Explicit solutions for carrier waves supporting surface waves and plate waves

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.