é, dada por um fluxo estocástico. Nosso principal resultado consiste nas equações de Lie para as simetrias estocásticas, permitindo detectar quando um fluxo estocástico é uma simetria estocástica. Além disso, apresentamos uma possível definição de coordenada canônica para as simetrias estocásticas e obtemos condições, assim como no caso clássico, para encontrá-la. Por fim, mostramos como obter, sistematicamente, transformações entre equações estocásticas / Abstract: In this thesis, we study stochastic differential equations, under the point of view of Lie point symmetries. We introduce the concept of stochastic Lie point symmetry, which consists of an action that keeps invariant the solutions of a differential equation, where such action is stochastic, i.e., given by a stochastic flow. Our main result is the Lie's equations for stochastic symmetries, which allows one to detect when a stochastic flow is a stochastic symmetry. Furthermore, we present a possible definition of canonical coordinates for the stochastic symmetries and we obtain conditions, like in the standard case, to find them. At last, we show how to obtain, systematically, transformations between stochastic differential equations / Doutorado / Matematica / Doutor em Matemática

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