Dispersive Constraints of Antiplane Shear Waves in a Strain-Gradient LoH Model under an Inflexible Boundary Plane and Initial Pressure

Abstract

This research work depicts the dispersive limitation of shear (SH) waves in an initially stressed strain-gradient layer over halfspace (LoH) model with an inflexible upper boundary plane. The gradient elasticity theory serves as the framework for this study. This theory is based on some cornerstones like the introduction of internal structures at different scales and the nonlinearity of the models, which, in other words, means incorporating intrinsic microstructural and nonlinear effects. As a result, the dispersion relations have been deduced analytically by imposing the required interface and the intrinsic boundary conditions. The agreement to the classical case is presented as a particular case along with various other cases obtained by freeing some assumptions from the model. The distinguished region of existence of the dispersion curves has been plotted and discussed in detail by deriving the upper and lower bounds for the phase velocity of the SH wave. Additionally, the influence of various strain-gradient elastic parameters has been examined using contour plots, and it has been found that the features of SH waves are a lot more diverse in the strain-gradient case compared to the classical situation.