Elastic stress analysis of rotating functionally graded long hollow shaft with variable angular velocity

The aim of this research is to examine the stress and displacement fields of periodically rotating long hollow shaft with fixed ends. It is presupposed that the shaft material is made of functionally graded material that obeys the power-law, and the geometry of the shaft is long enough to apply plane strain conditions. In accordance with these constraints, closed form solutions are revealed, and the stress fields are examined in detail. It is seen in the illustrative numerical examples that the material grading parameters of both Young’s modulus and density play an essential role on the variation of directional stress and displacement fields. For the same numerical values, both grading parameters may yield to different distributions along the radial thickness of the shaft. Due to the time-dependent periodic rotation that is taken into account, mentioned fields are given at different time frames as well. Additionally, obtained numerical results are compared with another related article. It is seen that matching results are achieved with negligible differences.