Influence of material damage on Rayleigh wave propagation along half-space boundary

Abstract

At present mechanics of damaged media studying both the stress-strain state of media and the accumulation of damages in materials develops intensively. In this paper, for an isotropic elastic half-space with damage in the material, a self-consistent problem is formulated, which includes the dynamic equation of the theory of elasticity and the kinetic equation of damage accumulation. We suppose that damage is uniformly distributed in the medium material. The study of surface wave propagation along the free boundary of the damaged half-space is performed. The wave propagates horizontally and decays in vertical directions. We assume that along the third axis all processes are homogeneous. It is shown that in this case a self-consistent system with boundary conditions expressing the absence of stresses at the boundary of a half-space is reduced to a complex dispersion equation. It is noted that in the limiting case, when there is no damage in the material, the dispersion equation obtained is reduced to the classical dispersion equation for the Rayleigh wave in polynomial form; the surface wave propagates along the half-space boundary without dispersion and attenuation. If damage is present in the medium, the surface wave attenuates in the direction of propagation, and low-frequency disturbances have frequency-dependent dissipation and dispersion. It is shown that dispersion has the abnormal character. It is established that with a decrease in the damage coefficient value, in the high-frequency region, the value of the phase velocity increases, and the group velocity decreases. At low frequencies, both speeds increase with decreasing damage rate