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.

Natural frequency analysis of a functionally graded rotor system using three-dimensional finite element method

“…After validation, the code is extended to different a FG material composed of Al 2 O 3 and SUS304 for 80 mm diameter shaft at room temperature. Radial variation of Young's Modulus from Python output is in good agreement with works of Gayen and Roy [10], which is shown in Fig. 2.…”

“…Thus, the code is adopted for further works in different FG shaft systems discussed in current work. The points in the plots show the value plotted which lies exactly above the curves obtained from [7,10].…”

Effect of Corrosion on the Natural and Whirl Frequencies of a Functionally Graded Rotor-Bearing System Subjected to Thermal Gradients

“…However, limited works are reported in the literature on the vibration analysis of functionally graded rotor-bearing systems. Gayen and Roy [ 16 ] carried out a vibration and stability analysis of an FG rotor-bearing system using a three-node finite beam element based on Timoshenko beam theory (TBT). Rao and Roy [ 17 ] carried out a dynamic analysis of a functionally graded rotating shaft system using the Timoshenko beam theory.…”

Parametric study on free vibration and instability of a functionally graded cracked shaft in a rotor-disc-bearing system: finite element approach

“…Shahba et al [5] presented free vibration and stability analysis for an axially tapered FG beams (Timoshenko) through a FE approach. Gayen and Roy [6] studied vibration and stability analysis of a FG spinning shaft system based on Timoshenko beam theory (TBT).…”