Explicit solutions for carrier waves supporting surface waves and plate waves

Abstract

Time-harmonic surface waves in a half-space ( x 3 ≥ 0) and plate waves in a layer (− h ≤ x 3 ≤ h) of a homogeneous transversely isotropic linearly elastic solid, where the x 1 x 2-plane is the plane of transverse isotropy, have been reconsidered. The displacement components are expressed in terms of a carrier wave which defines the propagation in the x 1 x 2-plane, and which supports the sub-surface motion in the half-space and the thickness motion of the plate. The carrier wave can be any solution of the reduced wave equation for a membrane.