The propagation of discontinuities in non-homogeneous thermoviscoelastic media

Abstract

In this study, the propagation of plane, cylindrical and spherical dilatational waves in non-homogeneous thermoviscoelastic media is investigated by employing the notion of singular surfaces and the method of characteristics. The inhomogeneity of the medium is such that the material properties depend in an arbitrary manner on the co-ordinate coinciding with the direction of the propagation. An integral type constitutive equation is considered for the heat flux which permits a finite propagation speed for thermal disturbances. It is found that the application of a dynamic input on the boundary surface gives rise to two different wave fronts along which mechanical and thermal effects are coupled. The growth and decay equations describing the change of the strength of the discontinuities on these two wave fronts are then obtained. By integrating the growth and decay equations along the rays the solutions valid at the wave fronts are found. The solutions are then reduced to two special cases: in one the heat flux equation is taken as the so-called modified Fourier equation, and in the other as the classical Fourier equation. The effects of inhomogeneity, geometry of the wave front, thermomechanical coupling and material internal friction on the strength of the discontinuity are discussed.