Finite element based vibration analysis of functionally graded spinning shaft system

Abstract

The present work deals with the study of vibration and stability analysis of a functionally graded spinning shaft system using three-noded beam element based on the Timoshenko beam theory. Material properties are assumed to be graded in radial direction according to power law gradation. In the present analysis, the mixture of aluminum oxide (Al2O3) and stainless steel (SUS304) has been considered as functionally graded material where metal (SUS304) content decreases towards the outer diameter of the shaft. The functionally graded shafts has been modeled as a Timoshenko beam, which contains discrete isotropic rigid disks supported by flexible bearing. The functionally graded shaft has been modeled based on first-order shear deformation beam theory with transverse shear deformation, rotary inertia, gyroscopic effect, strain and kinetic energy of shafts by adopting three-dimensional constitutive relations. The derivation of governing equations of motion has been obtained using Hamilton’s principle. Three-noded beam element with four degrees of freedom per node has been used to solve the govering equations. In this work, the effects of both internal viscous and hysteretic damping have also been incorporated in the finite element model. Various results have been obtained such as Campbell diagram, stability speed limit, damping ratio, and time responses for functionally graded shaft and also compared with conventional steel shaft. It has been found that the responses of the functionally graded spinning shaft are significantly influenced by material properties, radial thickness, power law gradient index, and internal (viscous and hysteretic) damping. The obtained results also show the advantages of functionally graded shaft over conventional steel shaft.