Thermoelastic Rayleigh waves in an isotropic half-space

The process of the Rayleigh wave propagation in an elastic isotropic half-space with consideration of the interaction between the temperature and the mechanical fields is studied. The mathematical setting of the problem includes a related system of equations of thermoelasticity in displacements. The solution is sought in the form of a progressing thermoelastic wave. A dispersion equation is obtained that relates the frequency of the propagating wave to the components of the wave vector, the solution of which is found analytically. Taking into account the trivial boundary conditions expressing the absence of mechanical loads and heat fluxes at the boundary of the half-space, an equation is formulated to determine the frequency of a thermoelastic Rayleigh wave. Analytical expressions for displacement amplitudes and temperature are obtained. A series of numerical calculations was performed for various materials. The calculation results are presented in the form of tables and graphs. The effect of the mechanical characteristics of materials on the amplitudes and frequencies of elastic and thermoelastic Rayleigh waves is studied. It is demonstrated that the interaction of mechanical and temperature fields in real materials is very weak, and the amplitudes and frequencies of Rayleigh waves coincide in the elastic and thermoelastic cases. Thermoelastic effects depend essentially on the linear thermal expansion coefficient, and the parameters of elastic and thermoelastic Rayleigh waves start to differ significantly as the latter increases.