Three-dimensional surface wave in half-space and edge waves in plates with mixed boundary conditions on the front edge

In the first part of this paper the propagation of sinusoidal three-dimensional surface waves is investigated for an isotropic elastic half-space with mixed boundary conditions. It is assumed that the boundary is fixed in one of the tangential directions and traction free in the other directions. The exact dispersion relation is derived which shows the existence and uniqueness of the three-dimensional surface wave. The speed of this wave depends on the angle of propagation and lies between the shear wave speed and Rayleigh wave speed. The graphs of this dependence are presented for various values of Poisson ratio. In the second part of this paper the three-dimensional edge waves in plates with mixed boundary conditions on the edge are investigated. The faces of the plate are assumed to be traction free. Both symmetric and antisymmetric solutions of three-dimensional dynamic equations of elasticity are considered. It is assumed that the edge is fixed in one of the tangential directions and traction free in the normal and the other tangential direction. Asymptotic analysis is performed, which shows that there is an infinite spectrum of higher order edge waves in such plates. The results of numerical calculations based on the modal expansion method are presented to confirm asymptotic analysis. In addition, by the numerical investigation the fundamental edge wave was found in the symmetric case (the edge is fixed in the tangential direction transversally to the faces). The phase velocity of this wave tends to some limit value depending on the Poisson ratio as the wave number increases. In the antisymmetric case the first higher order wave has the same limit value. The dispersion curves are presented for various values of Poisson ratio.