A Unified Model for Investigating the Propagation of SH Surface Waves in a Piezoelectric Layered Medium

In this paper, a thorough analysis is conducted to examine the propagation characteristics of SH surface waves in a layered medium with a nanoscale piezoelectric guiding layer deposited on an isotropic elastic substrate. Specifically, a two-dimensional analytical model is established, within which the effects of strain gradient, electric field gradient, inertia gradient, and flexoelectricity are considered, as well as interfacial imperfections at the interface between the piezoelectric guiding layer and the elastic substrate, which are characterized by spring models. Within the framework of the variational principle, the governing equations, boundary conditions, and continuity conditions at the interface are derived. Based on these equations, the dispersion relations for SH surface waves are deduced and numerically solved for both the electrically open-circuit and electrically short-circuit cases. A comprehensive investigation of the dispersion relations for the fundamental mode of SH surface waves is subsequently provided, with a detailed discussion on the influence of critical factors. The developed theoretical model, encompassing various size effects observed in nano-scale structures, enables a more precise prediction of surface wave propagation behavior, thereby enhancing the design and application of surface acoustic wave devices.