Mathematical Aspects of Reflection Phenomena at the Stress-Free Interface of Micropolar Transversely Isotropic Half-Space under Nonlocal Theory

In this paper, we have examined the reflection of plane waves at the stress-free boundary of nonlocal micropolar transversely isotropic half-space with nonlocal theory. Using convenient boundary conditions, the mathematical expression of reflection coefficients and phase velocity for the reflected waves are derived in closed form. The expressions of energy ratios are also obtained in explicit form. Numerical computations have been performed to exhibits the analytical findings for graphical means with the aid of numerical data. The effects of the nonlocal parameter on the reflection coefficients, phase velocity and energy ratios are discussed numerically and illustrated graphically. It has been verified that during reflection phenomena, the sum of energy ratios is equal to unity at each incident angle.