Analytical Investigation of Harmonic Magnetoelastic Stress Distribution in a Functionally Graded Infinite Cylinder

The primary objective of this study is to analyze the effect of inhomogeneity in an orthotropic elastic material within a magneto-elastic cylinder containing (i) an isotropic core and (ii) a rigid core. An analytical approach is developed to investigate the behavior of a non-homogeneous orthotropic material in the presence of a magnetic field. Stresses and displacement have been expressed in closed forms. The study focuses on the dynamical response of an orthotropic cylinder. Analytical expressions are derived for displacement components and stress components in both cases. Numerical calculations are performed to evaluate the radial variation of displacement and stress throughout the cylinder. By solving the dynamic problem, stress wave propagation and displacement are analyzed through graphical representations. The results reveal a significant influence of the magnetic field on both displacement and stress components. The Mathematica software is utilized to visualize and interpret these effects graphically.