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.

Mineral element and heavy metal poisoning in animals

Mineral elements are essential to animal health, survival and production because they are part of physiological, structural, catalytic and regulatory organism functions. Therefore, they should be present in diet. However, these minerals when ingested in excessive doses due to errors in balancing mineral supplements and/or complete ration, intake of plants with high mineral concentration, resulting from addition of fertilizers, herbicides, insecticides and fungicides in pasture or tillage where plants and/or grains will be used to feed animals, decomposition of urban and industrial wastes, leaks and accidental spills of pollutants may result in accumulation of toxic mineral elements in the environment poisoning the animals and may lead them to death. However, toxic doses, physiological changes during poisoning, symptoms and mineral concentration in tissues of poisoned animals to confirm diagnosis are not completely known. Thus, this study reviews mineral element doses that some authors considered toxic for animals intake, as its concentration in tissues of poisoned animals and its physiological effects, symptoms, diagnostic procedures and treatment for poisoning by cadmium, lead, copper, chromium, iodine, manganese, molybdenum, selenium and zinc.