Analytical Study on Propagation of G-Type Waves in a Transversely Isotropic Substrate beneath a Stratum considering Couple Stress

Abstract

The present paper is framed to study analytically the propagation characteristics of the G-type wave through a functionally graded transversely isotropic substrate beneath a stratum with the consideration of couple stress. The couple stress theory concerned with size-dependent continuum mechanics, with additional parameter-characteristic length, accounts for the internal microstructure of materials, which provides deeper insight into the analysis of wave propagation aspects. Elastodynamic equations are laid down for the two media (stratum and substrate), and the frequency equation is derived by enforcing admissible boundary conditions. The solution process involves separation of variable technique and the method of infinite determinants. The frequency equation is reduced and found to fairly match with the classical Love-wave equation. The expression of group velocity of the G-type wave is also deduced in closed form. Numerical simulation and graphic illustration of the phase velocity as well as group velocity profiles of G-type waves are performed taking into account three different rocks in the functionally graded transversely isotropic substrate, i.e., granite (igneous rock), sandstone (sedimentary rock), and marble (metamorphic rock). The substantial effects of characteristic length associated with couple stress stratum, anisotropy, and functional gradedness on phase velocity is revealed and also traced out graphically. Comparative analysis of phase velocity and group velocity profiles of G-type waves for the three distinct previously mentioned rocks is one of the finest features of this study.