On effect of anisotropy on anti-plane shear waves in elastic monoclinic half-space and plates

Abstract

Within the context of linear surface elasticity, we discuss the propagation of anti-plane surface waves, taking into account the anisotropy of the material. Here, we consider one of the most general crystal systems in the bulk, i.e. monoclinic symmetry. For the free surface, however, we consider rectangular symmetry. We derived the dispersion relations for three structures with surface energy: a half-space with a free surface; a layer of finite thickness; and a two-layered half-space. Surprisingly, these coincide with their isotropic counterparts, differing only in notation. Conversely, the anisotropy of the material in the bulk affects the displacement decay with depth. The pure exponential decay of displacements with the depth now transforms into decay with oscillations.