Analytical Solution of Classic Coupled Thermoelasticity Problem in a Rotating Disk

Abstract

A fully analytical solution of the classic coupled thermoelasticity problem in a rotating disk subjected to thermal and mechanical shock loads is presented. Axisymmetric thermal and mechanical boundary conditions are considered in general forms of arbitrary heat transfer and traction, respectively, at the inner and outer radii of the disk. To solve the governing system of equations, an analytical procedure based on the Fourier-Bessel transform is employed. Closed form formulations are presented for temperature and displacement fields. The results of the present formulations are in good agreement with the numerical results available in the literature. The radial distribution and time history of temperature, displacement and stresses are shown and discussed. The propagation of elastic waves and their reflection from the boundary of the disk are clearly shown. In addition, effects of coupling parameter and angular velocity on temperature, displacement and stress fields are investigated.