Dispersion equations for steady waves in an anisotropic elastic plate or a layered plate

Abstract

Steady waves propagating in a plate that consists of one or more layers of general anisotropic elastic material are studied. The surface of the plate can be a traction-free (F), rigid (R) or slippery surface (S). The interface between any two layers in the plate can be perfectly bonded (b) or in sliding contact (s). The thickness of the layers need not be the same. The purpose of this paper is to present dispersion equations for all possible combinations of the boundary and interface conditions. If the thickness h of one of the layers is very small, the dispersion equation allows us to expand the solution in an infinite series in the power of h from which an approximate solution can be obtained by keeping the terms up to O ( h n ) for any n . The special case of a sandwich plate that consists of a centre layer and two identical outside layers is studied. In the literature, the dispersion equations for a sandwich plate were studied for special elastic materials. The results presented here are for elastic materials of general anisotropy.