Influence of boundary conditions on the reflection and transmission of qP-wave at an interface between two nonlocal transversely isotropic elastic half-spaces (Q6576175)

The author conducts a mathematical study of reflection and transmission coefficients at an imperfect interface separating two transversely isotropic nonlocal elastic solid half-spaces when a longitudinal wave is incident. The study briefly discusses three cases of imperfect interfaces. For the incident quasi-P wave, expressions for the reflection and transmission coefficients in both the imperfect and perfect cases are presented. The effect of the nonlocality parameter on these coefficients is examined for both types of interfaces, along with the dependence of the velocities of the incident waves on the incident angle in nonlocal and local scenarios. The choice of the kernel in the relationship between nonlocal and local stress components leads to several of Eringen's nonlocal models: the purely nonlocal integral model (PNIM), the differential nonlocal model, and the two-phase nonlocal model (TPNM). In the cases of the PNIM and TPNM models, the characteristic equation for the two-dimensional problem of plane wave propagation in an unbounded medium, which does not have a closed-form solution, is solved numerically. The influence of some boundary conditions and nonlocality on transmission coefficients and reflection is also considered. Additionally, the author studies the dependence of the velocities of the incident waves on the incident angle in nonlocal and local cases.