Present work deals with the study of stresses developed in tapered functionally graded (FG) shaft system under both thermal and mechanical environment for three nodded beam element by using Timoshenko beam theory. The temperature distribution in radial direction is assumed based on one dimensional steady state temperature field by Fourier heat conduction equation without considering heat generation. Temperature dependent material properties are varied along the radial direction using power law gradation. Tapered FG shaft consists of rigid disk attached at its centre and shaft is mounted on two flexible bearings acts as spring and damper, inner radius of the tapered shaft is varying in x direction keeping thickness of hollow tapered shaft is constant. For the present analysis the Mixture of Stainless steel (SUS304) and Aluminum oxide (Al2O3) are considered as inner and outer surface material of the FG shaft. Three dimensional constitutive relations are derived based on first order shear deformation theory (FSDT) for Timoshenko beam element considering rotary inertia, strain and kinetic energy of shaft and gyroscopic effect. In present study, structural and hysteretic damping are incorporated. Hamilton’s principle is used to derive governing equation of motion for three nodded beam element for six degree of freedom per node. Complete MATLB code is generated and shows that temperature field and power law gradient index have important part on material properties. Comparative study is carried out for Stainless steel and FG tapered shaft, shows that stress developed in FG shaft is comparatively lower than Steel shaft. Various results are obtained for coupled and uncoupled environment. Transient stress are obtained for varying power law index value and speed as a parameter. Stress amplitude increases for increase in speed and power law index. Results achieved for FG shaft shows advantages over steel shaft.
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