Mathematical Investigation of Reflection and Transmission of Plane Wave at the Corrugated Interface of Orthotropic Layer Sandwiched Between Two Distinct Monoclinic Media

In this paper, we have investigated the reflection and transmission phenomena of plane waves scattered from corrugated interface of orthotropic layer sandwiched between two distinct monoclinic half spaces. We used Rayleigh’s method of approximation, expanding the Fourier series to the find reflection and transmission coefficients. A system of non-homogeneous equations for regular and irregular waves are solved with the aid of Cramer’s rule. The dynamics of intermediate orthotropic layer and monoclinic half-spaces are examined and the reflection and transmission coefficients, phase velocity, slowness vector and energy ratios for various reflected and transmitted waves have been derived. It has been observed that the total energy remains conserved in the entire reflection and transmission process. This study contributes valuable insights into the interactions of plane waves with layered structures, offering a comprehensive understanding of wave behavior at corrugated interfaces.