In this work, we introduce a mathematical model for the theory of generalized thermoelasticity with fractional heat conduction equation. The presented model will be applied to an infinitely long hollow cylinder whose inner surface is traction free and subjected to a thermal and mechanical shocks, while the external surface is traction free and subjected to a constant heat flux. Some theories of thermoelasticity can extracted as limited cases from our model. Laplace transform methods are utilized to solve the problem and the inverse of the Laplace transform is done numerically using the Fourier expansion techniques. The results for the temperature, the thermal stresses and the displacement components are illustrated graphically for various values of fractional order parameter. Moreover, some particular cases of interest have also been discussed.

This paper is concerned with two-dimensional (r, θ) thermoelastic dynamic responses of a long functionally graded hollow cylinder subjected to asysmmetrical thermal and mechanical loads. The material properties, except the Poisson's ratio, are assumed to be temperature independent and vary exponentially and continuously in the radial direction. By means of finite difference method and Newmark method, the motion governing equations of the long FGM hollow cylinder are solved. Comparisons between this paper's results and the corresponding analytical results validate the proposed solution. In addition, the effects of the volume fraction, temperature boundary conditions on the hollow cylinder's deformations and stresses distributions are examined, and many other valuable thermoelastic dynamic characteristics are revealed.