Reflection and transmission of qP wave at an imperfect interface between two prestressed elastic half‐spaces

Abstract The effects of prestress on the reflection and transmission waves at the imperfect interface between two orthotropic elastic half‐spaces are studied in this paper. First, the characteristic equation in the orthotropic half‐space is derived from the general dynamic equation with prestress taken into consideration. The form of the incident, reflected, and transmitted waves is derived. Then, from the interface conditions for two cases (perfect and imperfect interface), the displacement and stress are required to be satisfied. The algebraic equations resulting from the interface conditions are solved to obtain the amplitude ratio of various waves. To validate these findings, energy partitions of reflected and transmitted waves are computed, demonstrating adherence to the Law of Conservation of Energy. Numerical examples are provided to illustrate the effect of the imperfect interface, prestress, and incident angle on the reflection and transmission coefficients, energy ratios, reflection, and transmission angles of waves.