Influence of Boundaries on the Dispersion of Rayleigh Waves in a Functionally Graded Pre-Stressed Orthotropic Substrate

Abstract

The current research investigates the propagation behavior of Rayleigh-type waves in a prestressed functionally graded orthotropic substrate. Two types of material gradation, exponential and logarithmic, are considered. The influence of these gradation profiles is analyzed under two boundary conditions: stress-free and rigid. The derived dispersion relations account for the effects of gradient parameters, initial stress, and density variations. A comprehensive numerical analysis is performed to evaluate the phase velocity and attenuation coefficient. The results reveal that both gradient types significantly affect the wave dispersion and attenuation behavior. Specifically, the exponential gradient induces stronger changes at lower and moderate wave numbers, while the logarithmic gradient affects attenuation more at lower wave numbers and phase velocity at higher wave numbers. The initial stress parameter is found to decrease phase velocity across wave numbers, while density variation shows contrasting behavior depending on the boundary type. The findings provide critical insights into material design, seismic analysis, and non-destructive testing techniques.