Rayleigh waves in a layered thermoelastic structure

This paper aims to establish a general exact secular equation for Rayleigh surface waves propagating in an isotropic thermoelastic half-space coated by an isotropic thermoelastic layer of arbitrary thickness. The contact between the layer and the half-space is assumed to be welded on the interface. The outer surface of the layer is free of traction, and no heat transfer is allowed with the surrounding environment. When passing through the contact surface, the displacements and temperature fields, as well as the stresses and heat flux fields, are supposed to vary continuously, no jump being allowed. The explicit expressions of free Rayleigh waves in both the layer and the half-space are first presented, and then they are used to establish the general exact secular equation. Numerical illustrations are presented for a layered structure consisting of an aluminum layer welded on a half-space made of various thermoelastic materials outlining the main characteristics of Rayleigh wave propagation: the dimensionless propagation speed and the dimensionless damping in time of the wave’s amplitude. The exact effective boundary conditions for the Rayleigh waves are established in the thermoelastic half-spaces covered with thin films. Some limiting cases are also discussed: (1) when the thermoelastic layer is absent and (2) when the thermal effects are neglected.