Paper Title
Finite Element Analysis Of Functionally Graded Rotor Shaft Using Timoshenko Beam Theory

This article mainly deals with the dynamic analysis of functionally graded (FG) composite rotor shaft. The FG shaft is mounted on two flexible bearings at its ends. A theoretical study has been established for the kinetic energy and the strain energy of the shaft, and the equations of motion of FG shaft have been formulated by using finite element method based on Timoshenko beam theory (TBT). The FG shaft is assumed to have isotropic material properties.The material property distribution of the FG shaft takes through the thicknessis assumed to vary according to exponential-law distribution. The present shaft system has been verified by comparing critical speeds with the available literature. A numerical example is also given to illustrate the frequencies, mode shapes, and transient response due to unbalances mass of disks.