A novel approach to modelling non-local surface waves: refinements in boundary and interface conditions

Abstract

A comprehensive analysis of the refined boundary conditions on the surface and the interface of the layer over half-space for surface waves under the framework of non-local elasticity has been presented in this paper. Several recent studies have utilized traditional boundary conditions within Eringen’s non-local elasticity theory to investigate non-local wave propagation. However, the application of these traditional boundary conditions has led to inconsistencies and limitations in their applicability to a wide range of nonlocal elastic media. By utilizing asymptotic analysis, this research addresses the challenge of accurately formulating boundary and interface conditions for layered structures, with a particular focus on boundary layer effects. By employing a 2D non-local Bessel kernel, we have rigorously derived refined conditions that ensure equivalence between integral and differential formulations, achieved through additional constraints on specific stress components. Our analysis reveals that boundary layers develop at both the surface and the interface, necessitating significant refinements to both classical boundary and interface conditions. These refined conditions, derived by neglecting exponentially smaller terms, are crucial for accurately capturing the influence of non-local effects on wave dispersion. Furthermore, dispersion curves demonstrate how these conditions play a critical role in describing the dispersion characteristics of Love and Rayleigh waves in non-local layered media. © The Author(s) 2025.