Dispersion of Love-type wave and its limitation in a nonlocal elastic model of nonhomogeneous layer upon an orthotropic extended medium

Abstract

This research paper investigates the Love-type surface wave dispersion in a nonlocal elastic nonhomogeneous medium over a nonlocal orthotropic semi-infinite medium under the effect of interior initial stress component. A generalized linear elasticity theory with the nonlocal effect in the fundamental stress-strain relation is adopted to address the equation of motion in layered media. In the case of time-harmonic plane wave propagation, PDEs (cf. equations of motion) of the nonlocal elasticity are reduced to closed-form singular differential equations. The equation of dispersive wave is derived using appropriate plane stress-displacement-continuity conditions of the model. The dispersion of Love-type wave and its limitation in a nonlocal elastic media are analysed graphically using MATLAB software. For the specific model, it is observed that the attenuation of the dispersion of Love-type wave depends on a nonlocal parameter. Also, the dispersive wave becomes nondispersive with zero attenuation for large values (∼0.4) of the nonlocal parameter. In the case of dispersive wave, variation of the phase velocity of the fundamental wave mode for different values of nonlocality, nonhomogeneity, wave number and initial stress parameters are shown graphically. Some special cases are deduced from the original dispersion equation and validated with the published literature.