Dynamic Response of Waves on a Non-homogeneous Impedance Solid with Variable Amplitudes of Corrugated Surface under magnetic field

Abstract

In this investigation, a solution to model that characterize and analyzes the stresses and displacements occasioned by surface waves on a corrugated inhomogeneous fibre-reinforced material under  magneto-elastic influences with some underlying mechanical inclinations is proposed. The governing equations of the model problem is presented using the constitutive relations of the material. By normal mode method, we derived the analytical solution of the model whilst utilizing non-dimensionalization of the equations of motion to reduce redundant parameters, and so on. Also, the model envisages only a case where the corrugation or wavy-like phenomenon of the boundary possess amplitudes of various heights and inhomogeneous impedance conditions and thus, leading to a complex geometry. Following this, suitable applications of the formulated boundary conditions –variable amplitudes of corrugation and inhomogeneous impedance conditions along with the mechanical inclinations are utilized to ensure the complete solutions of the stresses and displacements of the wave on the inhomogeneous medium are derived. In addition these fields’ distributions of stresses and displacements are graphically presented using MATHEMATICA software for the graphics, in order to ascertain the variations and behaviors of the considered physical quantities of nonlocal parameter, variable amplitudes of corrugation and inhomogeneous impedance parameters, and angles of inclination. We witness that, these parameters hugely impacts the distribution of the surface wave on the material such that the nonlocal, angles of inclination, inhomogeneous parameter causes downward trends to the distribution profiles of the surface wave when increased. Special cases of constant amplitude can be obtained from our model if we neglect one of the quantities of variable amplitudes of corrugation,  and the magnetic impact on  the medium. This study should prove useful to examinations related to geophysics and seismology- where analysis of disturbances on surfaces are felt.