Free vibration analysis of an exponentially graded shaft system subjected to thermal gradients

Abstract

The present study aims to carry out finite element analysis to investigate the natural and whirl frequencies of a functionally graded (FG) rotor-bearing system modeled following the exponential law gradation. The FG shaft is modeled using the Timoshenko beam theory (TBT). The thermal gradation of FG shaft material properties is achieved following the exponential temperature distribution method (ETD). The derivation of element stiffness, mass and gyroscopic matrices has been carried out including the material and thermal gradation effects. FG shaft, consisting of a mixture of Stainless Steel (SS) and Zirconium Dioxide (ZrO2), is investigated, where the volume fraction of metal decreases toward the outer radius and ceramic volume fraction increases. A Python code has been developed to perform the finite element analysis to extract the Eigenvalues (natural frequencies) of the FG rotor bearing subjected to different thermal gradients. The analysis presents the effects of variations in material gradation and thermal gradients on the natural frequencies and whirl frequencies of the FG rotor-bearing system.