A closed-form solution to propagation of guided waves in a layered half-space under a time-harmonic load: An application of elastodynamic reciprocity

Abstract

This article is concerned with the application of reciprocity in computing guided wave motions generated by a time-harmonic load in a layer of uniform thickness joined to a half-space. Explicit expressions for free Rayleigh waves and Love waves propagating in the layered half-space are introduced. Exact solutions of Rayleigh waves and Love waves are derived from reciprocity relations between an actual state – guided waves generated by a time-harmonic line load and a virtual state – an appropriately chosen free wave traveling in the structure. Scattered amplitudes of the wave motions are thus determined. The validation of the reciprocity approach is shown through the computation of the lowest Rayleigh wave mode in the layered half-space, which approaches the calculation of the Rayleigh surface wave in the half-space once the layer thickness approaches zero in the limit.