Microbialitos da formação Codó (Aptiano Superior) às margens do rio Tocantins em São Miguel do Tocantins (TO)

The southwestern region of the São Luís-Grajaú Basin has a rare outcrop of the Codó Formation (upper Aptian) with seven outstanding microbialite bioherms along the left margin of the Tocantins river, near Imperatriz (MA). Resting on sandstones of the Grajaú Formation, the Codó Formation presents: 1) a 20 cm thick basal calcilutite with gypsite pseudomorphs and some fossil tree stems; 2) metric dark shales with carbonate nodules and thin intercalated carbonate layers, enclosing some microbial laminites; 3) a 2 cm thick upper breccia composed of microbialite fragments and other carbonate clasts, with halite hoppers on the top; 4) the carbonate bioherms, which partially overlie the extensive shales and interrupt them laterally, as well as the breccia. The bioherms in the northern part of the outcrop are thicker (<2 m) and have interbedded dark shales, whereas the southern are thinner and continuous in the vertical direction. In general, they are composed of irregular gently to strongly wavy microbial laminites, sometimes with pseudocolumnar to conical lamination. All microbialites with highest synoptic relief (<20 cm) look like columnar stromatolites on weathered lateral expositions. In plan view, the horizontal sections of these microbialites are circular to slightly elliptic, sometimes forming very small channels (N60W) filled with fine breccia. The highest bed of the northern bioherm has mixed microbial laminites and columnar stromatolites, where intercolumnar spaces were filled with microbialite clasts, fish bones, plant fragments and very small probable crustacean coprolites. Several fractures and deformation in this upper bed indicate an initial brecciation process probably caused by subaerial exposure. In microscopic scale, the lamination is smooth, diffuse, defined by subtle granulation differences of very fine granular calcite crystals within micrite, but oxide levels, dissolution surfaces or thin precipitated calcite veneers...

Análise das forças de reação vertical do solo em função das variações dos centros de massa de indivíduos a partir de movimentos de tronco com variação de carga

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Análise do comportamento dinâmico de um rotor vertical através do método dos elementos finitos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Complex modal analysis of a slender vertical rotor by finite elements method

In this paper, natural frequencies were analyzed (axial, torsional and flexural) and frequency response of a vertical rotor with a hard disk at the edge through the classical modal and complex analysis. The equation that rules the movement was obtained through the Lagrangian formulation. The model considered the effects of bending, torsion and axial deformation of the shaft, besides the gravitational and gyroscopic effects. The finite element method was used to discretize the structure into hollow cylindrical elements with 12 degrees of freedom. Mass, stiffness and gyroscopic matrices were explained consistently. The classical modal analysis, usually applied to stationary structures, does not consider an important characteristic of rotating machinery which are the methods of forward and backward whirl. Initially, through the traditional modal analysis, axial and torsional natural frequencies were obtained in a static shaft, since they do not suffer the influence of gyroscopic effects. Later research was performed by complex modal analysis. This type of tool, based on the use of complex coordinates to describe the dynamic behavior of rotating shaft, allows the decomposition of the system in two submodes, backward and forward. Thus, it is possible to clearly visualize that the orbit and direction of the precessional motion around the line of the rotating shaft is not deformed. A finite element program was developed using MATLAB (TM) and numerical simulations were performed to validate this model. Natural frequencies and directional frequency forced response (dFRF) were obtained using the complex modal analysis for a simple vertical rotor and also for a typical drill string used in the construction of oil wells.

Complex modal analysis of a vertical rotor through finite element method

Natural frequencies were analyzed (axial, torsional and flexural) and frequency response of a vertical rotor with a hard disk at the edge through the classical and complex modal analysis. The mathematical modeling was based on the theory of Euler-Bernoulli beam. The equation that rules the movement was obtained through the Lagrangian formulation. The model considered the effects of bending, torsion and axial deformation of the shaft, besides the gravitational and gyroscopic effects. The finite element method was used to discretize the structure into hollow cylindrical elements with 12 degrees of freedom. Mass, stiffness and gyroscopic matrices were explained consistently. This type of tool, based on the use of complex coordinates to describe the dynamic behavior of rotating shaft, allows the decomposition of the system in two submodes, backward and forward. Thus, it is possible to clearly visualize that the orbit and direction of the precessional motion around the line of the rotating shaft is not deformed. A finite element program was developed using Matlab ®, and numerical simulations were performed to validate this model.