Anti-plane shear waves in an elastic strip rigidly attached to an elastic half-space

We consider the anti-plane shear waves in a domain consisting of an infinite layer with thin coating lying on elastic half-space. The properties coating, layer, and half-space are assumed to be different. On free upper surface we assume compatibility condition within Gurtin–Murdoch elasticity, whereas at plane interface perfect contact. For this problem there exist two possible regimes related exponentially decaying first one, called transversely exponential–transversely exponential (TE–TE) regime, is described by transverse direction functions; second, harmonic–transversely (TH–TE) corresponds which have harmonic behaviour direction. Detailed analysis derived dispersion equations for both provided. In particular, effects stresses, thickness as well ratio moduli curves analysed.