Eur. Phys. J. Plus (2019) 134: 35
https://doi.org/10.1140/epjp/i2019-12379-6

Regular Article

Analysis on propagation characteristics of the shear wave in a triple layered concentric infinite long cylindrical structure: An analytical approach

Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, 826004, Jharkhand, India

^* e-mail: mahantymoumita@gmail.com

Received: 20 April 2018
Accepted: 5 November 2018
Published online: 22 January 2019

Abstract

The present work delves into the propagation of a horizontally polarised shear (SH) wave in an infinitely long cylindrical structure comprised of three concentric isotropic layered media. The model has been formulated in cylindrical co-ordinates and an analytical approach is employed to achieve the closed form of the dispersion relation. The application of the Debye Asymptotic Analysis to tackle the complexity arisen due to the involvement of Hankel’s function in the solution treatment is one of the key features of the present article. With the aid of the Debye Asymptotic Analysis, the dispersion equation is shown to be in well agreement with the classical Love wave equation in the absence of the outermost layer medium. The present analysis highlights the influence of the wave number and various radii ratios of the concentric cylindrical layered elastic medium on the phase velocity of the shear wave propagating in the embraced structure. Numerical computations have been carried out to accomplish the graphical demonstration unravelling some important peculiarities associated with the propagation characteristics of the shear wave in the considered cylindrical structure.