Analyzing hall current effects and fractional order nonlocal theory on plane wave reflection in a rotating isotropic medium

Abstract

This research focuses on studying the influence of the Hall current on the propagation and reflection of elastic waves in a non-local isotropic rotating solid. The dispersion relation is derived to determine the speed of propagation, revealing the presence of three coupled quasi-waves within the solid: coupled qP-wave, qT-wave and qSV-wave. The rotational motion and the Hall current introduce anisotropic characteristics to the medium, leading to the emergence of quasi-type waves. The rotation disrupts the isotropic nature of the solid, transforming it into an anisotropic medium. Consequently, the purely longitudinal and transverse waves are converted into quasi-longitudinal and quasi-transverse waves. The speed of the propagating waves is dependent on specific elastic parameters. By employing free boundary conditions, the mathematical calculation and graphical representation of wave amplitude ratios are determined. The influence of rotational frequency, non-locality, fractional order and Hall current parameters on the computed results is investigated. The conservation of energy validates the accuracy of the obtained results. Furthermore, it is observed that the previously reported results in the literature can be obtained as a special case when rotation and the Hall current are absent.