Nonlocal theory on plane waves in a higher-order thermo-diffusive semiconducting medium under the gravitational field

This article explores the reflection of elastic waves in nonlocally generalized thermo-diffusive semiconducting elastic solids under the influence of gravity. The problem is framed within the higher-order fractional derivative heat equation. The frequency dispersion relation reveals the presence of five coupled waves. The wave speeds are graphed against angular frequency for the nonlocal parameter under the influence of gravity, and the cut-off frequency of the waves is visually represented. The incident wave at the free surface of the solid is the coupled longitudinal P-wave, and its reflection coefficients are computed. The study investigates the impact of gravity, fractional order, and nonlocal parameters on propagation speed and amplitude ratios, revealing their significant influence. The findings are substantiated in the context of energy conservation. This research provides valuable insights for scientists engaged in geophysics and various branches of mechanics.