Reduced model for the surface dynamics of a generally anisotropic elastic half-space

Near-surface resonance phenomena often arise in semi-infinite solids. For instance, when a moving load with a speedv close to the surface wave speedv R is applied to the surface of an elastic half-space, it will give rise to a large-amplitude disturbance inversely proportional tov  − v R . The latter can be determined by a multiple-scale approach using an extra slow time variable. It has also been shown for isotropic elastic half-spaces that the reduced governing equation thus derived is capable of describing the surface wave contribution even for arbitrary dynamic loading. In this paper, we first derive the analogous evolution equation for a generally anisotropic elastic half-space, and then assess its applicability in the study of travelling waves in a half-space that is coated with a continuous array of spring-like vertical resonators or bonded to an elastic layer of different properties. Our results are validated by comparison with previously known results, and illustrative calculations are carried out for a fibre-reinforced half-space and a coated half-space that is subjected to a finite deformation.