Factorization by invariant embedding of elliptic problems: circular and star-shaped domains

Dissertação apresentada para obtenção do grau de Doutor em Matemática na especialidade de Equações Diferenciais, pela Universidade Nova de Lisboa,Faculdade de Ciências e Tecnologia

Estudo numérico de uma técnica de redução de esforços numa estrutura cilíndrica circular

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do Grau de Mestre em Engenharia Mecânica

Transverse Vibrations in Beams Supported by a Piece-Wise Homogeneous Visco- Elastic Foundation

Transversal vibrations induced by a load moving uniformly along an infinite beam resting on a piece-wise homogeneous visco-elastic foundation are studied. Special attention is paid to the additional vibrations, conventionally referred to as transition radiations, which arise as the point load traverses the place of foundation discontinuity. The governing equations of the problem are solved by the normalmode analysis. The solution is expressed in a form of infinite sum of orthogonal natural modes multiplied by the generalized coordinate of displacement. The natural frequencies are obtained numerically exploiting the concept of the global dynamic stiffness matrix. This ensures that the frequencies obtained are exact. The methodology has restrictions neither on velocity nor on damping. The approach looks simple, though, the numerical expression of the results is not straightforward. A general procedure for numerical implementation is presented and verified. To illustrate the utility of the methodology parametric optimization is presented and influence of the load mass is studied. The results obtained have direct application in analysis of railway track vibrations induced by high-speed trains when passing regions with significantly different foundation stiffness.

Estudo da influência de chapas de ligação com cavilha na resistência à encurvadura de colunas de aço de secção tubular circular

Neste trabalho estuda-se a resistência à encurvadura (compressão uniforme) de tubos de aço de secção circular, com extremidades rotuladas por meio de cavilhas, tendo em conta a influência da chapa de ligação (gusset plate na designação em língua inglesa). Para o efeito, estuda-se uma ligação-tipo comum com chapa soldada e efetuam-se estudos paramétricos, recorrendo a modelos de elementos finitos de casca, para determinar a influência da chapa na (i) carga crítica e na (ii) carga de colapso do elemento. Os resultados mostram que a influência da chapa não pode ser desprezada para valores reduzidos da esbelteza do elemento. Propõe-se um método expedito e preciso para determinar a carga crítica tendo em conta a influência da chapa.

Cylindrical spinning rotor gauge — A new approach for vacuum measurement

The spinning rotor gauge (SRG) is one of the most interesting vacuum gauges ever made, covering a pressure range of over seven orders of magnitude, with minimal gas interference (no pumping, ionization or heating of the measured gas), and a great stability of less than 1% drift per year. But despite its remarkable properties, apparently the SRG has not been further developed since the eighties, when it gained commercial interest. In this context, this dissertation aims at providing a starting point for a new line of investigation regarding this instrument, focused on the rotor itself. A brief study of different rotor geometries is provided, including a comparison between a cylindrical rotor and a spherical one. A cylindrical spinning rotor gauge (CSRG) is then proposed, based on the original SRG, but requiring a completely new lateral damping system. A prototype was built and tested against a non calibrated reference gauge.