Influence of Material Damage on the Rayleigh Wave Propagation along Half-Space Boundary

— At present, mechanics of damage media, which studies both the stress–strain state of media and the damage accumulation in materials, is being actively developed. In this study, a self-consistent problem, including the dynamic equation of the theory of elasticity and the kinetic equation of damage accumulation in a material, is formulated for an isotropic elastic half-space with damage in the material. It is assumed that damage is distributed uniformly over the medium. The surface-wave propagation along the free boundary of damaged half-space has been investigated. The wave propagates horizontally and decays in the vertical direction. All processes are assumed to be homogeneous along the third axis. It is shown that a self-consistent system with boundary conditions expressing the absence of stress at the half-space boundary is reduced to a complex dispersion equation in this case. In the limiting case (damage-free material), the obtained dispersion equation is reduced to the classical dispersion equation for a Rayleigh wave in the 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 along the propagation direction, and low-frequency disturbances have frequency-dependent dissipation and dispersion. It is shown that dispersion has abnormal character. It is established that, in the high-frequency region, the phase and group velocities increase and decrease, respectively, with an increase in the damage coefficient. At low frequencies, both velocities increase with a decrease in the damage coefficient.