On three-dimensional edge waves in semi-infinite isotropic plates subject to mixed face boundary conditions

Abstract

This paper is concerned with the propagation of three-dimensional waves localized near the edge of a semi-infinite elastic plate subject to mixed face boundary conditions. In the linear isotropic case it is shown that the problem is closely related to that of Rayleigh surface wave propagation along the free surface of the corresponding half-space. The cut-off frequencies of the analyzed edge waves coincide with the natural frequencies of the associated cross-sectional semi-infinite strip. It is also demonstrated that the eigenspectrum of a rectangular rod can be expressed in terms of the considered three-dimensional waves. The results are then generalized to a prestressed isotropic incompressible material. It is noted that the density of the edge wave spectrum is strongly influenced by the prestress. It is illustrated that the areas of negative group velocity may exist for large primary deformation. Long-wave asymptotic expansions in the vicinity of the cut-off frequencies are presented.