Wave propagation in different theories of fractional thermoelasticity

Abstract

In the present paper, the theories of fractional thermoelasticity with derivative and integral fractional orders are employed to study the homogeneous plane waves and the Rayleigh surface waves. The governing equations of homogeneous and isotropic generalized fractional thermoelasticity are solved for plane wave solutions and a dispersive velocity equation is obtained. There exists one transverse and two coupled longitudinal waves in a two-dimensional model of fractional thermoelastic medium where the speeds of coupled longitudinal waves are found to be dependent on the derivative and integral fractional orders. The Rayleigh waves is also studied along the traction-free surface of a half-space of a generalized fractional thermoelastic solid. The governing equations are solved for the general surface wave solutions which follow the decaying conditions in the half-space. A Rayleigh wave secular equation is obtained for thermally insulated surface. For a particular example of the present model, the numerical values of the speeds of coupled longitudinal waves and the Rayleigh wave are computed and graphically illustrated to visualize the effects of derivative and integral fractional orders and the circular frequency on the wave speeds.