Discipline of Mathematics

Dr. Santanu Manna

Assistant Professor

(Applied Mathematics & Computing Group)

The work is focused on the surface wave field in functionally graded multi-layer transversely isotropic heterogeneous magneto-elastic reinforced media. The Geometry of the problem is formulated by considering the (n−1) finite layer composite structure over a semi-infinite substance. A generalized Haskell’s matrix technique has been applied to obtain the wave scattering equation in multi-layer heterogeneous magneto-elastic media using suitable boundary conditions. A finite difference technique is derived to obtain the group and phase velocities with shear deformation in the magneto-elastic heterogeneous reinforced media. To study the group and phase velocity in a square grid, stability conditions for introducing finite difference techniques have been derived (cf. figs. 1-2). Using graphical representation, it has been examined that phase velocity, group velocity, and wave scattering in the layered media are affected by heterogeneity, reinforced, magneto-elastic coupling parameters, and stability ratio.

       Fig. 1.: Stability analysis of FDM for dimensionless phase velocity

  Fig. 2.: Stability analysis of FDM for dimensionless group velocity