Love wave fields in a non-local elastic model with reinforced and inhomogeneous media

Abstract

The primary intent of this paper is to study the propagation of a Love-type wave and its failure in a model consisting of a non-local elastic fiber-reinforced material and a continuously inhomogeneous non-local elastic semi-infinite medium. The inhomogeneity parameters in the lower medium corresponding to the rigidity and density vary quadratically with the z-direction. Expressions for displacement components of the Love-type wave in both the media are derived separately by solving the second-order hyperbolic type differential equation. In the lower medium, we obtain approximate solutions to the displacement component using asymptotic expansions of the Bessel functions. As a result, the dispersion relation obtained by applying appropriate boundary conditions involves inhomogeneity and non-local elastic parameters of both the media. Furthermore, the time-dependent Finite Difference Scheme (FDS) is used to model the propagation of the Love-type wave, and stability conditions are developed to derive the expressions for the phase and group velocities. This scheme is one of the most efficient schemes in modeling seismic wave propagation because of its higher accuracy, applicability to complex structures, and computational benefits. The numerical and graphical discussions are then carried out using MATLAB software to analyze the stability of the Finite Difference Scheme and also to describe the limiting behavior of the Love-type wave due to the non-local elasticity. The developed model provides a more realistic approach to solving the seismological problems concerned with reinforcement due to the inclusion of non-local elastic behavior in a layered media.