Impact of Magnetic Field on Waves in A Rotating Inhomogeneous Material Under Imperfect Boundary and Inclined Mechanical Load: Inhomogeneous Impedance Consideration

Abstract

We present in this investigation a Mathematical wave analysis and model for surface waves in an imperfect boundary of a rotating inhomogeneous medium under a mechanical inclination. The imperfect boundary of the material is assumed to be in the form of impedance-corrugated surface. Mathematically, we assumed this corrugation in the form of trigonometric Fourier series. While the inhomogeneous nature (both of the material and impedance parameters) is taken to be an exponentially decaying function of the material parameters. In modelling this, the dynamical equations for the rotating impedance-corrugated boundary of an inhomogeneous fibre-reinforced solid influenced by magnetic fields and inclined mechanical load were analytically derived and presented using the fundamental constitutive laws of stress-strain relations in solid Mechanics of materials. We employ the Eigenvalue method also called the normal mode analysis approach in deriving the analytical solution of the fields’ distributions of the system; displacement components, and normal and shear stresses. Computational solutions in graphical forms were presented using MATHEMATICA 11 software, for the derived fields’ distributions of displacement components, normal and shear stresses on the material as occasioned by the wave propagation. We observed that the impact of the inhomogeneous parameter, rotation, magnetic field, angle of inclinations, impedance-corrugated surface parameters on the fields’ profiles on the material is remarkable. This is such that an increase in rotation, and angle of inclination of the medium produces an increase behavior of the fields’ profiles. The magnetic field influenced the normal stress in a decreasing manner when increased whilst noting mixed behavior of the displacements and shear stress. The angles of inclinations caused upward trends to the behavior of the displacements and stresses of the wave on the medium. A resistant-like effects were observed along the normal stress components when the inhomogeneous normal impedance is increased.