Love‐like wave dispersion in a highly non‐homogeneous viscoelastic orthotropic layer under the effect of non‐local elasticity

Abstract

This paper examines the effects of non‐local elasticity on the propagation of Love‐like waves in a Voigt‐type viscoelastic layer over an elastic half‐space. The model's geometry is considered orthotropic, highly non‐homogeneous, and initially stressed media in the context of non‐local continuum mechanics. The non‐homogeneity functions are regarded as binomial functions with a positive real exponent. Two different non‐local parameters have been defined by considering different internal characteristic lengths for the layer and half‐space. Modified Bessel functions of the first and second kinds are used to determine displacement functions. Asymptotic representations of derivatives of modified Bessel's functions have been derived to get the compact form of the dispersion equation. A comparison of phase velocity equations with classical Love wave equations has demonstrated the validity of our model. It is found that different modes of Love‐like waves are dispersive and highly affected by the attenuation coefficient. Additionally, non‐local parameters significantly influence the limitation of phase velocity modes of Love‐like waves. The phase and damped velocity versus non‐local parameters have been depicted with the effect of different parameters in the model. It has been found that the non‐local parameters decrease the particle displacement amplitude in elastic half‐space and rapidly eliminate waves with depth.