Nonlocal Analysis of Rayleigh Wave Propagation in Layered Media With Interface Imperfections and Surface Irregularities

ABSTRACT This study focuses on the propagation of Rayleigh‐type waves in a sandy layer lying over a weakly orthotropic half‐space based on the principles of nonlocal elasticity theory. Both perfect and imperfect mechanical bonding conditions at the interface are examined. The governing second‐order hyperbolic differential equations are solved analytically using the method of separation of variables to obtain displacement fields in closed form. The frequency equation is formulated by setting the determinant of the system of equations to zero for different interfacial conditions. Numerical evaluation of the resulting dispersion relation is performed, and the influence of parameters such as layer thickness, phase velocity, corrugation amplitude, nonlocal parameter, and imperfection parameter is studied in detail. Simulated results using Mathematica provide graphical illustrations of the variation in wave number and phase velocity for different physical scenarios. The novelty of the present study lies in the combined consideration of nonlocal elasticity, granular behavior, orthotropy, and corrugated geometry within a single analytical framework. The results reveal the distinct and sometimes opposite roles of layer and substrate nonlocality on wave dispersion.