Propagation of elastic waves in a magneto-elastic layer laying over a light Winkler foundation with rotation

Abstract

In connection to plane harmonic waves in an elastic thin layer amidst light Winkler elastic foundations, two configurations for long-wave low-frequency motion have recently been the subject of research. Thus, in our study, we considered an elastic thin layer resting over the Winkler elastic foundation while posing the more complex Rayleigh–Lamb dispersion relation and further endowing it with the existence of rotating effects and magnetic field forces. Approximate analytical solution of the model comprising the respective displacements and stresses has been determined in a rare scenario, in addition to determining and analyzing the exact Rayleigh–Lamb dispersion relation. Furthermore, we investigated the variational influences of the dimensionless Winkler elastic foundation stiffness parameter P, rotation parameter presided by the angular velocity ℧ and the magnetic field intensity on the lowest dispersion branch of the harmonic waves, using Mathematica software. These analyses have been shown graphically and discussed; we also appended some inclusive remarks in the conclusion section.