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.

Influence of nonlinear stiffness on the dynamics of a slender elastic beam under torsional oscillations

This study focuses on analysing the effects of nonlinear torsional stiffness on the dynam-ics of a slender elastic beam under torsional oscillations, which can be subject to helical buckling.The helical buckling of an elastic beam confined in a cylinder is relevant to many applications. Someexamples include oil drilling, medical cateters and even the conformation and functioning of DNAmolecules. A recent study showed that the formation of the helical configuration is a result of onlythe torsional load, confirming that there is a different path to helical buckling which is not related tothe sinusoidal buckling, stressing the importance of the geometrical behaviour of the beam. A lowdimensional model of an elastic beam under torsional oscillations is used to analyse its dynamical be-haviour with different stiffness characteristics, which are present before and after the helical buckling.Hardening and softening characteristics are present, as the effects of torsion and bending are coupled.With the use of numerical algorithms applied to nonlinear dynamics, such as bifurcation diagramsand basins of attraction, it is shown that the nonlinear stiffness can shift the bifurcations and inducechanges in the stability of the desirable and undesirable solutions. Therefore, the proper modellingof these stiffness nonlinearities seems to be important for a better understanding of the dynamicalbehaviour of such beams.

Ex vivo torsional properties of the Targon Vet Nail System in canine femurs: comparison with the 2.4 mm LC-DCP Plate

Pós-graduação em Cirurgia Veterinária - FCAV

Determinações territoriais da agricultura mundializada: a soja nos espaços rurais e urbanos de Uruçuí-PI

Pós-graduação em Geografia - IGCE

Influência do comprimento do parafuso nas propriedades biomecânicas da placa de reconstrução bloqueada

Pós-graduação em Biotecnologia Animal - FMVZ