Propagation of shear waves in homogeneous and inhomogeneous fibre-reinforced media on a cylindrical Earth model

Abstract

• Shear wave propagations in the cylindrical structure are studied in fibre-reinforced media. • Dispersion relations have been obtained in closed form analytically. • Fibre-reinforcement, radial heterogeneity and radii ratio have significant effect on propagation. • Special cases are established with or without having dimensionless parameters. • Numerical computations are illustrated to show the effect of dimensionless parameters. The present paper is concerned with the propagation of shear wave in a cylindrical structure comprised of two concentric media by two distinct cases. In first case, media are homogeneous and in second case, media are heterogeneous. The heterogeneities are caused due to the radial variation in both the media distinctly. The dispersion relation for shear wave propagation in homogeneous and heterogeneous, fibre-reinforced media have been derived analytically in the closed form using Debye Asymptotic Expansion and verified with the existing literature and classical results. Numerical computation and graphical demonstration have been carried out to show the remarkable effect of various parameter viz. fibre-reinforcement, heterogeneities and radii ratio of the media on the intensity of frequency of shear wave propagation against the dimensionless wave number. A comparative study between the reinforcement and isotropic material with or without heterogeneity has been discussed extensively and unravel some important peculiarities.